The Research On Some Theory For FAHP Based On Fuzzy Reciprocal Judgment Matrix

Analytic hierarchy process (AHP) is a practical and effective decision-making method. It has been widely applied to society, economy, management and engineering systems. With the development of AHP theory and the actual requirements of applications, the fuzzy idea and fuzzy methods are introduced to AHP, so the fuzzy analytic hierarchy process (FAHP) has been shaping. And this is consistent with the fuzziness of men's thought. Therefore, the research on the FAHP problems based on fuzzy reciprocal judgment matrix has attracted more and more attention.This paper studies some theory for FAHP based on fuzzy reciprocal judgment matrix. The main research works are as follows:In Chapter I, the conceptions of fuzzy reciprocal judgment matrix and fuzzy consistent matrix are proposed. Then, the recent research on theory for FAHP based on fuzzy reciprocal judgment matrix is briefly reviewed. The main research problems in this paper are also involved.In Chapter 2, from more aspects, the additive consistent matrix iscompared with the multiplicative consistent matrix, the fuzzy reciprocal judgment matrix is also compared with the positive reciprocal judgment matrix.In Chapter 3, two new ranking methods of fuzzy reciprocal judgment matrix is presented. The existing ranking methods of fuzzy reciprocal judgment matrix based on fuzzy consistent matrix are reviewed and compared.Chapter 4 presents three new consistency checking methods for the fuzzy reciprocal judgment matrix.Chapter 5 presents four new methods for improving the consistency of the fuzzy reciprocal judgment matrix.In Chapter 6, the conception of rank preservation for the fuzzy reciprocal judgment matrix is firstly proposed. Then, under a sing criterion, the conditions of rank preservation for adding a new element in the fuzzy reciprocal judgment matrix are discussed, and the conditions of rank preservation for adding a group of elements are also given.In the end, this paper is summarized, and the suggestions about the studied contents of FAHP based on fuzzy reciprocal judgment matrix in the future are proposed.