The Research On Several Problems Of Measuring The Consistency Of Reciprocal Comparison Matrices

Abstract:An issue how to measure the consistency of reciprocal comparison matrices and modify the inconsistency is hot and difficult in the research field of decision sciences, which has found an important research background in economy, management science, military application and other fields. Many experts in the world have made a deep investigation on this issue, and there have been a lot of relevant contributions. In this dissertation, a new method for description of consistency is proposed on the basis of the existent results. The main contributions are summarized as follows:1. This paper is devoted to present a new consistency index and some theorems for judging the consistency on the basis of analyzing the perfect consistent properties of three-order crisp reciprocal comparison matrices and the definition of three-order transitivity matrices. With new measure of inconsistency, a modification algorithm is designed for the inconsistent crisp reciprocal comparison matrices. This algorithm not only ensures the interaction with the decision makers, but also is convergent. Examples show that the new method is effective.2. In this paper, a mathematical model of convex combination is employed to transform an interval reciprocal comparison matrix into three crisp reciprocal comparison matrices. Feasibility of such method is investigated. By definition of consistency for the interval reciprocal comparison matrices, the measure of consistency is converted into testing the consistency of crisp reciprocal comparison matrices. A new method is proposed to solve the interval weights and a new algorithm is designed for modifying the inconsistent one’s. Examples demonstrate the advantages of the proposed methods.3. In this paper, on the basis of prefect consistency of incomplete reciprocal comparison matrices, multi-objective programming model and goal programming model are designed to amend the missing values for this type of incomplete reciprocal comparison matrices by solving the two models. Thus, the judgment of consistency for such matrix is converted into measuring the consistency of the crisp reciprocal comparison matrices. Examples show that our model is effective.