Estimating Interval Priority Weights Based on Minimum Ranges Associated with Fuzzy Preference Relations

Abstract

The fuzzy preference relation evaluates alternatives by a pairwise comparison matrix similar to the AHP. Unlike the AHP, the components of a pairwise comparison matrix are nonnegative and satisfy the condition that the sum of the symmetric components is one. There are several interpretations of the values in [0, 1] of the components of a fuzzy preference relation. In this paper, we concentrate on the multiplicative case. In the multiplicative case, the (i, j)-component of the fuzzy preference relation expressed by a pairwise comparison matrix shows the ratio of the i-th priority weight to the sum of the i-th and j-th priority weights. Under this interpretation, the priority weights of all items are estimated as intervals from a given fuzzy preference relation. As they are proposed in the interval AHP, the estimation methods based on minimum ranges, i.e., the maximizing minimum range method and the averaging minimum range method, are proposed and examined their usefulness by numerical experiments investing the accuracies in the interval priority weight estimation as well as those in the ranking alternatives.