Research on Similarity Values Relevant for Fuzzy Matrix Consistency Check

Abstract

There is a problem of inherent inconsistency when forming pairwise comparison matrices in both classical and fuzzy Analytic Hierarchy Process. The smallest decision making element of fuzzy Analytic Hierarchy Process is square, positive, fuzzy reciprocal matrix 3x3, and this paper focus to the research on fuzzy numbers' similarities regarding the consistency check of fuzzy matrix 3x3. The research is performed using Java application created specifically for this purpose. The application, for the selected fuzzy scale, forms all 3x3 matrices, for each matrix calculates all similarities values relevant for consistency check, average similarity and determines the minimal similarity value. The application calculates CR (consistency ratio) values for corresponding classical matrices. Research results are presented and future research suggested.