General transitivity conditions for fuzzy reciprocal preference matrices

A reciprocal fuzzy matrix (relation) is a non-negative matrix Q = {q(ij)} such that q(ij) + q(ji) = 1 for all i, j is an element of {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). (C) 2002 Elsevier Science B.V. All rights reserved.