Analytic Hierarchy Process (AHP) method

Description

AHP is a multi-criteria decision analysis method which was originally developed by Thomas L. Saaty in 1970s.

Usage

AHP(criteriaWeightsPairwiseComparisons, alternativesPairwiseComparisonsList)

Arguments

Value

The function returns a vector containing the AHP score for each alternative.

References

The Analytic Hierarchy Process: Planning, Priority Setting (1980), ISBN 0-07-054371-2, McGraw-Hill

Examples

alts <- c("Corsa","Clio","Fiesta","Sandero")
style <- matrix(c(1.0, 1/4, 4.0, 1/6,
                  4.0, 1.0, 4.0, 1/4,
                  1/4, 1/4, 1.0, 1/5,
                  6.0, 4.0, 5.0, 1.0), 
                nrow=length(alts), ncol=length(alts), byrow=TRUE, 
                dimnames=list(alts,alts))
reliability <- matrix(c(1.0, 2.0, 5.0, 1.0,
                        1/2, 1.0, 3.0, 2.0,
                        1/5, 1/3, 1.0, 1/4,
                        1.0, 1/2, 4.0, 1.0), 
                      nrow=length(alts), ncol=length(alts), byrow=TRUE, 
                      dimnames=list(alts,alts))
fuel <- matrix(c(1.0, 2.0, 4.0, 1.0,
                 0.5, 1.0, 3.0, 2.0,
                 1/4, 1/3, 1.0, 1/5,
                 1.0, 1/2, 5.0, 1.0), 
               nrow=length(alts), ncol=length(alts), byrow=TRUE, 
               dimnames=list(alts,alts))
alternativesPairwiseComparisonsList <- list(style       = style, 
                                            reliability = reliability, 
                                            fuel        = fuel)
crit <- c("style","reliability","fuel")
criteriaWeightsPairwiseComparisons <- matrix(c(1.0, 1/2, 3.0,
                                               2.0, 1.0, 4.0,
                                               1/3, 1/4, 1.0), 
                                             nrow=length(crit), 
                                             ncol=length(crit), 
                                             dimnames=list(crit,crit))
# All attributes have pairwise comparisons
AHP(criteriaWeightsPairwiseComparisons, alternativesPairwiseComparisonsList)
# Fuel is a score
newFuel <- c(Corsa=34, Clio=27, Fiest=24, Sandero=28)
newFuel <- newFuel/sum(newFuel)
alternativesPairwiseComparisonsList$fuel <- newFuel
AHP(criteriaWeightsPairwiseComparisons, alternativesPairwiseComparisonsList)

ELimination Et Choice Translating REality - ELECTRE-III

Description

ELECTRE (ELimination Et Choice Translating REality) is an outranking method proposed by Bernard Roy and his colleagues at SEMA consultancy company. This is the implementation of ELECTRE-III.

Usage

ELECTRE3(scores, q, p, v, w)

Arguments

Value

The function returns the Concordance, Discordance, Credibility, Dominance, and Scoring tables.

References

Roy, Bernard (1968). "Classement et choix en présence de points de vue multiples (la méthode ELECTRE)". La Revue d'Informatique et de Recherche Opérationelle (RIRO) (8): 57–75.

Examples

library(MCDA)
scores <- matrix( c(-0.2,-2.3,-2.4,-1,3,9,10,7), 
                  nrow = 4, 
                  dimnames = list(
                    c("School-A","School-B","School-C", "School-D"), 
                    c("Location","Quality")) )

q <- c( 0.2, 1)
p <- c(   1, 2)
v <- c( 3.5, 4)
w <- c(0.25, 0.75)

res <- ELECTRE3(scores, q, p, v, w)
print(res)

ELECTRE III ranking

Description

This function computes the two ELECTRE III distillations, or rankings.

Usage

ELECTREIIIDistillation(
  performanceTable,
  criteriaWeights,
  minMaxcriteria,
  preferenceThresholds,
  indifferenceThresholds,
  vetoThresholds
)

Arguments

Value

The function returns two lists, one for each distillation.

Examples

performanceTable <- rbind(
c(10,20,5,10,16),
c(0,5,5,16,10),
c(0,10,0,16,7),
c(20,5,10,10,13),
c(20,10,15,10,13),
c(20,10,20,13,13))
rownames(performanceTable) <-c("P1","P2","P3","P4","P5","P6")
colnames(performanceTable) <-c("CRIT1","CRIT2","CRIT3","CRIT4","CRIT5")
## vector indicating the direction of the criteria evaluation .
minMaxcriteria <-c("max","max","max","max","max")
names(minMaxcriteria) <- colnames(performanceTable)
## criteriaWeights vector
criteriaWeights <- c(3,2,3,1,1)
names(criteriaWeights) <- colnames(performanceTable)

indifferenceThresholds<-c(3,3,3,3,3)
names(indifferenceThresholds) <- colnames(performanceTable)
preferenceThresholds<-c(5,5,5,5,5)
names(preferenceThresholds) <- colnames(performanceTable)
vetoThresholds<-c(11,11,11,11,11)
names(vetoThresholds) <- colnames(performanceTable)

ELECTREIIIDistillation(performanceTable,criteriaWeights,minMaxcriteria,
                       preferenceThresholds,indifferenceThresholds,
                       vetoThresholds)

MRSort that takes into account large performance differences.

Description

MRSort is a simplified ElectreTRI method that uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. LPDMRSort considers both a binary discordance and a binary concordance conditions including several interactions between them.

Usage

LPDMRSort(
  performanceTable,
  categoriesLowerProfiles,
  categoriesRanks,
  criteriaWeights,
  criteriaMinMax,
  majorityThreshold,
  criteriaVetos = NULL,
  criteriaDictators = NULL,
  majorityRule = "M",
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  categoriesIDs = NULL
)

Arguments

Value

The function returns a vector containing the assignments of the alternatives to the categories.

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompensatory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

Meyer, P. and Olteanu, A-L. Integrating large positive and negative performance differences in majority-rule sorting models. European Journal of Operational Research, submitted, 2015.

Examples

# the performance table

performanceTable <- rbind(c(10,10,9), c(10,9,10), c(9,10,10), c(9,9,10), 
                          c(9,10,9), c(10,9,9), c(10,10,7), c(10,7,10), 
                          c(7,10,10), c(9,9,17), c(9,17,9), c(17,9,9), 
                          c(7,10,17), c(10,17,7), c(17,7,10), c(7,17,10), 
                          c(17,10,7), c(10,7,17), c(7,9,17), c(9,17,7), 
                          c(17,7,9), c(7,17,9), c(17,9,7), c(9,7,17))

profilesPerformances <- rbind(c(10,10,10),c(0,0,0))

vetoPerformances <- rbind(c(7,7,7),c(0,0,0))

dictatorPerformances <- rbind(c(17,17,17),c(0,0,0))

rownames(performanceTable) <- c("a1", "a2", "a3", "a4", "a5", "a6", "a7", 
                                "a8", "a9", "a10", "a11", "a12",  "a13", 
                                "a14", "a15", "a16", "a17", "a18", "a19", 
                                "a20", "a21", "a22", "a23", "a24")

rownames(profilesPerformances) <- c("P","F")

rownames(vetoPerformances) <- c("P","F")

rownames(dictatorPerformances) <- c("P","F")

colnames(performanceTable) <- c("c1","c2","c3")

colnames(profilesPerformances) <- c("c1","c2","c3")

colnames(vetoPerformances) <- c("c1","c2","c3")

colnames(dictatorPerformances) <- c("c1","c2","c3")

lambda <- 0.5

weights <- c(1/3,1/3,1/3)

names(weights) <- c("c1","c2","c3")

categoriesRanks <-c(1,2)

names(categoriesRanks) <- c("P","F")

criteriaMinMax <- c("max","max","max")

names(criteriaMinMax) <- colnames(performanceTable)

assignments <-rbind(c("P","P","P","F","F","F","F","F","F","F","F","F",
                    "F","F","F","F","F","F","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","P","P","P","P","P","P",
                    "P","P","P","P","P","P","P","P","P","P","P","P"), 
                    c("P","P","P","F","F","F","F","F","F","F","F","F",
                    "P","P","P","P","P","P","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","P","P","P","P","P","P",
                    "P","P","P","P","P","P","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "F","F","F","F","F","F","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "P","P","P","P","P","P","P","P","P","P","P","P"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "P","P","P","P","P","P","F","F","F","F","F","F"))

colnames(assignments) <- rownames(performanceTable)

majorityRules <- c("V","D","v","d","dV","Dv","dv")

for(i in 1:7)
{
  ElectreAssignments<-LPDMRSort(performanceTable, profilesPerformances, 
                                categoriesRanks,
                                weights, criteriaMinMax, lambda, 
                                criteriaVetos=vetoPerformances,
                                criteriaDictators=dictatorPerformances,
                                majorityRule = majorityRules[i])

  print(all(ElectreAssignments == assignments[i,]))
}

Identifies all sets of assignment examples which are incompatible with the MRSort sorting method extended to handle large performance differences.

Description

MRSort is a simplified ElectreTRI method that uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. LPDMRSort considers both a binary discordance and a binary concordance conditions including several interactions between them. This function outputs all (or a fixed number of) sets of incompatible assignment examples ranging in size from the minimal size and up to a given threshold. The retrieved sets are also not contained in each other.

Usage

LPDMRSortIdentifyIncompatibleAssignments(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  majorityRule = "M",
  incompatibleSetsLimit = 100,
  largerIncompatibleSetsMargin = 0,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns NULL if there is a problem, or a list containing a list of incompatible sets of alternatives as vectors and the status of the execution.

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompen-satory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

Meyer, P. and Olteanu, A-L. Integrating large positive and negative performance differences in majority-rule sorting models. European Journal of Operational Research, submitted , 2015.

Examples

# the performance table

performanceTable <- rbind(c(10,10,9), c(10,9,10), c(9,10,10), c(9,9,10), 
                          c(9,10,9), c(10,9,9), c(10,10,7), c(10,7,10), 
                          c(7,10,10), c(9,9,17), c(9,17,9), c(17,9,9), 
                          c(7,10,17), c(10,17,7), c(17,7,10), c(7,17,10), 
                          c(17,10,7), c(10,7,17), c(7,9,17), c(9,17,7), 
                          c(17,7,9), c(7,17,9), c(17,9,7), c(9,7,17), 
                          c(7,7,7))

rownames(performanceTable) <- c("a1", "a2", "a3", "a4", "a5", "a6", "a7", 
                                "a8", "a9", "a10", "a11", "a12", "a13", 
                                "a14", "a15", "a16", "a17", "a18", "a19", 
                                "a20", "a21", "a22", "a23", "a24", "a25")

colnames(performanceTable) <- c("c1","c2","c3")

assignments <-rbind(c("P","P","P","F","F","F","F","F","F","F","F","F",
                    "F","F","F","F","F","F","F","F","F","F","F","F","P"), 
                    c("P","P","P","F","F","F","P","P","P","P","P","P",
                    "P","P","P","P","P","P","P","P","P","P","P","P","P"), 
                    c("P","P","P","F","F","F","F","F","F","F","F","F",
                    "P","P","P","P","P","P","F","F","F","F","F","F","P"), 
                    c("P","P","P","F","F","F","P","P","P","P","P","P",
                    "P","P","P","P","P","P","F","F","F","F","F","F","P"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "F","F","F","F","F","F","F","F","F","F","F","F","P"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "P","P","P","P","P","P","P","P","P","P","P","P","P"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "P","P","P","P","P","P","F","F","F","F","F","F","P"))

colnames(assignments) <- rownames(performanceTable)

categoriesRanks <-c(1,2)

names(categoriesRanks) <- c("P","F")

criteriaMinMax <- c("max","max","max")

names(criteriaMinMax) <- colnames(performanceTable)

majorityRules <- c("V","D","v","d","dV","Dv","dv")

for(i in 1:1)# change to 7 in order to perform all tests
{
  incompatibleAssignmentsSets<-LPDMRSortIdentifyIncompatibleAssignments(
                                 performanceTable, assignments[i,], 
                                 categoriesRanks, criteriaMinMax,
                                 majorityRule = majorityRules[i])
  
  filteredAlternativesIDs <- setdiff(rownames(performanceTable),
                                     incompatibleAssignmentsSets[[1]][1])
  
  x<-LPDMRSortInferenceExact(performanceTable, assignments[i,], 
                             categoriesRanks, criteriaMinMax, 
                             majorityRule = majorityRules[i], 
                             readableWeights = TRUE, 
                             readableProfiles = TRUE, 
                             minmaxLPD =  TRUE, 
                             alternativesIDs = filteredAlternativesIDs)
  
  ElectreAssignments<-LPDMRSort(performanceTable, x$profilesPerformances, 
                                categoriesRanks,
                                x$weights, criteriaMinMax, x$lambda, 
                                criteriaVetos=x$vetoPerformances,
                                criteriaDictators=x$dictatorPerformances, 
                                majorityRule = majorityRules[i],
                                alternativesIDs = filteredAlternativesIDs)
  
  print(all(ElectreAssignments == assignments[i,filteredAlternativesIDs]))
}

Identify dictator profiles evaluations that have an impact on the final assignments of MRSort with large performance differences

Description

MRSort is a simplified ELECTRE-TRI approach which assigns alternatives to a set of ordered categories using delimiting profiles evaluations. In this case, we also take into account large performance differences. This method is used to identify which dictator profiles evaluations have an impact on the final assignment of at least one of the input alternatives.

Usage

LPDMRSortIdentifyUsedDictatorProfiles(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  majorityThreshold,
  criteriaWeights,
  profilesPerformances,
  dictatorPerformances,
  vetoPerformances = NULL,
  majorityRule = "D",
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a matrix containing TRUE/FALSE inficators for each evaluation of the veto profiles.

Examples

# the performance table

performanceTable <- rbind(
  c(1,27,1),
  c(6,20,1),
  c(2,20,0),
  c(6,40,0),
  c(30,10,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# lower profiles of the categories (best category in the first position of the list)

categoriesLowerProfiles <- rbind(c(3, 11, 3),c(7, 25, 2),c(NA,NA,NA))

colnames(categoriesLowerProfiles) <- colnames(performanceTable)

rownames(categoriesLowerProfiles)<-c("Good","Medium","Bad")

# the order of the categories, 1 being the best

categoriesRanks <-c(1,2,3)

names(categoriesRanks) <- c("Good","Medium","Bad")

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# dictators

criteriaDictators <- rbind(c(1, 1, -1),c(1, 20, 0),c(NA,NA,NA))

colnames(criteriaDictators) <- colnames(performanceTable)
rownames(criteriaDictators) <- c("Good","Medium","Bad")

# vetos

criteriaVetos <- rbind(c(9, 50, 5),c(50, 50, 5),c(NA,NA,NA))

colnames(criteriaVetos) <- colnames(performanceTable)
rownames(criteriaVetos) <- c("Good","Medium","Bad")

# weights

criteriaWeights <- c(1/6,3/6,2/6)

names(criteriaWeights) <- colnames(performanceTable)

# assignments

assignments <- c("Good","Medium","Bad","Bad","Bad")


# LPDMRSortIndetifyUsedVetoProfiles

used<-LPDMRSortIdentifyUsedDictatorProfiles(performanceTable, assignments,
                                        categoriesRanks, criteriaMinMax,
                                        0.5, criteriaWeights,
                                        categoriesLowerProfiles,
                                        criteriaDictators,
                                        criteriaVetos,
                                        "dv")

Identify veto profiles evaluations that have an impact on the final assignments of MRSort with large performance differences

Description

MRSort is a simplified ELECTRE-TRI approach which assigns alternatives to a set of ordered categories using delimiting profiles evaluations. In this case, we also take into account large performance differences. This method is used to identify which veto profiles evaluations have an impact on the final assignment of at least one of the input alternatives.

Usage

LPDMRSortIdentifyUsedVetoProfiles(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  majorityThreshold,
  criteriaWeights,
  profilesPerformances,
  vetoPerformances,
  dictatorPerformances = NULL,
  majorityRule = "V",
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a matrix containing TRUE/FALSE inficators for each evaluation of the veto profiles.

Examples

# the performance table

performanceTable <- rbind(
  c(1,27,1),
  c(6,20,1),
  c(2,20,0),
  c(6,40,0),
  c(30,10,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# lower profiles of the categories (best category in the first position of the list)

categoriesLowerProfiles <- rbind(c(3, 11, 3),c(7, 25, 2),c(NA,NA,NA))

colnames(categoriesLowerProfiles) <- colnames(performanceTable)

rownames(categoriesLowerProfiles)<-c("Good","Medium","Bad")

# the order of the categories, 1 being the best

categoriesRanks <-c(1,2,3)

names(categoriesRanks) <- c("Good","Medium","Bad")

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# dictators

criteriaDictators <- rbind(c(1, 1, -1),c(1, 20, 0),c(NA,NA,NA))

colnames(criteriaDictators) <- colnames(performanceTable)
rownames(criteriaDictators) <- c("Good","Medium","Bad")

# vetos

criteriaVetos <- rbind(c(9, 50, 5),c(50, 50, 5),c(NA,NA,NA))

colnames(criteriaVetos) <- colnames(performanceTable)
rownames(criteriaVetos) <- c("Good","Medium","Bad")

# weights

criteriaWeights <- c(1/6,3/6,2/6)

names(criteriaWeights) <- colnames(performanceTable)

# assignments

assignments <- c("Good","Medium","Bad","Bad","Bad")


# LPDMRSortIndetifyUsedVetoProfiles

used<-LPDMRSortIdentifyUsedVetoProfiles(performanceTable, assignments,
                                        categoriesRanks, criteriaMinMax,
                                        0.5, criteriaWeights,
                                        categoriesLowerProfiles,
                                        criteriaVetos,
                                        criteriaDictators,
                                        "dv")

Identification of profiles, weights, majority threshold, veto and dictator thresholds for LPDMRSort using a genetic algorithm.

Description

MRSort is a simplified ElectreTRI method that uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. LPDMRSort considers both a binary discordance and a binary concordance conditions including several interactions between them. The identification of the profiles, weights, majority threshold and veto thresholds is done by taking into account assignment examples.

Usage

LPDMRSortInferenceApprox(
  performanceTable,
  criteriaMinMax,
  categoriesRanks,
  assignments,
  majorityRules = c("M", "V", "D", "v", "d", "dV", "Dv", "dv"),
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = 60,
  populationSize = 20,
  mutationProb = 0.1
)

Arguments

Value

The function returns a list containing:

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompen- satory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

no reference yet for the algorithmic approach; one should become available in 2018

Examples

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

rownames(performanceTable) <- c("a1", "a2", "a3", "a4", "a5", "a6", "a7", "a8", "a9", "a10", "a11",
                                "a12", "a13", "a14", "a15", "a16", "a17", "a18", "a19", "a20",
                                "a21", "a22", "a23", "a24")

colnames(performanceTable) <- c("c1","c2","c3")

assignments <-c("P","P","P","F","F","F","F","F","F","P","P","P","P","P","P","P","P","P","F","F",
                "F","F","F","F")

names(assignments) <- rownames(performanceTable)

categoriesRanks <- c(1,2)

names(categoriesRanks) <- c("P","F")

criteriaMinMax <- c("max","max","max")

names(criteriaMinMax) <- colnames(performanceTable)

set.seed(1)

x<-LPDMRSortInferenceApprox(performanceTable, criteriaMinMax, categoriesRanks, assignments,
                            majorityRules = c("dV","Dv","dv"),
                            timeLimit = 180, populationSize = 30,
                            alternativesIDs = c("a1","a2","a3","a4","a5","a6","a7"))

Identification of profiles, weights, majority threshold and veto and dictator thresholds for the MRSort sorting approach extended to handle large performance differences.

Description

MRSort is a simplified ElectreTRI method that uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. LPDMRSort considers both a binary discordance and a binary concordance conditions including several interactions between them. The identification of the profiles, weights, majority threshold and veto and dictator thresholds are done by taking into account assignment examples.

Usage

LPDMRSortInferenceExact(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  majorityRule = "M",
  readableWeights = FALSE,
  readableProfiles = FALSE,
  minmaxLPD = FALSE,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a list structured as follows :

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompen- satory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

Meyer, P. and Olteanu, A-L. Integrating large positive and negative performance differences in majority-rule sorting models. European Journal of Operational Research, submitted, 2015.

Examples

# the performance table

performanceTable <- rbind(c(10,10,9), c(10,9,10), c(9,10,10), c(9,9,10), 
                          c(9,10,9), c(10,9,9), c(10,10,7), c(10,7,10), 
                          c(7,10,10), c(9,9,17), c(9,17,9), c(17,9,9), 
                          c(7,10,17), c(10,17,7), c(17,7,10), c(7,17,10), 
                          c(17,10,7), c(10,7,17), c(7,9,17), c(9,17,7), 
                          c(17,7,9), c(7,17,9), c(17,9,7), c(9,7,17))

rownames(performanceTable) <- c("a1", "a2", "a3", "a4", "a5", "a6", "a7", 
                                "a8", "a9", "a10", "a11", "a12", "a13", 
                                "a14", "a15", "a16", "a17", "a18", "a19", 
                                "a20", "a21", "a22", "a23", "a24")

colnames(performanceTable) <- c("c1","c2","c3")

categoriesRanks <-c(1,2)

names(categoriesRanks) <- c("P","F")

criteriaMinMax <- c("max","max","max")

names(criteriaMinMax) <- colnames(performanceTable)

assignments <-rbind(c("P","P","P","F","F","F","F","F","F","F","F","F",
                    "F","F","F","F","F","F","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","P","P","P","P","P","P",
                    "P","P","P","P","P","P","P","P","P","P","P","P"), 
                    c("P","P","P","F","F","F","F","F","F","F","F","F",
                    "P","P","P","P","P","P","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","P","P","P","P","P","P",
                    "P","P","P","P","P","P","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "F","F","F","F","F","F","F","F","F","F","F","F"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "P","P","P","P","P","P","P","P","P","P","P","P"), 
                    c("P","P","P","F","F","F","F","F","F","P","P","P",
                    "P","P","P","P","P","P","F","F","F","F","F","F"))

colnames(assignments) <- rownames(performanceTable)

majorityRules <- c("V","D","v","d","dV","Dv","dv")

for(i in 1:1)# change to 7 in order to perform all tests
{
  x<-LPDMRSortInferenceExact(performanceTable, assignments[i,],
                             categoriesRanks, criteriaMinMax, 
                             majorityRule = majorityRules[i], 
                             readableWeights = TRUE,
                             readableProfiles = TRUE,
                             minmaxLPD = TRUE)
  
  ElectreAssignments<-LPDMRSort(performanceTable, x$profilesPerformances, 
                                categoriesRanks,
                                x$weights, criteriaMinMax, x$lambda, 
                                criteriaVetos=x$vetoPerformances, 
                                criteriaDictators=x$dictatorPerformances, 
                                majorityRule = majorityRules[i])
  
  print(x)
  
  print(all(ElectreAssignments == assignments[i,]))
}

Multi-Attribute Range Evaluations (MARE)

Description

MARE is a multi-criteria decision analysis method which was originally developed by Hodgett et al. in 2014.

Usage

MARE(
  performanceTableMin,
  performanceTable,
  performanceTableMax,
  criteriaWeights,
  criteriaMinMax,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns an element of type mare which contains the MARE scores for each alternative.

References

Richard E. Hodgett, Elaine B. Martin, Gary Montague, Mark Talford (2014). Handling uncertain decisions in whole process design. Production Planning & Control, Volume 25, Issue 12, 1028-1038.

Examples

performanceTableMin <- t(matrix(c(78,87,79,19,8,68,74,8,90,89,74.5,9,20,81,30),
                  nrow=3,ncol=5, byrow=TRUE)) 
performanceTable <- t(matrix(c(80,87,86,19,8,70,74,10,90,89,75,9,33,82,30),
                              nrow=3,ncol=5, byrow=TRUE))
performanceTableMax <- t(matrix(c(81,87,95,19,8,72,74,15,90,89,75.5,9,36,84,30),
                                 nrow=3,ncol=5, byrow=TRUE))  

row.names(performanceTable) <- c("Yield","Toxicity","Cost","Separation","Odour")
colnames(performanceTable) <- c("Route One","Route Two","Route Three")
row.names(performanceTableMin) <- row.names(performanceTable)
colnames(performanceTableMin) <- colnames(performanceTable)
row.names(performanceTableMax) <- row.names(performanceTable)
colnames(performanceTableMax) <- colnames(performanceTable)

weights <- c(0.339,0.077,0.434,0.127,0.023) 
names(weights) <- row.names(performanceTable)

criteriaMinMax <- c("max", "max", "max", "max", "max")
names(criteriaMinMax) <- row.names(performanceTable)

overall1 <- MARE(performanceTableMin, 
                   performanceTable, 
                   performanceTableMax, 
                   weights, 
                   criteriaMinMax)

overall2 <- MARE(performanceTableMin, 
                    performanceTable,
                    performanceTableMax,
                    weights,
                    criteriaMinMax,
                    alternativesIDs = c("Route Two","Route Three"),
                    criteriaIDs = c("Yield","Toxicity","Cost","Separation"))

Electre TRI-like sorting method axiomatized by Bouyssou and Marchant.

Description

This simplification of the Electre TRI method uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. Only a binary discordance condition is considered, i.e. a veto forbids an outranking in any possible concordance situation, or not.

Usage

MRSort(
  performanceTable,
  categoriesLowerProfiles,
  categoriesRanks,
  criteriaWeights,
  criteriaMinMax,
  majorityThreshold,
  criteriaVetos = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  categoriesIDs = NULL
)

Arguments

Value

The function returns a vector containing the assignments of the alternatives to the categories.

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompen- satory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

Examples

# the performance table

performanceTable <- rbind(
  c(1,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# lower profiles of the categories 
# (best category in the first position of the list)

categoriesLowerProfiles <- rbind(c(3, 11, 3),c(7, 25, 2),c(NA,NA,NA))

colnames(categoriesLowerProfiles) <- colnames(performanceTable)

rownames(categoriesLowerProfiles)<-c("Good","Medium","Bad")

# the order of the categories, 1 being the best

categoriesRanks <-c(1,2,3)

names(categoriesRanks) <- c("Good","Medium","Bad")

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# vetos

criteriaVetos <- rbind(c(10, NA, NA),c(NA, NA, 1),c(NA,NA,NA))

colnames(criteriaVetos) <- colnames(performanceTable)
rownames(criteriaVetos) <- c("Good","Medium","Bad")

# weights

criteriaWeights <- c(1,3,2)

names(criteriaWeights) <- colnames(performanceTable)


# MRSort

assignments<-MRSort(performanceTable, categoriesLowerProfiles,
                    categoriesRanks,criteriaWeights,
                    criteriaMinMax, 3, 
                    criteriaVetos = criteriaVetos)
 
print(assignments)

# un peu de filtrage

assignments<-MRSort(performanceTable, categoriesLowerProfiles, 
                    categoriesRanks, criteriaWeights,
                    criteriaMinMax, 2,
                    categoriesIDs = c("Medium","Bad"), 
                    criteriaIDs = c("Price","Time"), 
                    alternativesIDs = c("RER", "BUS"))

print(assignments)

Identifies all sets of assignment examples which are incompatible with the MRSort method.

Description

This MRSort method, which is a simplification of the Electre TRI method, uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. Only a binary discordance condition is considered, i.e. a veto forbids an outranking in any possible concordance situation, or not. This function outputs for all (or a fixed number of) sets of incompatible assignment examples ranging in size from the minimal size and up to a given threshold. The retrieved sets are also not contained in each other.

Usage

MRSortIdentifyIncompatibleAssignments(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  veto = FALSE,
  incompatibleSetsLimit = 100,
  largerIncompatibleSetsMargin = 0,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns NULL if there is a problem, or a list containing a list of incompatible sets of alternatives as vectors and the status of the execution.

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompen- satory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

Examples

performanceTable <- rbind(c(10,10,9), c(10,9,10), c(9,10,10), c(9,9,10), 
                          c(9,10,9), c(10,9,9), c(10,10,7), c(10,7,10), 
                          c(7,10,10), c(9,9,17), c(9,17,9), c(17,9,9), 
                          c(7,10,17), c(10,17,7), c(17,7,10), c(7,17,10), 
                          c(17,10,7), c(10,7,17), c(7,9,17), c(9,17,7), 
                          c(17,7,9), c(7,17,9), c(17,9,7), c(9,7,17))

rownames(performanceTable) <- c("a1", "a2", "a3", "a4", "a5", "a6", "a7", 
                                "a8", "a9", "a10", "a11", "a12", "a13", 
                                "a14", "a15", "a16", "a17", "a18", "a19", 
                                "a20", "a21", "a22", "a23", "a24")

colnames(performanceTable) <- c("c1","c2","c3")

assignments <-c("P", "P", "P", "F", "F", "F", "F", "F", "F", "P", "F", 
                "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", 
                "F", "F")

names(assignments) <- rownames(performanceTable)

categoriesRanks <-c(1,2)

names(categoriesRanks) <- c("P","F")

criteriaMinMax <- c("max","max","max")

names(criteriaMinMax) <- colnames(performanceTable)

incompatibleAssignmentsSets<-MRSortIdentifyIncompatibleAssignments(
                               performanceTable, assignments, 
                               categoriesRanks, criteriaMinMax, 
                               veto = TRUE, 
                               alternativesIDs = c("a1","a2","a3","a4",
                               "a5","a6","a7","a8","a9","a10"))

print(incompatibleAssignmentsSets)

filteredAlternativesIDs <- setdiff(c("a1","a2","a3","a4","a5","a6","a7","a8","a9"),
                                   incompatibleAssignmentsSets[[1]][1])

print(filteredAlternativesIDs)

x<-MRSortInferenceExact(performanceTable, assignments, categoriesRanks, 
                        criteriaMinMax, veto = TRUE, 
                        readableWeights = TRUE, readableProfiles = TRUE,
                        alternativesIDs = filteredAlternativesIDs)

ElectreAssignments<-MRSort(performanceTable, x$profilesPerformances,
                           categoriesRanks, x$weights,
                           criteriaMinMax, x$lambda, 
                           criteriaVetos=x$vetoPerformances,
                           alternativesIDs = filteredAlternativesIDs)

Identify veto profiles evaluations that have an impact on the final assignments of MRSort

Description

MRSort is a simplified ELECTRE-TRI approach which assigns alternatives to a set of ordered categories using delimiting profiles evaluations. In addition, veto profiles may also be used in order to circumvent a sufficient majority coalition in favor of an alternative being assigned to a certain category. This method is used to identify which veto profiles evaluations have an impact on the final assignment of at least one of the input alternatives.

Usage

MRSortIdentifyUsedVetoProfiles(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  majorityThreshold,
  criteriaWeights,
  profilesPerformances,
  vetoPerformances,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a matrix containing TRUE/FALSE inficators for each evaluation of the veto profiles.

Examples

# the performance table

performanceTable <- rbind(
  c(1,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,10,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# lower profiles of the categories (best category in the first position of the list)

categoriesLowerProfiles <- rbind(c(3, 11, 3),c(7, 25, 2),c(NA,NA,NA))

colnames(categoriesLowerProfiles) <- colnames(performanceTable)

rownames(categoriesLowerProfiles)<-c("Good","Medium","Bad")

# the order of the categories, 1 being the best

categoriesRanks <-c(1,2,3)

names(categoriesRanks) <- c("Good","Medium","Bad")

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# vetos

criteriaVetos <- rbind(c(9, 50, -1),c(50, 50, 0),c(NA,NA,NA))

colnames(criteriaVetos) <- colnames(performanceTable)
rownames(criteriaVetos) <- c("Good","Medium","Bad")

# weights

criteriaWeights <- c(1/6,3/6,2/6)

names(criteriaWeights) <- colnames(performanceTable)

# assignments

assignments <- c("Good","Medium","Bad","Bad","Bad")

# MRSortIndetifyUsedVetoProfiles

used<-MRSortIdentifyUsedVetoProfiles(performanceTable, assignments,
                                     categoriesRanks, criteriaMinMax,
                                     0.5, criteriaWeights,
                                     categoriesLowerProfiles,
                                     criteriaVetos)

Identification of profiles, weights, majority threshold and veto thresholds for MRSort using a genetic algorithm.

Description

MRSort is a simplification of the Electre TRI method that uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. Only a binary discordance condition is considered, i.e. a veto forbids an outranking in any possible concordance situation, or not. The identification of the profiles, weights, majority threshold and veto thresholds are done by taking into account assignment examples.

Usage

MRSortInferenceApprox(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  veto = FALSE,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = 60,
  populationSize = 20,
  mutationProb = 0.1
)

Arguments

Value

The function returns a list containing:

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompen- satory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

no reference yet for the algorithmic approach; one should become available in 2018

Examples

performanceTable <- rbind(c(10,10,9), c(10,9,10), c(9,10,10), c(9,9,10), c(9,10,9), c(10,9,9),
                          c(10,10,7), c(10,7,10), c(7,10,10), c(9,9,17), c(9,17,9), c(17,9,9),
                          c(7,10,17), c(10,17,7), c(17,7,10), c(7,17,10), c(17,10,7), c(10,7,17),
                          c(7,9,17), c(9,17,7), c(17,7,9), c(7,17,9), c(17,9,7), c(9,7,17))

rownames(performanceTable) <- c("a1", "a2", "a3", "a4", "a5", "a6", "a7", "a8", "a9", "a10", "a11",
                                "a12", "a13", "a14", "a15", "a16", "a17", "a18", "a19", "a20",
                                "a21", "a22", "a23", "a24")

colnames(performanceTable) <- c("c1","c2","c3")

assignments <-c("P", "P", "P", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F",
                "F", "F", "F", "F", "F", "F", "F")

names(assignments) <- rownames(performanceTable)

categoriesRanks <- c(1,2)

names(categoriesRanks) <- c("P","F")

criteriaMinMax <- c("max","max","max")

names(criteriaMinMax) <- colnames(performanceTable)

set.seed(1)

x<-MRSortInferenceApprox(performanceTable, assignments, categoriesRanks, 
                         criteriaMinMax, veto = TRUE,
                         alternativesIDs = c("a1","a2","a3","a4","a5","a6","a7"))

Identification of profiles, weights and majority threshold for the MRSort sorting method using an exact approach.

Description

The MRSort method, a simplification of the Electre TRI method, uses the pessimistic assignment rule, without indifference or preference thresholds attached to criteria. Only a binary discordance condition is considered, i.e. a veto forbids an outranking in any possible concordance situation, or not. The identification of the profiles, weights and majority threshold are done by taking into account assignment examples.

Usage

MRSortInferenceExact(
  performanceTable,
  assignments,
  categoriesRanks,
  criteriaMinMax,
  veto = FALSE,
  readableWeights = FALSE,
  readableProfiles = FALSE,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a list structured as follows :

References

Bouyssou, D. and Marchant, T. An axiomatic approach to noncompen- satory sorting methods in MCDM, II: more than two categories. European Journal of Operational Research, 178(1): 246–276, 2007.

Examples

performanceTable <- rbind(c(10,10,9), c(10,9,10), c(9,10,10), c(9,9,10), 
                          c(9,10,9), c(10,9,9), c(10,10,7), c(10,7,10), 
                          c(7,10,10), c(9,9,17), c(9,17,9), c(17,9,9), 
                          c(7,10,17), c(10,17,7), c(17,7,10), c(7,17,10), 
                          c(17,10,7), c(10,7,17), c(7,9,17), c(9,17,7), 
                          c(17,7,9), c(7,17,9), c(17,9,7), c(9,7,17))

rownames(performanceTable) <- c("a1", "a2", "a3", "a4", "a5", "a6", "a7", 
                                "a8", "a9", "a10", "a11", "a12", "a13", 
                                "a14", "a15", "a16", "a17", "a18", "a19", 
                                "a20", "a21", "a22", "a23", "a24")

colnames(performanceTable) <- c("c1","c2","c3")

assignments <-c("P", "P", "P", "F", "F", "F", "F", "F", "F", "F", "F", "F", 
                "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F", "F")

names(assignments) <- rownames(performanceTable)

categoriesRanks <-c(1,2)

names(categoriesRanks) <- c("P","F")

criteriaMinMax <- c("max","max","max")

names(criteriaMinMax) <- colnames(performanceTable)

x<-MRSortInferenceExact(performanceTable, assignments, categoriesRanks, 
                         criteriaMinMax, veto = TRUE, readableWeights = TRUE, 
                         readableProfiles = TRUE, 
                         alternativesIDs = c("a1","a2","a3","a4","a5","a6","a7"))

ElectreAssignments<-MRSort(performanceTable, x$profilesPerformances, 
                           categoriesRanks,
                           x$weights, criteriaMinMax, x$lambda, 
                           criteriaVetos=x$vetoPerformances,
                           alternativesIDs = c("a1","a2","a3","a4","a5","a6","a7"))

MRSort with imprecise evaluations

Description

This method is an extension of the classical MRSort, that allows the handling of problems where the decision alternatives contain imprecise or even missing evaluations. Unlike MRSort, where an alternative is assigned to one category, MRSortInterval offers the possibility of assigning an alternative to one or more neighboring categories.

Usage

MRSortInterval(
  performanceTable,
  categoriesLowerProfiles,
  categoriesRanks,
  criteriaWeights,
  criteriaMinMax,
  majorityThresholdPes,
  majorityThresholdOpt
)

Arguments

Value

The function returns a list containing the assignments of the alternatives to all possibles categories.

Examples

# the performance table

performanceTable <- as.list(numeric(6*5))
dim(performanceTable)=c(6,5)
performanceTable[[1,1]]<-0
performanceTable[[1,2]]<-0
performanceTable[[1,3]]<-0
performanceTable[[1,4]]<-0
performanceTable[[1,5]]<-0
performanceTable[[2,1]]<-0
performanceTable[[2,2]]<-0
performanceTable[[2,3]]<-1
performanceTable[[2,4]]<-0
performanceTable[[2,5]]<-0
performanceTable[[3,1]]<-0
performanceTable[[3,2]]<-0
performanceTable[[3,3]]<-2
performanceTable[[3,4]]<-0
performanceTable[[3,5]]<-0
performanceTable[[4,1]]<-0
performanceTable[[4,2]]<-0
performanceTable[[4,3]]<-0:1
performanceTable[[4,4]]<-0
performanceTable[[4,5]]<-0
performanceTable[[5,1]]<-0
performanceTable[[5,2]]<-0
performanceTable[[5,3]]<-NA
performanceTable[[5,4]]<-0
performanceTable[[5,5]]<-0
performanceTable[[6,1]]<-0
performanceTable[[6,2]]<-0
performanceTable[[6,3]]<-0
performanceTable[[6,4]]<-0
performanceTable[[6,5]]<-NA

rownames(performanceTable)<-c("a1","a2","a3","a4","a5","a6")
colnames(performanceTable)<-c("c1","c2","c3","c4","c5")

# lower profiles of the categories (best category in the first position of the list)

categoriesLowerProfiles <- rbind(c(1,1,1,1,1),c(0,0,0,2,2))
colnames(categoriesLowerProfiles) <- colnames(performanceTable)

rownames(categoriesLowerProfiles)<-c("Medium","Good")

categoriesRanks <-c(1,2,3)

names(categoriesRanks) <- c("Good","Medium","Bad")

# weights

criteriaWeights <- c(1/5,1/5,1/5,1/5,1/5)
names(criteriaWeights) <- colnames(performanceTable)

#pessimistic and optimistic majority thresholds
majorityThresholdPes=majorityThresholdOpt=3/5

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","min","max","max")
names(criteriaMinMax) <- colnames(performanceTable)

#MRSortInterval

assignments<-MRSortInterval(performanceTable,categoriesLowerProfiles,
                            categoriesRanks,criteriaWeights,
                            criteriaMinMax,majorityThresholdPes,
                            majorityThresholdOpt)

PROMETHEE I

Description

The PROMETHEE I constructs preference indices from the criteria evaluations of alternatives and outputs three preference relations (P - preference, I - indifference, R - incomparability) based on the outranking flows between the alternatives.

Usage

PROMETHEEI(
  performanceTable,
  preferenceFunction,
  preferenceThreshold,
  indifferenceThreshold,
  gaussParameter,
  criteriaWeights,
  criteriaMinMax
)

Arguments

Value

The function returns three matrices: The first one contains the preference relations between the alternatives, the second one contains the indifference relations between the alternatives and the third one contains the incomparability relations between the alternatives.

Examples

# The evaluation table

performanceTable <- rbind(
  c(1,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))
rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")
colnames(performanceTable) <- c("Price","Time","Comfort")

# The preference functions 
preferenceFunction<-c("Gaussian","Level","V-shape-Indiff")

#Preference threshold
preferenceThreshold<-c(5,15,3)
names(preferenceThreshold)<-colnames(performanceTable)

#Indifference threshold
indifferenceThreshold<-c(3,11,1)
names(indifferenceThreshold)<-colnames(performanceTable)

#Parameter of the Gaussian preference function
gaussParameter<-c(4,0,0)
names(gaussParameter)<-colnames(performanceTable)

#weights

criteriaWeights<-c(0.2,0.3,0.5)
names(criteriaWeights)<-colnames(performanceTable)

# criteria to minimize or maximize

criteriaMinMax<-c("min","min","max")
names(criteriaMinMax)<-colnames(performanceTable)

PROMETHEEI(performanceTable, preferenceFunction,preferenceThreshold,
          indifferenceThreshold,gaussParameter,criteriaWeights,criteriaMinMax)

PROMETHEE II

Description

The PROMETHEE II constructs preference indices from the criteria evaluations of alternatives and outputs a pre-order based on the outranking flows between the alternatives.

Usage

PROMETHEEII(
  performanceTable,
  preferenceFunction,
  preferenceThreshold,
  indifferenceThreshold,
  gaussParameter,
  criteriaWeights,
  criteriaMinMax
)

Arguments

Value

The function returns a list containing the alternatives IDs in decreasing order of preference. Each elements of the list can be a vector of alternatives IDs.

Examples

# The evaluation table

performanceTable <- rbind(
  c(1,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))
rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")
colnames(performanceTable) <- c("Price","Time","Comfort")

# The preference functions 
preferenceFunction<-c("Gaussian","Level","V-shape-Indiff")

#Preference threshold
preferenceThreshold<-c(5,15,3)
names(preferenceThreshold)<-colnames(performanceTable)

#Indifference threshold
indifferenceThreshold<-c(3,11,1)
names(indifferenceThreshold)<-colnames(performanceTable)

#Parameter of the Gaussian preference function
gaussParameter<-c(4,0,0)
names(gaussParameter)<-colnames(performanceTable)

#weights

criteriaWeights<-c(0.2,0.3,0.5)
names(criteriaWeights)<-colnames(performanceTable)

# criteria to minimize or maximize

criteriaMinMax<-c("min","min","max")
names(criteriaMinMax)<-colnames(performanceTable)

PROMETHEEII(performanceTable, preferenceFunction,preferenceThreshold,
            indifferenceThreshold,gaussParameter,criteriaWeights,
            criteriaMinMax)

Outranking flows for the PROMETHEE methods

Description

This function computes the positive and negative outranking flows for the PROMETHEE methods. It takes as input a performance table and converts the evaluations to preference indices based on the given function types and parameters for each criterion.

Usage

PROMETHEEOutrankingFlows(
  performanceTable,
  preferenceFunction,
  preferenceThreshold,
  indifferenceThreshold,
  gaussParameter,
  criteriaWeights,
  criteriaMinMax
)

Arguments

Value

The function returns two vectors: The first one contains the positive outranking flows and the second one contains the negative outranking flows.

Examples

# The evaluation table

performanceTable <- rbind(
  c(1,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))
rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")
colnames(performanceTable) <- c("Price","Time","Comfort")

# The preference functions 
preferenceFunction<-c("Gaussian","Level","V-shape-Indiff")

#Preference threshold
preferenceThreshold<-c(5,15,3)
names(preferenceThreshold)<-colnames(performanceTable)

#Indifference threshold
indifferenceThreshold<-c(3,11,1)
names(indifferenceThreshold)<-colnames(performanceTable)

#Parameter of the Gaussian preference function
gaussParameter<-c(4,0,0)
names(gaussParameter)<-colnames(performanceTable)

#weights

criteriaWeights<-c(0.2,0.3,0.5)
names(criteriaWeights)<-colnames(performanceTable)

# criteria to minimize or maximize

criteriaMinMax<-c("min","min","max")
names(criteriaMinMax)<-colnames(performanceTable)


# Outranking flows

outrankingFlows<-PROMETHEEOutrankingFlows(performanceTable, preferenceFunction,
                                          preferenceThreshold,indifferenceThreshold,
                                          gaussParameter,criteriaWeights,
                                          criteriaMinMax)

Preference indices for the PROMETHEE methods

Description

This function computes the preference indices from a performance table based on the given function types and parameters for each criterion.

Usage

PROMETHEEPreferenceIndices(
  performanceTable,
  preferenceFunction,
  preferenceThreshold,
  indifferenceThreshold,
  gaussParameter,
  criteriaWeights,
  criteriaMinMax
)

Arguments

Value

The function returns a matrix containing all the aggregated preference indices.

Examples

# The evaluation table

performanceTable <- rbind(
  c(1,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))
rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")
colnames(performanceTable) <- c("Price","Time","Comfort")

# The preference functions 
preferenceFunction<-c("Gaussian","Level","V-shape-Indiff")

#Preference threshold
preferenceThreshold<-c(5,15,3)
names(preferenceThreshold)<-colnames(performanceTable)

#Indifference threshold
indifferenceThreshold<-c(3,11,1)
names(indifferenceThreshold)<-colnames(performanceTable)

#Parameter of the Gaussian preference function
gaussParameter<-c(4,0,0)
names(gaussParameter)<-colnames(performanceTable)

#weights

criteriaWeights<-c(0.2,0.3,0.5)
names(criteriaWeights)<-colnames(performanceTable)

# criteria to minimize or maximize

criteriaMinMax<-c("min","min","max")
names(criteriaMinMax)<-colnames(performanceTable)


#Preference indices

preferenceTable<-PROMETHEEPreferenceIndices(performanceTable, preferenceFunction,
                                            preferenceThreshold, indifferenceThreshold,
                                            gaussParameter, criteriaWeights,
                                            criteriaMinMax)

SRMP: a simple ranking method using reference profiles

Description

SRMP is a ranking method that uses dominating reference profiles, in a given lexicographic ordering, in order to output a total preorder of a set of alternatives.

Usage

SRMP(
  performanceTable,
  referenceProfiles,
  lexicographicOrder,
  criteriaWeights,
  criteriaMinMax,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a vector containing the ranks of the alternatives (the higher the better).

References

A. Rolland. Procédures d’agrégation ordinale de préférences avec points de référence pour l’aide a la décision. PhD thesis, Université Paris VI, 2008.

Examples

# the performance table

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

referenceProfiles <- rbind(c(5,5,5),c(10,10,10),c(15,15,15))

lexicographicOrder <- c(2,1,3)

weights <- c(0.2,0.44,0.36)

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11","a12",
                                "a13","a14","a15","a16","a17","a18","a19","a20","a21","a22",
                                "a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

colnames(referenceProfiles) <- c("c1","c2","c3")

names(weights) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

expectedpreorder <- list('a16','a13',c('a3','a9'),'a14','a17',c('a1','a7'),'a18','a15',
                         c('a2','a8'),c('a11','a20','a22'),'a5',c('a10','a19','a24'),
                         'a4',c('a12','a21','a23'),'a6')

preorder<-SRMP(performanceTable, referenceProfiles, lexicographicOrder, weights, criteriaMinMax)

Exact inference of an SRMP model given a maximum number of reference profiles

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method outputs an SRMP model that is as consistent as possible with the provided pairwise comparisons (i.e. the model - the number of profiles and their lexicographic order - that maximizes the number of fulfilled pairwise comparisons). The method will search for a model with the minimum possible number of profiles up to a given maximum value.

Usage

SRMPInference(
  performanceTable,
  criteriaMinMax,
  maxProfilesNumber,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = NULL
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11","a12",
                                "a13","a14","a15","a16","a17","a18","a19","a20","a21","a22",
                                "a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11","a5",
                            "a10","a4","a12","a13","a3","a14","a17","a1","a18","a15","a2",
                            "a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12","a12",
                              "a21","a9","a7","a8","a20","a22","a22","a19","a24","a24","a21",
                              "a23","a23"),12,2)

result<-SRMPInference(performanceTable, criteriaMinMax, 3, preferencePairs, indifferencePairs,
                      alternativesIDs = c("a1","a3","a7","a9","a13","a14","a15","a16","a17",
                      "a18"))

Approximative inference of an SRMP model

Description

Approximative inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method outputs an SRMP model that fulfils as many pairwise comparisons as possible. Neither the number of reference profiles, nor the lexicographic order are fixed beforehand, however a maximum value for the number of reference profiles needs to be provided.

Usage

SRMPInferenceApprox(
  performanceTable,
  criteriaMinMax,
  maxProfilesNumber,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = 60,
  populationSize = 20,
  mutationProb = 0.1
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11",
                                "a12","a13","a14","a15","a16","a17","a18","a19","a20",
                                "a21","a22","a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

# expected result for the tests below

expectedpreorder <- list("a16","a13",c("a3","a9"),"a14","a17",c("a1","a7"),"a18","a15")

# test - preferences and indifferences

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11",
                            "a5","a10","a4","a12","a13","a3","a14","a17","a1","a18",
                            "a15","a2","a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12",
                              "a12","a21","a9","a7","a8","a20","a22","a22","a19","a24",
                              "a24","a21","a23","a23"),12,2)

set.seed(1)

result<-SRMPInferenceApprox(performanceTable, criteriaMinMax, 3, preferencePairs,
                            indifferencePairs, alternativesIDs = c("a1","a3","a7",
                            "a9","a13","a14","a15","a16","a17","a18"))

Approximative inference of an SRMP model given the lexicographic order of the profiles

Description

Approximative inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method outputs an SRMP model that fulfils as many pairwise comparisons as possible. The number of reference profiles and their lexicographic order is fixed beforehand.

Usage

SRMPInferenceApproxFixedLexicographicOrder(
  performanceTable,
  criteriaMinMax,
  lexicographicOrder,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = 60,
  populationSize = 20,
  mutationProb = 0.1
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

lexicographicOrder <- c(1,2,3)

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11",
                                "a12","a13","a14","a15","a16","a17","a18","a19","a20",
                                "a21","a22","a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

# expected result for the tests below

expectedpreorder <- list("a16","a13",c("a3","a9"),"a14","a17",c("a1","a7"),"a18","a15")

# test - preferences and indifferences

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11",
                            "a5","a10","a4","a12","a13","a3","a14","a17","a1","a18",
                            "a15","a2","a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12",
                              "a12","a21","a9","a7","a8","a20","a22","a22","a19","a24",
                              "a24","a21","a23","a23"),12,2)

set.seed(1)

result<-SRMPInferenceApproxFixedLexicographicOrder(performanceTable, criteriaMinMax,
                                                   lexicographicOrder, preferencePairs,
                                                   indifferencePairs, alternativesIDs =
                                                   c("a1","a3","a7","a9","a13","a14",
                                                   "a15","a16","a17","a18"))

Approximative inference of an SRMP model given the number of reference profiles

Description

Approximative inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method outputs an SRMP model that fulfils as many pairwise comparisons as possible. The number of reference profiles is fixed beforehand, however the algorithm will explore any lexicographic order between them.

Usage

SRMPInferenceApproxFixedProfilesNumber(
  performanceTable,
  criteriaMinMax,
  profilesNumber,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = 60,
  populationSize = 20,
  mutationProb = 0.1
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

# the performance table

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11",
                                "a12","a13","a14","a15","a16","a17","a18","a19","a20",
                                "a21","a22","a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

# expected result for the tests below

expectedpreorder <- list("a16","a13",c("a3","a9"),"a14",c("a1","a7"),"a15")

# test - preferences and indifferences

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11",
                            "a5","a10","a4","a12","a13","a3","a14","a17","a1","a18",
                            "a15","a2","a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12",
                              "a12","a21","a9","a7","a8","a20","a22","a22","a19","a24",
                              "a24","a21","a23","a23"),12,2)

set.seed(1)

result<-SRMPInferenceApproxFixedProfilesNumber(performanceTable, criteriaMinMax, 3,
                                               preferencePairs, indifferencePairs,
                                               alternativesIDs = c("a1","a3","a7","a9",
                                               "a13","a14","a15","a16"))

Exact inference of an SRMP model given the lexicographic order of the profiles

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method outputs an SRMP model that maximizes the number of fulfilled pairwise comparisons. The number of reference profiles and their lexicographic order is fixed.

Usage

SRMPInferenceFixedLexicographicOrder(
  performanceTable,
  criteriaMinMax,
  lexicographicOrder,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = NULL
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

# the performance table

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

lexicographicOrder <- c(2,1,3)

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11","a12",
                                "a13","a14","a15","a16","a17","a18","a19","a20","a21","a22",
                                "a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11","a5",
                            "a10","a4","a12","a13","a3","a14","a17","a1","a18","a15","a2",
                            "a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12","a12",
                              "a21","a9","a7","a8","a20","a22","a22","a19","a24","a24","a21",
                              "a23","a23"),12,2)

result<-SRMPInferenceFixedLexicographicOrder(performanceTable, criteriaMinMax,
                                             lexicographicOrder, preferencePairs,
                                             indifferencePairs, alternativesIDs = 
                                             c("a1","a3","a7","a9","a13","a14","a16","a17"))

Exact inference of an SRMP model given the number of reference profiles

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method outputs an SRMP model that is as consistent as possible with the provided pairwise comparisons (i.e. the model - and the lexicographic order of the reference profiles - that maximizes the number of fulfilled pairwise comparisons). The number of reference profiles is fixed and needs to be provided.

Usage

SRMPInferenceFixedProfilesNumber(
  performanceTable,
  criteriaMinMax,
  profilesNumber,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = NULL
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11","a12",
                                "a13","a14","a15","a16","a17","a18","a19","a20","a21","a22",
                                "a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11","a5",
                            "a10","a4","a12","a13","a3","a14","a17","a1","a18","a15","a2",
                            "a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12","a12",
                              "a21","a9","a7","a8","a20","a22","a22","a19","a24","a24","a21",
                              "a23","a23"),12,2)

result<-SRMPInferenceFixedProfilesNumber(performanceTable, criteriaMinMax, 3, preferencePairs,
                                         indifferencePairs, alternativesIDs = c("a1","a3",
                                         "a7","a9","a13","a14","a15","a16","a17","a18"))

Exact inference of an SRMP model given a maximum number of reference profiles - no inconsistencies

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method only outputs a result when an SRMP model consistent with the provided pairwise comparisons exists. The method will search for a model with the minimum possible number of profiles up to a given maximum value. If such a model exists, this method is significantly faster than the one which handles inconsistencies.

Usage

SRMPInferenceNoInconsist(
  performanceTable,
  criteriaMinMax,
  maxProfilesNumber,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = NULL
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11","a12",
                                "a13","a14","a15","a16","a17","a18","a19","a20","a21","a22",
                                "a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11","a5",
                            "a10","a4","a12","a13","a3","a14","a17","a1","a18","a15","a2",
                            "a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12","a12",
                              "a21","a9","a7","a8","a20","a22","a22","a19","a24","a24","a21",
                              "a23","a23"),12,2)

result<-SRMPInferenceNoInconsist(performanceTable, criteriaMinMax, 3, preferencePairs,
                                 indifferencePairs, alternativesIDs = c("a1","a2","a3","a4",
                                 "a5","a6","a7","a8","a10","a11","a12","a14","a16","a17","a18",
                                 "a19","a20","a21","a23","a24"))

Exact inference of an SRMP model given the lexicographic order of the profiles - no inconsistencies

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method only outputs a result when an SRMP model consistent with the provided pairwise comparisons exists. The number of reference profiles and their lexicographic order is fixed. If such a model exists, this method is significantly faster than the one which handles inconsistencies.

Usage

SRMPInferenceNoInconsistFixedLexicographicOrder(
  performanceTable,
  criteriaMinMax,
  lexicographicOrder,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = NULL
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

# the performance table

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

lexicographicOrder <- c(2,1,3)

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11","a12",
                                "a13","a14","a15","a16","a17","a18","a19","a20","a21","a22",
                                "a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11","a5",
                            "a10","a4","a12","a13","a3","a14","a17","a1","a18","a15","a2",
                            "a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12","a12",
                              "a21","a9","a7","a8","a20","a22","a22","a19","a24","a24","a21",
                              "a23","a23"),12,2)

result<-SRMPInferenceNoInconsistFixedLexicographicOrder(performanceTable, criteriaMinMax,
                                                        lexicographicOrder, preferencePairs,
                                                        indifferencePairs, alternativesIDs =
                                                        c("a1","a2","a3","a4","a5","a6","a7",
                                                        "a8","a10","a11","a12","a14","a16",
                                                        "a17","a18","a19","a20","a21","a23",
                                                        "a24"))

Exact inference of an SRMP model given the number of reference profiles - no inconsistencies

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method only outputs a result when an SRMP model consistent with the provided pairwise comparisons exists. The number of reference profiles is fixed and need to be provided. If such a model exists, this method is significantly faster than the one which handles inconsistencies.

Usage

SRMPInferenceNoInconsistFixedProfilesNumber(
  performanceTable,
  criteriaMinMax,
  profilesNumber,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = NULL
)

Arguments

Value

The function returns a list containing:

References

A-L. OLTEANU, V. MOUSSEAU, W. OUERDANE, A. ROLLAND, Y. ZHENG, Preference Elicitation for a Ranking Method based on Multiple Reference Profiles, forthcoming 2018.

Examples

performanceTable <- rbind(c(10,10,9),c(10,9,10),c(9,10,10),c(9,9,10),c(9,10,9),c(10,9,9),
                          c(10,10,7),c(10,7,10),c(7,10,10),c(9,9,17),c(9,17,9),c(17,9,9),
                          c(7,10,17),c(10,17,7),c(17,7,10),c(7,17,10),c(17,10,7),c(10,7,17),
                          c(7,9,17),c(9,17,7),c(17,7,9),c(7,17,9),c(17,9,7),c(9,7,17))

criteriaMinMax <- c("max","max","max")

rownames(performanceTable) <- c("a1","a2","a3","a4","a5","a6","a7","a8","a9","a10","a11","a12",
                                "a13","a14","a15","a16","a17","a18","a19","a20","a21","a22",
                                "a23","a24")

colnames(performanceTable) <- c("c1","c2","c3")

names(criteriaMinMax) <- colnames(performanceTable)

preferencePairs <- matrix(c("a16","a13","a3","a14","a17","a1","a18","a15","a2","a11","a5",
                            "a10","a4","a12","a13","a3","a14","a17","a1","a18","a15","a2",
                            "a11","a5","a10","a4","a12","a6"),14,2)
indifferencePairs <- matrix(c("a3","a1","a2","a11","a11","a20","a10","a10","a19","a12","a12",
                              "a21","a9","a7","a8","a20","a22","a22","a19","a24","a24","a21",
                              "a23","a23"),12,2)

result<-SRMPInferenceNoInconsistFixedProfilesNumber(performanceTable, criteriaMinMax, 3,
                                                    preferencePairs, indifferencePairs,
                                                    alternativesIDs = c("a1","a2","a3","a4",
                                                    "a5","a6","a7","a8","a10","a11","a12",
                                                    "a14","a16","a17","a18","a19","a20","a21",
                                                    "a23","a24"))

Simulated Uncertainty Range Evaluations (SURE)

Description

SURE is a multi-criteria decision analysis method which was developed by Richard Hodgett and Sajid Siraj. More details on the method are available in https://doi.org/10.1016/j.eswa.2018.08.048

Usage

SURE(
  performanceTableMin,
  performanceTable,
  performanceTableMax,
  criteriaWeights,
  criteriaMinMax,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  NoOfSimulations = 1e+05
)

Arguments

Value

The function returns an element of type SURE which contains the SURE simulated scores for each alternative.

References

Richard E. Hodgett, Sajid Siraj (2019). SURE: A method for decision-making under uncertainty. Expert Systems with Applications, Volume 115, 684-694.

Examples

performanceTableMin <- t(matrix(c(78,87,79,19,8,68,74,8,90,89,74.5,9,20,81,30),
                  nrow=3,ncol=5, byrow=TRUE)) 
performanceTable <- t(matrix(c(80,87,86,19,8,70,74,10,90,89,75,9,33,82,30),
                              nrow=3,ncol=5, byrow=TRUE))
performanceTableMax <- t(matrix(c(81,87,95,19,8,72,74,15,90,89,75.5,9,36,84,30),
                                 nrow=3,ncol=5, byrow=TRUE))  

row.names(performanceTable) <- c("Yield","Toxicity","Cost","Separation","Odour")
colnames(performanceTable) <- c("Route One","Route Two","Route Three")
row.names(performanceTableMin) <- row.names(performanceTable)
colnames(performanceTableMin) <- colnames(performanceTable)
row.names(performanceTableMax) <- row.names(performanceTable)
colnames(performanceTableMax) <- colnames(performanceTable)

criteriaWeights <- c(0.339,0.077,0.434,0.127,0.023) 
names(criteriaWeights) <- row.names(performanceTable)

criteriaMinMax <- c("max", "max", "max", "max", "max")
names(criteriaMinMax) <- row.names(performanceTable)

test1 <- SURE(performanceTableMin, 
                 performanceTable, 
                 performanceTableMax, 
                 criteriaWeights, 
                 criteriaMinMax, NoOfSimulations = 101)

summary(test1)
plotSURE(test1)
plotSURE(test1, greyScale = TRUE, separate = TRUE)

test2 <- SURE(performanceTableMin, 
              performanceTable,
              performanceTableMax,
              criteriaWeights,
              criteriaMinMax,
              alternativesIDs = c("Route Two","Route Three"),
              criteriaIDs = c("Yield","Toxicity","Separation"),
              NoOfSimulations = 101)

summary(test2)
plotSURE(test2)
plotSURE(test2, greyScale = TRUE, separate = TRUE)

Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method

Description

TOPSIS is a multi-criteria decision analysis method which was originally developed by Hwang and Yoon in 1981.

Usage

TOPSIS(
  performanceTable,
  criteriaWeights,
  criteriaMinMax,
  positiveIdealSolutions = NULL,
  negativeIdealSolutions = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a vector containing the TOPSIS score for each alternative.

References

Hwang, C.L.; Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. New York: Springer-Verlag. http://hodgett.co.uk/topsis-in-excel/

Examples

performanceTable <- matrix(c(5490,51.4,8.5,285,6500,70.6,7,
                              288,6489,54.3,7.5,290),
                              nrow=3,
                              ncol=4,
                              byrow=TRUE)

row.names(performanceTable) <- c("Corsa","Clio","Fiesta")

colnames(performanceTable) <- c("Purchase Price","Economy",
                                   "Aesthetics","Boot Capacity")

weights <- c(0.35,0.25,0.25,0.15)

criteriaMinMax <- c("min", "max", "max", "max")

positiveIdealSolutions <- c(0.179573776, 0.171636015, 0.159499658, 0.087302767)
negativeIdealSolutions <- c(0.212610118, 0.124958799, 0.131352659, 0.085797547)

names(weights) <- colnames(performanceTable)
names(criteriaMinMax) <- colnames(performanceTable)
names(positiveIdealSolutions) <- colnames(performanceTable)
names(negativeIdealSolutions) <- colnames(performanceTable)

overall1 <- TOPSIS(performanceTable, weights, criteriaMinMax)

overall2 <- TOPSIS(performanceTable,
                       weights, 
                       criteriaMinMax,
                       positiveIdealSolutions,
                       negativeIdealSolutions)

overall3 <- TOPSIS(performanceTable,
                      weights,
                      criteriaMinMax,
                      alternativesIDs = c("Corsa","Clio"),
                      criteriaIDs = c("Purchase Price","Economy","Aesthetics"))

overall4 <- TOPSIS(performanceTable, 
                    weights,
                    criteriaMinMax,
                    positiveIdealSolutions,
                    negativeIdealSolutions,
                    alternativesIDs = c("Corsa","Clio"), 
                    criteriaIDs = c("Purchase Price","Economy","Aesthetics"))

UTA method to elicit value functions.

Description

Elicits value functions from a ranking of alternatives, according to the UTA method.

Usage

UTA(
  performanceTable,
  criteriaMinMax,
  criteriaNumberOfBreakPoints,
  epsilon,
  alternativesRanks = NULL,
  alternativesPreferences = NULL,
  alternativesIndifferences = NULL,
  criteriaLBs = NULL,
  criteriaUBs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  kPostOptimality = NULL
)

Arguments

Value

The function returns a list structured as follows :

References

E. Jacquet-Lagreze, J. Siskos, Assessing a set of additive utility functions for multicriteria decision-making, the UTA method, European Journal of Operational Research, Volume 10, Issue 2, 151–164, June 1982.

Examples

# the separation threshold

epsilon <-0.05

# the performance table

performanceTable <- rbind(
  		c(3,10,1),
			c(4,20,2),
			c(2,20,0),
			c(6,40,0),
			c(30,30,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# ranks of the alternatives

alternativesRanks <- c(1,2,2,3,4)

names(alternativesRanks) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# number of break points for each criterion

criteriaNumberOfBreakPoints <- c(3,4,4)

names(criteriaNumberOfBreakPoints) <- colnames(performanceTable)

x<-UTA(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon, 
        alternativesRanks = alternativesRanks)

# plot the value functions obtained

plotPiecewiseLinearValueFunctions(x$valueFunctions)

# apply the value functions on the original performance table

transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
  x$valueFunctions, 
  performanceTable)

# calculate the overall score of each alternative

weightedSum(transformedPerformanceTable,c(1,1,1))

# ----------------------------------------
# ranking some cars (from original article on UTA by Siskos and Lagreze, 1982)

# the separation threshold

epsilon <-0.01

# the performance table

performanceTable <- rbind(      
c(173, 11.4, 10.01, 10, 7.88, 49500),
c(176, 12.3, 10.48, 11, 7.96, 46700),
c(142, 8.2, 7.30, 5, 5.65, 32100),
c(148, 10.5, 9.61, 7, 6.15, 39150), 
c(178, 14.5, 11.05, 13, 8.06, 64700), 
c(180, 13.6, 10.40, 13, 8.47, 75700),
c(182, 12.7, 12.26, 11, 7.81, 68593), 
c(145, 14.3, 12.95, 11, 8.38, 55000),
c(161, 8.6, 8.42, 7, 5.11, 35200), 
c(117, 7.2, 6.75, 3, 5.81, 24800)
)

rownames(performanceTable) <- c(
  "Peugeot 505 GR",
  "Opel Record 2000 LS",
  "Citroen Visa Super E",
  "VW Golf 1300 GLS",
  "Citroen CX 2400 Pallas",
  "Mercedes 230",
  "BMW 520",
  "Volvo 244 DL",
  "Peugeot 104 ZS",
  "Citroen Dyane")

colnames(performanceTable) <- c(
  "MaximalSpeed",
  "ConsumptionTown",
  "Consumption120kmh",
  "HP",
  "Space",
  "Price")

# ranks of the alternatives

alternativesRanks <- c(1,2,3,4,5,6,7,8,9,10)

names(alternativesRanks) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("max","min","min","max","max","min")

names(criteriaMinMax) <- colnames(performanceTable)

# number of break points for each criterion

criteriaNumberOfBreakPoints <- c(5,4,4,5,4,5)

names(criteriaNumberOfBreakPoints) <- colnames(performanceTable)

# lower bounds of the criteria for the determination of value functions

criteriaLBs=c(110,7,6,3,5,20000)

names(criteriaLBs) <- colnames(performanceTable)

# upper bounds of the criteria for the determination of value functions

criteriaUBs=c(190,15,13,13,9,80000)

names(criteriaUBs) <- colnames(performanceTable)

x<-UTA(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon, 
        alternativesRanks = alternativesRanks,
        criteriaLBs = criteriaLBs, criteriaUBs = criteriaUBs)
        

# plot the value functions obtained

plotPiecewiseLinearValueFunctions(x$valueFunctions)

# apply the value functions on the original performance table

transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
      x$valueFunctions, 
      performanceTable)

# calculate the overall score of each alternative

weights<-c(1,1,1,1,1,1)

names(weights)<-colnames(performanceTable)

weightedSum(transformedPerformanceTable,c(1,1,1,1,1,1))

# the same analysis with less extreme value functions 
# from the post-optimality analysis

x<-UTA(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon,
        alternativesRanks = alternativesRanks,
        criteriaLBs = criteriaLBs, 
        criteriaUBs = criteriaUBs, 
        kPostOptimality = 0.01)
        
# plot the value functions obtained

plotPiecewiseLinearValueFunctions(x$averageValueFunctionsPO)

# apply the value functions on the original performance table

transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
      x$averageValueFunctionsPO, 
      performanceTable)

# calculate the overall score of each alternative

weights<-c(1,1,1,1,1,1)

names(weights)<-colnames(performanceTable)

weightedSum(transformedPerformanceTable,c(1,1,1,1,1,1))


# ----------------------------------------
# Let us consider only 2 criteria : Price and MaximalSpeed. What happens ? 

# x<-UTA(performanceTable, criteriaMinMax, 
#         criteriaNumberOfBreakPoints, epsilon,
#         alternativesRanks = alternativesRanks,
#         criteriaLBs = criteriaLBs, criteriaUBs = criteriaUBs,
#         criteriaIDs = c("MaximalSpeed","Price"))
        

# plot the value functions obtained

# plotPiecewiseLinearValueFunctions(x$valueFunctions, 
#                                   criteriaIDs = c("MaximalSpeed","Price"))

# apply the value functions on the original performance table

# transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
#   x$valueFunctions, 
#   performanceTable, 
#   criteriaIDs = c("MaximalSpeed","Price")
#   )

# calculate the overall score of each alternative

# weights<-c(1,1,1,1,1,1)

# names(weights)<-colnames(performanceTable)

# weightedSum(transformedPerformanceTable,
#          weights, criteriaIDs = c("MaximalSpeed","Price"))

# ----------------------------------------
# An example without alternativesRanks, but with alternativesPreferences
# and alternativesIndifferences

alternativesPreferences <- rbind(c("Peugeot 505 GR","Opel Record 2000 LS"),
                                c("Opel Record 2000 LS","Citroen Visa Super E"))

alternativesIndifferences <- rbind(c("Peugeot 104 ZS","Citroen Dyane"))

x<-UTA(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon = 0.1,
        alternativesPreferences = alternativesPreferences,
        alternativesIndifferences = alternativesIndifferences,
        criteriaLBs = criteriaLBs, criteriaUBs = criteriaUBs
        )

UTADIS method to elicit value functions in view of sorting alternatives in ordered categories

Description

Elicits value functions from assignment examples, according to the UTADIS method.

Usage

UTADIS(
  performanceTable,
  criteriaMinMax,
  criteriaNumberOfBreakPoints,
  alternativesAssignments,
  categoriesRanks,
  epsilon,
  criteriaLBs = NULL,
  criteriaUBs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  categoriesIDs = NULL
)

Arguments

Value

The function returns a list structured as follows :

References

J.M. Devaud, G. Groussaud, and E. Jacquet-Lagrèze, UTADIS : Une méthode de construction de fonctions d'utilité additives rendant compte de jugements globaux, European Working Group on Multicriteria Decision Aid, Bochum, 1980.

Examples

# the separation threshold

epsilon <-0.05

# the performance table

performanceTable <- rbind(
  c(3,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# ranks of the alternatives

alternativesAssignments <- c("good","medium","medium","bad","bad")

names(alternativesAssignments) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# number of break points for each criterion

criteriaNumberOfBreakPoints <- c(3,4,4)

names(criteriaNumberOfBreakPoints) <- colnames(performanceTable)

# ranks of the categories

categoriesRanks <- c(1,2,3)

names(categoriesRanks) <- c("good","medium","bad")

x<-UTADIS(performanceTable, criteriaMinMax, criteriaNumberOfBreakPoints, 
           alternativesAssignments, categoriesRanks,0.1)

# filtering out category "good" and assigment examples "RER" and "TAXI" 

y<-UTADIS(performanceTable, criteriaMinMax, criteriaNumberOfBreakPoints, 
           alternativesAssignments, categoriesRanks,0.1, 
           categoriesIDs=c("medium","bad"), 
           alternativesIDs=c("METRO1","METRO2","BUS"))

# working furthermore on only 2 criteria : "Comfort" and "Time"

z<-UTADIS(performanceTable, criteriaMinMax, criteriaNumberOfBreakPoints, 
            alternativesAssignments, categoriesRanks,0.1, 
            criteriaIDs=c("Comfort","Time"))

UTASTAR method to elicit value functions.

Description

Elicits value functions from a ranking of alternatives, according to the UTASTAR method.

Usage

UTASTAR(
  performanceTable,
  criteriaMinMax,
  criteriaNumberOfBreakPoints,
  epsilon,
  alternativesRanks = NULL,
  alternativesPreferences = NULL,
  alternativesIndifferences = NULL,
  criteriaLBs = NULL,
  criteriaUBs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  kPostOptimality = NULL
)

Arguments

Value

The function returns a list structured as follows :

References

Siskos, Y. and D. Yannacopoulos, UTASTAR: An ordinal regression method for building additive value functions, Investigacao Operacional , 5 (1), 39–53, 1985.

Examples

# the separation threshold

epsilon <-0.05

# the performance table

performanceTable <- rbind(
  		c(3,10,1),
			c(4,20,2),
			c(2,20,0),
			c(6,40,0),
			c(30,30,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# ranks of the alternatives

alternativesRanks <- c(1,2,2,3,4)

names(alternativesRanks) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# number of break points for each criterion

criteriaNumberOfBreakPoints <- c(3,4,4)

names(criteriaNumberOfBreakPoints) <- colnames(performanceTable)

x<-UTASTAR(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon,
        alternativesRanks = alternativesRanks)

# plot the value functions obtained

plotPiecewiseLinearValueFunctions(x$valueFunctions)

# apply the value functions on the original performance table

transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
  x$valueFunctions, 
  performanceTable)

# calculate the overall score of each alternative

weightedSum(transformedPerformanceTable,c(1,1,1))

# ----------------------------------------
# ranking some cars (from original article on UTA by Siskos and Lagreze, 1982)

# the separation threshold

epsilon <-0.01

# the performance table

performanceTable <- rbind(      
c(173, 11.4, 10.01, 10, 7.88, 49500),
c(176, 12.3, 10.48, 11, 7.96, 46700),
c(142, 8.2, 7.30, 5, 5.65, 32100),
c(148, 10.5, 9.61, 7, 6.15, 39150), 
c(178, 14.5, 11.05, 13, 8.06, 64700), 
c(180, 13.6, 10.40, 13, 8.47, 75700),
c(182, 12.7, 12.26, 11, 7.81, 68593), 
c(145, 14.3, 12.95, 11, 8.38, 55000),
c(161, 8.6, 8.42, 7, 5.11, 35200), 
c(117, 7.2, 6.75, 3, 5.81, 24800)
)

rownames(performanceTable) <- c(
  "Peugeot 505 GR",
  "Opel Record 2000 LS",
  "Citroen Visa Super E",
  "VW Golf 1300 GLS",
  "Citroen CX 2400 Pallas",
  "Mercedes 230",
  "BMW 520",
  "Volvo 244 DL",
  "Peugeot 104 ZS",
  "Citroen Dyane")

colnames(performanceTable) <- c(
  "MaximalSpeed",
  "ConsumptionTown",
  "Consumption120kmh",
  "HP",
  "Space",
  "Price")

# ranks of the alternatives

alternativesRanks <- c(1,2,3,4,5,6,7,8,9,10)

names(alternativesRanks) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("max","min","min","max","max","min")

names(criteriaMinMax) <- colnames(performanceTable)

# number of break points for each criterion

criteriaNumberOfBreakPoints <- c(5,4,4,5,4,5)

names(criteriaNumberOfBreakPoints) <- colnames(performanceTable)

# lower bounds of the criteria for the determination of value functions

criteriaLBs=c(110,7,6,3,5,20000)

names(criteriaLBs) <- colnames(performanceTable)

# upper bounds of the criteria for the determination of value functions

criteriaUBs=c(190,15,13,13,9,80000)

names(criteriaUBs) <- colnames(performanceTable)

x<-UTASTAR(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon, 
        alternativesRanks = alternativesRanks,
        criteriaLBs = criteriaLBs, criteriaUBs = criteriaUBs)
        

# plot the value functions obtained

plotPiecewiseLinearValueFunctions(x$valueFunctions)

# apply the value functions on the original performance table

transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
      x$valueFunctions, 
      performanceTable)

# calculate the overall score of each alternative

weights<-c(1,1,1,1,1,1)

names(weights)<-colnames(performanceTable)

weightedSum(transformedPerformanceTable,c(1,1,1,1,1,1))

# the same analysis with less extreme value functions
# from the post-optimality analysis

x<-UTASTAR(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon, 
        alternativesRanks = alternativesRanks,
        criteriaLBs = criteriaLBs, 
        criteriaUBs = criteriaUBs, 
        kPostOptimality = 0.01)
        
# plot the value functions obtained

plotPiecewiseLinearValueFunctions(x$averageValueFunctionsPO)

# apply the value functions on the original performance table

transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
      x$averageValueFunctionsPO, 
      performanceTable)

# calculate the overall score of each alternative

weights<-c(1,1,1,1,1,1)

names(weights)<-colnames(performanceTable)

weightedSum(transformedPerformanceTable,c(1,1,1,1,1,1))


# ----------------------------------------
# Let us consider only 2 criteria : Price and MaximalSpeed. What happens ? 

x<-UTASTAR(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon, 
        alternativesRanks = alternativesRanks,
        criteriaLBs = criteriaLBs, criteriaUBs = criteriaUBs,
        criteriaIDs = c("MaximalSpeed","Price"))
        

# plot the value functions obtained

plotPiecewiseLinearValueFunctions(x$valueFunctions, 
                                  criteriaIDs = c("MaximalSpeed","Price"))

# apply the value functions on the original performance table

transformedPerformanceTable <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(
  x$valueFunctions, 
  performanceTable, 
  criteriaIDs = c("MaximalSpeed","Price")
  )

# calculate the overall score of each alternative

weights<-c(1,1,1,1,1,1)

names(weights)<-colnames(performanceTable)

weightedSum(transformedPerformanceTable,
          weights, criteriaIDs = c("MaximalSpeed","Price"))


# ----------------------------------------
# An example without alternativesRanks, but with alternativesPreferences
# and alternativesIndifferences

alternativesPreferences <- rbind(c("Peugeot 505 GR","Opel Record 2000 LS"),
                                c("Opel Record 2000 LS","Citroen Visa Super E"))

alternativesIndifferences <- rbind(c("Peugeot 104 ZS","Citroen Dyane"))

x<-UTASTAR(performanceTable, criteriaMinMax, 
        criteriaNumberOfBreakPoints, epsilon = 0.1,
        alternativesPreferences = alternativesPreferences,
        alternativesIndifferences = alternativesIndifferences,
        criteriaLBs = criteriaLBs, criteriaUBs = criteriaUBs
        )

VIKOR method

Description

VIKOR is a multi-criteria decision analysis method originally developed by Serafim Opricovic in his 1979 Ph.D. Thesis, and later published in 1998.

Usage

VIKOR(
  performanceTable,
  criteriaWeights,
  criteriaMinMax,
  v = 0.5,
  positiveIdealSolutions = NULL,
  negativeIdealSolutions = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a vector containing the VIKOR score for each alternative.

References

Opricovic, S. (1998). Multicriteria optimization of civil engineering systems. Faculty of civil engineering, Belgrade, 2(1), 5-21.

Examples

alts <- c("Corsa","Clio","Fiesta")
crit <- c("price","economy", "aesthetics","bootCapacity")
performanceTable <- matrix(c(5490, 51.4, 8.5, 285,
                             6500, 70.6, 7.0, 288,
                             6489, 54.3, 7.5, 290), 
                             nrow=3, ncol=4, byrow=TRUE, 
                             dimnames=list(alts, crit))
criteriaWeights <- setNames(c(0.35,0.25,0.25,0.15), crit)
criteriaMinMax  <- setNames(c("min", "max", "max", "max"), crit)
positiveIdealSolutions <- setNames(c(4500, 80, 9, 300), crit)
negativeIdealSolutions <- setNames(c(7000, 52, 7, 150), crit)

# Overall
VIKOR(performanceTable, criteriaWeights, criteriaMinMax)
# Assuming different ideal and worst solutions
VIKOR(performanceTable, criteriaWeights, criteriaMinMax,
      v=0.5, positiveIdealSolutions, negativeIdealSolutions)
# Using a subset of alternatives and criteria
VIKOR(performanceTable, criteriaWeights, criteriaMinMax,
      v=0.5, positiveIdealSolutions, negativeIdealSolutions,
      alternativesIDs = c("Clio","Fiesta"),
      criteriaIDs = c("price","economy","aesthetics"))

Elicitation of a general additive value function.

Description

Elicits a general additive value function from a ranking of alternatives.

Usage

additiveValueFunctionElicitation(
  performanceTable,
  criteriaMinMax,
  epsilon,
  alternativesRanks = NULL,
  alternativesPreferences = NULL,
  alternativesIndifferences = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a list structured as follows :

References

Based on the UTA algorithm (E. Jacquet-Lagreze, J. Siskos, Assessing a set of additive utility functions for multicriteria decision-making, the UTA method, European Journal of Operational Research, Volume 10, Issue 2, 151–164, June 1982) except that the breakpoints of the value functions are the actual performances of the alternatives on the criteria.

Examples

# ----------------------------------------
# ranking some cars (from original article on UTA by Siskos and Lagreze, 1982)

# the separation threshold

epsilon <-0.01

# the performance table

performanceTable <- rbind(      
c(173, 11.4, 10.01, 10, 7.88, 49500),
c(176, 12.3, 10.48, 11, 7.96, 46700),
c(142, 8.2, 7.30, 5, 5.65, 32100),
c(148, 10.5, 9.61, 7, 6.15, 39150), 
c(178, 14.5, 11.05, 13, 8.06, 64700), 
c(180, 13.6, 10.40, 13, 8.47, 75700),
c(182, 12.7, 12.26, 11, 7.81, 68593), 
c(145, 14.3, 12.95, 11, 8.38, 55000),
c(161, 8.6, 8.42, 7, 5.11, 35200), 
c(117, 7.2, 6.75, 3, 5.81, 24800)
)

rownames(performanceTable) <- c(
  "Peugeot 505 GR",
  "Opel Record 2000 LS",
  "Citroen Visa Super E",
  "VW Golf 1300 GLS",
  "Citroen CX 2400 Pallas",
  "Mercedes 230",
  "BMW 520",
  "Volvo 244 DL",
  "Peugeot 104 ZS",
  "Citroen Dyane")

colnames(performanceTable) <- c(
  "MaximalSpeed",
  "ConsumptionTown",
  "Consumption120kmh",
  "HP",
  "Space",
  "Price")

# ranks of the alternatives

alternativesRanks <- c(1,2,3,4,5,6,7,8,9,10)

names(alternativesRanks) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("max","min","min","max","max","min")

names(criteriaMinMax) <- colnames(performanceTable)

x<-additiveValueFunctionElicitation(performanceTable,  
                                      criteriaMinMax, epsilon,
                                      alternativesRanks = alternativesRanks)

Applies value functions on a performance table.

Description

Transforms a performance table via given piecewise linear value functions.

Usage

applyPiecewiseLinearValueFunctionsOnPerformanceTable(
  valueFunctions,
  performanceTable,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a performance table which has been transformed through the given value functions.

Examples

# the value functions

v<-list(
  Price = array(c(30, 0, 16, 0, 2, 0.0875), 
    dim=c(2,3), dimnames = list(c("x", "y"), NULL)), 
  Time = array(c(40, 0, 30, 0, 20, 0.025, 10, 0.9), 
    dim = c(2, 4), dimnames = list(c("x", "y"), NULL)), 
  Comfort = array(c(0, 0, 1, 0, 2, 0.0125, 3, 0.0125), 
    dim = c(2, 4), dimnames = list(c("x", "y"), NULL)))

# the performance table

performanceTable <- rbind(
    	c(3,10,1),
			c(4,20,2),
			c(2,20,0),
			c(6,40,0),
			c(30,30,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# the transformed performance table

applyPiecewiseLinearValueFunctionsOnPerformanceTable(v,performanceTable)

Assign alternatives to categories according to thresholds.

Description

Assign alternatives to categories according to thresholds representing the lower bounds of the categories.

Usage

assignAlternativesToCategoriesByThresholds(
  alternativesScores,
  categoriesLowerBounds,
  alternativesIDs = NULL,
  categoriesIDs = NULL
)

Arguments

Value

The function returns a vector containing the assignments of the alternatives to the categories.

Examples

# the separation threshold

epsilon <-0.05

# the performance table

performanceTable <- rbind(
  c(3,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# ranks of the alternatives

alternativesAssignments <- c("good","medium","medium","bad","bad")

names(alternativesAssignments) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# number of break points for each criterion

criteriaNumberOfBreakPoints <- c(3,4,4)

names(criteriaNumberOfBreakPoints) <- colnames(performanceTable)

# ranks of the categories

categoriesRanks <- c(1,2,3)

names(categoriesRanks) <- c("good","medium","bad")

x<-UTADIS(performanceTable, criteriaMinMax, criteriaNumberOfBreakPoints, 
            alternativesAssignments, categoriesRanks,0.1)

npt <- applyPiecewiseLinearValueFunctionsOnPerformanceTable(x$valueFunctions, 
                                                             performanceTable)

scores <- weightedSum(npt, c(1,1,1))

# add a lower bound for the "bad" category

lbs <- c(x$categoriesLBs,0)

names(lbs) <- c(names(x$categoriesLBs),"bad")

assignments<-assignAlternativesToCategoriesByThresholds(scores,lbs)

Function to normalize (or rescale) the columns (or criteria) of a performance table.

Description

Standardizes the range of the criteria according to a few methods : percentage of max, scale between 0 and 1, scale to 0 mean and 1 standard deviation, scale to euclidian unit length.

Usage

normalizePerformanceTable(
  performanceTable,
  normalizationTypes = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Examples

library(MCDA)

performanceTable <- matrix(runif(5*9), ncol=5)

row.names(performanceTable) <- c("x1","x2","x3","x4","x5","x6","x7","x8","x9")

colnames(performanceTable) <- c("g1","g2","g3","g4", "g5")

normalizationTypes <- c("percentageOfMax","rescaling",
                        "standardization","scaleToUnitLength", "none")

names(normalizationTypes) <- c("g1","g2","g3","g4","g5")

normalizedPerformanceTable <- normalizePerformanceTable(performanceTable,
                                                        normalizationTypes)

Consistency Measures for Pairwise Comparison Matrices

Description

This function calculates four pairwise consistency checks: Consistency Ratio (CR) from Saaty (1980), Koczkodaj's Measure from Koczkodaj (1993) and Congruence / Dissonance Measures from Siraj et al. (2015).

Usage

pairwiseConsistencyMeasures(matrix)

Arguments

Value

The function returns a list of outputs for the four pairwise consistency checks

References

Thomas Saaty (1980). The Analytic Hierarchy Process: Planning, Priority Setting, ISBN 0-07-054371-2, McGraw-Hill.

W.W. Koczkodaj (1993). A new definition of consistency of pairwise comparisons. Mathematical and Computer Modelling. 18 (7).

Sajid Siraj, Ludmil Mikhailov & John A. Keane (2015). Contribution of individual judgments toward inconsistency in pairwise comparisons. European Journal of Operational Research. 242(2).

Examples

examplematrix <- t(matrix(c(1,0.25,4,1/6,4,1,4,0.25,0.25,0.25,1,0.2,6,4,5,1),nrow=4,ncol=4))
pairwiseConsistencyMeasures(examplematrix)

Function to plot a preorder of alternatives, based on some score or ranking.

Description

Plots a preorder of alternatives as a graph, representing the ranking of the alternatives, w.r.t. some scores or ranks. A decreasing order or increasing order can be specified, w.r.t. to these scores or ranks.

Usage

plotAlternativesValuesPreorder(
  alternativesValues,
  decreasing = TRUE,
  alternativesIDs = NULL,
  silent = FALSE
)

Arguments

Value

A character vector with the names of alternatives sorted (invisibly).

Examples

library(MCDA)

alternativesValues <- c(10,1,8,3,8,3,4,4,8,5)

names(alternativesValues) <- c("x10","x1","x9","x2","x8",
                                "x3","x7","x4","x6","x5")

plotAlternativesValuesPreorder(alternativesValues, 
                                decreasing=TRUE, 
                                alternativesIDs=c("x10","x3","x7",
                                                    "x4","x6","x5"))

Plot Multi-Attribute Range Evaluations (MARE)

Description

Plots the output of function MARE()

Usage

plotMARE(x)

Arguments

Examples

performanceTableMin <- t(matrix(c(78,87,79,19,8,68,74,8,90,89,74.5,9,20,81,30),
                                  nrow=3,ncol=5, byrow=TRUE)) 
performanceTable <- t(matrix(c(80,87,86,19,8,70,74,10,90,89,75,9,33,82,30),
                                nrow=3,ncol=5, byrow=TRUE))
performanceTableMax <- t(matrix(c(81,87,95,19,8,72,74,15,90,89,75.5,9,36,84,30),
                                   nrow=3,ncol=5, byrow=TRUE))  

row.names(performanceTable) <- c("Yield","Toxicity","Cost","Separation","Odour")
colnames(performanceTable) <- c("Route One","Route Two","Route Three")
row.names(performanceTableMin) <- row.names(performanceTable)
colnames(performanceTableMin) <- colnames(performanceTable)
row.names(performanceTableMax) <- row.names(performanceTable)
colnames(performanceTableMax) <- colnames(performanceTable)

weights <- c(0.339,0.077,0.434,0.127,0.023) 
names(weights) <- row.names(performanceTable)

criteriaMinMax <- c("max", "max", "max", "max", "max")
names(criteriaMinMax) <- row.names(performanceTable)

overall1 <- MARE(performanceTableMin, performanceTable, performanceTableMax, 
                           weights, criteriaMinMax)
plotMARE(overall1)

overall2 <- MARE(performanceTableMin,
                    performanceTable,
                    performanceTableMax, 
                    weights,
                    criteriaMinMax, 
                    alternativesIDs = c("Route Two","Route Three"),
                    criteriaIDs = c("Yield","Toxicity","Cost","Separation"))
plotMARE(overall2)

Plot the categories and assignments of an Electre TRI-like sorting problem (via separation profiles).

Description

The profiles shown are the separation profiles between the classes. They are stored as the lower profiles of the categories.

Usage

plotMRSortSortingProblem(
  performanceTable,
  categoriesLowerProfiles,
  categoriesRanks,
  assignments,
  criteriaMinMax,
  criteriaUBs,
  criteriaLBs,
  categoriesDictators = NULL,
  categoriesVetoes = NULL,
  majorityRule = NULL,
  criteriaWeights = NULL,
  majorityThreshold = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  legendRatio = 0.2
)

Arguments

Examples

# the performance table

performanceTable <- rbind(
  c(1,10,1),
  c(4,20,2),
  c(2,20,0),
  c(6,40,0),
  c(30,30,3))

rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI")

colnames(performanceTable) <- c("Price","Time","Comfort")

# lower profiles of the categories 
# (best category in the first position of the list)

categoriesLowerProfiles <- rbind(c(3, 11, 3),c(7, 25, 2),c(30,30,0))

colnames(categoriesLowerProfiles) <- colnames(performanceTable)

rownames(categoriesLowerProfiles)<-c("Good","Medium","Bad")

categoriesRanks <-c(1,2,3)

names(categoriesRanks) <- c("Good","Medium","Bad")

# criteria to minimize or maximize

criteriaMinMax <- c("min","min","max")

names(criteriaMinMax) <- colnames(performanceTable)

# lower bounds of the criteria for the determination of value functions

criteriaLBs=c(0,5,0)

names(criteriaLBs) <- colnames(performanceTable)

# upper bounds of the criteria for the determination of value functions

criteriaUBs=c(50,50,4)

names(criteriaUBs) <- colnames(performanceTable)

# weights

criteriaWeights <- c(1,3,2)

names(criteriaWeights) <- colnames(performanceTable)

assignments <- assignments<-MRSort(performanceTable, 
                                   categoriesLowerProfiles, 
                                   categoriesRanks,
                                   criteriaWeights, 
                                   criteriaMinMax, 3)

names(assignments) <- rownames(performanceTable)

plotMRSortSortingProblem(performanceTable, categoriesLowerProfiles, 
                         categoriesRanks, assignments, criteriaMinMax, 
                         criteriaUBs, criteriaLBs)

Function to plot piecewise linear value functions.

Description

Plots piecewise linear value function.

Usage

plotPiecewiseLinearValueFunctions(valueFunctions, criteriaIDs = NULL)

Arguments

Examples

v<-list(
  Price = array(c(30, 0, 16, 0, 2, 0.0875), 
    dim=c(2,3), dimnames = list(c("x", "y"), NULL)), 
  Time = array(c(40, 0, 30, 0, 20, 0.025, 10, 0.9), 
    dim = c(2, 4), dimnames = list(c("x", "y"), NULL)), 
  Comfort = array(c(0, 0, 1, 0, 2, 0.0125, 3, 0.0125), 
    dim = c(2, 4), dimnames = list(c("x", "y"), NULL)))

# plot the value functions

plotPiecewiseLinearValueFunctions(v)

Function to plot radar plots of alternatives of a performance table.

Description

Plots radar plots of alternatives contained in a performance table, either in one radar plot, or on multiple radar plots. For a given alternative, the plot shows how far above/below average (the thick black line) each of the criteria performances values are (average taken w.r.t. to the filtered performance table).

Usage

plotRadarPerformanceTable(
  performanceTable,
  criteriaMinMax = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  overlay = FALSE,
  bw = FALSE,
  lwd = 2
)

Arguments

Examples

library(MCDA)

performanceTable <- matrix(runif(6*9), ncol=6)

row.names(performanceTable) <- c("x1","x2","x3","x4","x5","x6","x7","x8","x9")

colnames(performanceTable) <- c("g1","g2","g3","g4","g5","g6")

criteriaMinMax <- c("min","max","min","max","min","max")

names(criteriaMinMax) <- c("g1","g2","g3","g4","g5","g6")

# plotRadarPerformanceTable(performanceTable, criteriaMinMax, overlay=TRUE)

plotRadarPerformanceTable(performanceTable, criteriaMinMax, 
                          alternativesIDs = c("x1","x2","x3","x4"), 
                          criteriaIDs = c("g1","g3","g4","g5","g6"), 
                          overlay=FALSE, bw=FALSE)

# plotRadarPerformanceTable(performanceTable, criteriaMinMax, 
#                          alternativesIDs = c("x1","x2"), 
#                          criteriaIDs = c("g1","g3","g4","g5","g6"),
#                          overlay=FALSE)

Plot SURE kernel density plots.

Description

Plots the output of function SURE()

Usage

plotSURE(SURE, greyScale = FALSE, separate = FALSE)

Arguments

Examples

performanceTableMin <- t(matrix(c(78,87,79,19,8,68,74,8,90,89,74.5,9,20,81,30),
                  nrow=3,ncol=5, byrow=TRUE)) 
performanceTable <- t(matrix(c(80,87,86,19,8,70,74,10,90,89,75,9,33,82,30),
                              nrow=3,ncol=5, byrow=TRUE))
performanceTableMax <- t(matrix(c(81,87,95,19,8,72,74,15,90,89,75.5,9,36,84,30),
                                 nrow=3,ncol=5, byrow=TRUE))  

row.names(performanceTable) <- c("Yield","Toxicity","Cost","Separation","Odour")
colnames(performanceTable) <- c("Route One","Route Two","Route Three")
row.names(performanceTableMin) <- row.names(performanceTable)
colnames(performanceTableMin) <- colnames(performanceTable)
row.names(performanceTableMax) <- row.names(performanceTable)
colnames(performanceTableMax) <- colnames(performanceTable)

criteriaWeights <- c(0.339,0.077,0.434,0.127,0.023) 
names(criteriaWeights) <- row.names(performanceTable)

criteriaMinMax <- c("max", "max", "max", "max", "max")
names(criteriaMinMax) <- row.names(performanceTable)

test1 <- SURE(performanceTableMin, 
                 performanceTable, 
                 performanceTableMax, 
                 criteriaWeights, 
                 criteriaMinMax,
                 NoOfSimulations = 101)

summary(test1)
plotSURE(test1)
plotSURE(test1, greyScale = TRUE, separate = TRUE)

Weighted sum of evaluations of alternatives.

Description

Computes the weighted sum of the evaluations of alternatives, stored in a performance table, with respect to a vector of criteria weights.

Usage

weightedSum(
  performanceTable,
  criteriaWeights,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

Value

The function returns a vector containing the weighted sum of the alternatives with respect to the criteria weights.

Examples

alts <- paste0("alt", 1:4)
crit <- paste0("x", 1:3)
performanceTable <- matrix(runif(length(alts)*length(crit)), 
                           nrow=length(alts), ncol=length(crit), 
                           dimnames=list(alts, crit))
weights <- setNames(c(1,2,3), crit)
# Overall
weightedSum(performanceTable, weights)
# Subset of alteratives and criteria
weightedSum(performanceTable, weights, 
            alternativesIDs=c("alt2","alt3"), criteriaIDs=c("x2","x3"))