Strong transitivity, rationality and weak monotonicity in fuzzy pairwise comparisons

Strong transitivity and weak monotonicity are two important axioms in the theory of value and utility measurement. In this paper we define strong transitivity and weak monotonicity for fuzzy pairwise comparisons matrices. Using the requirements of strong transitivity, we develop a metric for measuring the degree of strong transitivity in fuzzy pairwise comparisons. We further demonstrate that a matrix which satisfies the metric of strong transitivity will satisfy the weak monotonicity axiom as well. (C) 1998 Elsevier Science B.V.