Multi-Attribute Decision Making Based On Consistency Of Fuzzy Complementary Judgement Matrix

The purpose of this paper is to study multi-attribute decision making on the basis of consistency of fuzzy complementary judgment matrix. A theorem on sufficiency and necessity of fuzzy positive matrix is proposed after much analysis. Based on the thought of minimun deviationan, an optimization model is constructed first, and then a formula with parameter is taken advantage to approximate the corresponding element in the fuzzy complementary matrix and results in obtaining a fuzzy positive matrix. Meanwhile, the ordering vector of the fuzzy positive matrix is calculated. Otherwise, by using a simple formula, the new method in the paper can be applied in the situation where positive reciprocal matrices are given. At the end, for the ranked fuzzy numbers, a cuts of the fuzzy numbers are used and the possibility matrix of these α cuts is constructed. Based on the ordering vector of the possibility matrix, the problem of ranking fuzzy numbers is transformed into the one of solving ranking vector of possibility matrix which is actually a fuzzy complementary matrix. After analyzing, this paper proposes a new method to determine the ordering vector of fuzzy complementary matrix, and the new method can be used by a formula when decision makers give positive reciprocal matrices. And the problem of ranking fuzzy numbers is studied when membership functions are not given, so do the discrimination of ranking vector and rank reservation. Through the studying, some conclusions are given: New ranking method is different from the traditional ones. The traditional ones just produced only one rank vector but this new one has a family of ordering vectors. Additionally, it can change the discrimination of ranked objects by altering the value of parameter in the formula appropriatly.