SRMPInferenceFixedProfilesNumber {MCDA}

Exact inference of an SRMP model given the number of reference profiles

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method outputs an SRMP model that is as consistent as possible with the provided pairwise comparisons (i.e. the model - and the lexicographic order of the reference profiles - that maximizes the number of fulfilled pairwise comparisons). The number of reference profiles is fixed and needs to be provided.

Usage

SRMPInferenceFixedProfilesNumber(
  performanceTable,
  criteriaMinMax,
  profilesNumber,
  preferencePairs,
  indifferencePairs = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL,
  timeLimit = NULL
)

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.

profilesNumber

A strictly pozitive numerical value which gives the number of reference profiles in the sought SRMP model.

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. By default NULL (which corresponds to no time limit).

Value

The function returns a list containing:

criteriaWeights

The inferred criteria weights.

referenceProfiles

The inferred reference profiles.

lexicographicOrder

The inferred lexicographic order of the profiles.

fitness

The percentage (0 to 1) of fulfilled pair-wise relations.

solverStatus

The solver status as given by glpk.

humanReadableStatus

A description of the solver status.

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.

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))

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)

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)

result<-SRMPInferenceFixedProfilesNumber(performanceTable, criteriaMinMax, 3, preferencePairs,
                                         indifferencePairs, alternativesIDs = c("a1","a3",
                                         "a7","a9","a13","a14","a15","a16","a17","a18"))