SRMPInference: Exact inference of an SRMP model given a maximum number of...

In MCDA: Support for the Multicriteria Decision Aiding Process

Exact inference of an SRMP model given a maximum 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 - the number of profiles and their lexicographic order - that maximizes the number of fulfilled pairwise comparisons). The method will search for a model with the minimum possible number of profiles up to a given maximum value.

Usage

SRMPInference(
  performanceTable,
  criteriaMinMax,
  maxProfilesNumber,
  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.
maxProfilesNumber	A strictly pozitive numerical value which gives the highest number of reference profiles the sought SRMP model should have.
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).

Value

The function returns a list containing:

criteriaWeights	The inferred criteria weights.
referenceProfilesNumber	The inferred reference profiles number.
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<-SRMPInference(performanceTable, criteriaMinMax, 3, preferencePairs, indifferencePairs,
                      alternativesIDs = c("a1","a3","a7","a9","a13","a14","a15","a16","a17",
                      "a18"))

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