General transitivity conditions for fuzzy reciprocal preference matrices

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). © 2002 Elsevier Science B.V. All rights reserved.