# Identification of profiles, weights, majority threshold and veto thresholds for MRSort using a genetic algorithm. 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. ```r 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). ## Returns 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). ## Examples ```r 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")) ``` ## 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

MRSortInferenceApprox function