MRSortInterval {MCDA}

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

performanceTable

Two-dimmensionnal list containing the performance table. Each row corresponds to an alternative, and each column to a criterion. Rows (resp. columns) must be named according to the IDs of the alternatives (resp. criteria). This list may contain imprecise performances of alternatives on the criteria, represented by interval evaluations, as well as missing performances.

categoriesLowerProfiles

Matrix containing, in each row, the lower profiles of the categories. The columns are named according to the criteria, and the rows are named according to the categories except of the last one.

categoriesRanks

A vector containing the ranks of the categories (1 for the best, with higher values for increasingly less preferred categories). The vector needs to be named with the categories names, whereas the ranks need to be a range of values from 1 to the number of categories.

criteriaWeights

Vector containing the weights of the criteria. The elements are named according to the IDs of the criteria.

criteriaMinMax

Vector containing the preference direction on each of the criteria. "min" (resp. "max") indicates that the criterion has to be minimized (maximized).

majorityThresholdPes

The cut threshold for the pessimistic concordance relation.

majorityThresholdOpt

The cut threshold for the optimistic concordance relation.

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)