MRSortInferenceApprox {MCDA}

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

performanceTable

Matrix or data frame 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).

assignments

Vector containing the assignments (IDs of the categories) of the alternatives to the categories. The elements are named according to the alternatives.

categoriesRanks

Vector containing the ranks of the categories. The elements are named according to the IDs of the categories.

criteriaMinMax

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

veto

Boolean parameter indicating whether veto profiles are to be used or not.

alternativesIDs

Vector containing IDs of alternatives, according to which the data should be filtered.

criteriaIDs

Vector containing IDs of criteria, according to which the data should be filtered.

timeLimit

Allows to fix a time limit of the execution, in seconds (default 60).

populationSize

Allows to change the size of the population used by the genetic algorithm (default 20).

mutationProb

Allows to change the mutation probability used by the genetic algorithm (default 0.1).

Value

The function returns a list containing:

majorityThreshold

The inferred majority threshold (single numeric value).

criteriaWeights

The inferred criteria weights (a vector named with the criteria IDs).

profilesPerformances

The inferred category limits (a matrix with the column names given by the criteria IDs and the rownames given by the upper categories each profile delimits).

vetoPerformances

The inferred vetoes (a matrix with the column names given by the criteria IDs and the rownames given by the categories to which each profile applies).

fitness

The classification accuracy of the inferred model (from 0 to 1).

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"))