Objective weights with intuitionistic fuzzy entropy measures and computational experiment analysis

Abstract

It is important to properly assess the weights of attributes when solving multi-attribute decision problems because variations in the weights often influence the rankings of the alternatives. In this paper, we propose an alternative objective weighting method to generate objective weights based on intuitionistic fuzzy (IF) entropy measures, which depend on the nature of a decision matrix in an intuitionistic fuzzy environment. Instead of the traditional fuzzy entropy measure, which is characterized by using the discriminating power to calculate the attribute weights, the proposed approach adopts the IF entropy measure, which emphasizes the credibility of the data. The IF entropy measure applied here is derived from a geometric interpretation of intuitionistic fuzzy sets and incorporates the concept of a ratio of distance measures. We implement four distance measures in the proposed approach and compare them in a computational experiment. The experimental results indicate that different IF entropy measures used in weighting methods can generate distinct objective attribute weights. In particular, when the number of attributes increases, the discrepancy between the IF entropy measures increases.