# Approximative inference of an SRMP model given the lexicographic order of the profiles 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. ```r SRMPInferenceApproxFixedLexicographicOrder( performanceTable, criteriaMinMax, lexicographicOrder, preferencePairs, indifferencePairs = NULL, 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). - `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. - `lexicographicOrder`: A vector containing the indexes of the reference profiles in a given order. The number of reference profiles to be used is derrived implicitly from the size of this vector. The elements of this vector need to be a permutation of the indices from 1 to its size. - `preferencePairs`: A two column matrix containing on each row a pair of alternative names where the first alternative is considered to be strictly preferred to the second. - `indifferencePairs`: A two column matrix containing on each row a pair of alternative names the two alternatives are considered to indifferent with respect to each other. - `alternativesIDs`: Vector containing IDs of alternatives, according to which the datashould 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: - **criteriaWeights**: The inferred criteria weights. - **referenceProfiles**: The inferred reference profiles. - **lexicographicOrder**: The lexicographic order of the reference profiles, in this case the one that was originally given as input. - **fitness**: The percentage of fulfilled pair-wise relations. ## 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)) 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")) ``` ## 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.

SRMPInferenceApproxFixedLexicographicOrder function