Similarity–divergence intuitionistic fuzzy decision using particle swarm optimization

Abstract

Many existing intuitionistic fuzzy (IF) decision methods focus on a reasonable ranking for alternatives under unknown weight information. Traditionally, the weight information is usually determined from a multiobjective optimization model based on real-valued measures such as IF distance or similarity measures, which may lose divergence information. In this paper, we propose one new type of optimization model for determining the weights based on a fuzzy measure called the similarity–divergence measure (S–D measure). First, we develop similarity and divergence measures of IF sets respectively, and a 2-tuple consisting of similarity and divergence is defined as a S–D measure. This measure is further proven to be an IF similarity degree and has practical semantics of similarity and divergence features in human’s cognition. Second, we utilize such measure to calculate fuzzy similarities of each alternative and construct a nonlinear optimization model to determine the weights. Third, we design an algorithm for solving the model with the aid of particle swarm optimization and thus develop an IF decision method. Finally, two examples are given to demonstrate our method and then it is compared with existing methods to explain its effectiveness and superiority.