General transitivity conditions for fuzzy reciprocal preference matrices

Authors:
Zbigniew Świtalski
Affiliations:
Department of Operations Research, University of Economics, Al. Niepodleglosci 10, 60-967 Poznan, Poland
Venue:
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Year:
2003

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Abstract

A reciprocal fuzzy matrix (relation) is a non-negative matrix Q = {qij} such that qij + qji = 1 for all i,j ∈ {1,2,..., n}. We define general transitivity conditions (named FG-transitivities) for fuzzy reciprocal preference relations and show that they generalize some well-known transitivities. We also study relationships of these conditions with two models of rational preferences (the so-called "utility" model and the "multidimensional" model).