SRMPInferenceNoInconsistFixedLexicographicOrder: Exact inference of an SRMP model given the lexicographic...

In MCDA: Support for the Multicriteria Decision Aiding Process

Exact inference of an SRMP model given the lexicographic order of the profiles - no inconsistencies

Description

Exact inference approach from pairwise comparisons of alternatives for the SRMP ranking model. This method only outputs a result when an SRMP model consistent with the provided pairwise comparisons exists. The number of reference profiles and their lexicographic order is fixed. If such a model exists, this method is significantly faster than the one which handles inconsistencies.

Usage

SRMPInferenceNoInconsistFixedLexicographicOrder(
  performanceTable,
  criteriaMinMax,
  lexicographicOrder,
  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.
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. 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.
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

# the performance table

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(2,1,3)

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)

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<-SRMPInferenceNoInconsistFixedLexicographicOrder(performanceTable, criteriaMinMax,
                                                        lexicographicOrder, preferencePairs,
                                                        indifferencePairs, alternativesIDs =
                                                        c("a1","a2","a3","a4","a5","a6","a7",
                                                        "a8","a10","a11","a12","a14","a16",
                                                        "a17","a18","a19","a20","a21","a23",
                                                        "a24"))

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