MRSortInferenceApprox: Identification of profiles, weights, majority threshold and...

In MCDA: Support for the Multicriteria Decision Aiding Process

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"))

MCDA documentation built on Nov. 24, 2023, 5:10 p.m.