A New Judging and Revising Method for Ordinal Consistency of Fuzzy Judgment Matrix

Abstract

In uncertainty decision making, experts can use interval-fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, linguistic 2-tuple or linguistic indices to express their preferences. Using kernel function, the fuzzy numbers can be converted into fuzzy number range from 0 to 1. Thus, different fuzzy judgment matrix can be expressed in a unified style. A judging method for ordinal consistency of fuzzy judgment matrix was proposed according to the transitivity of binary relation. And two concepts of non-transitive route number(NTRN) and non-transitive route contribution number(NTCN) were put forward. Through the non-transitive route number and non-transitive route contribution number guidance, a revising method for fuzzy judgment matrix without ordinal consistency was put forward, in which the irrational element can be identified. The revising method can help the decision-maker revise his/her judgment matrix effectively. Finally, the non-financial performance evaluation attributes were selected and experts were asked to give the judgment matrix, fuzzy matrix without ordinal consistency was used to demonstrate the idea of the new judging and revising method for ordinal consistency of the fuzzy judgment matrix.