An effective similarity/distance measure between intuitionistic fuzzy sets based on the areas of transformed isosceles right triangle and its applications

Abstract

Since the intuitionistic fuzzy set (IFS) was proposed by Atanassov, many explorations of this particular fuzzy set were conducted. One of the most important areas is the study of similarity and distance between IFSs, which can measure the degree of deviation of objects with uncertain and vague features, and this technique has great value and potential to solve the fuzzy and uncertain problems in the real world. Based on our previous similarity/distance measure model D _JJ  (α, β), a new method is proposed for improving the performance of similarity/distance measure model of IFSs, which is derived from the sum of the areas of two triangles constructed by the transformed isosceles triangles of two IFSs. A great effort is made to prove the validity of the proposed method by mathematical derivation. In order to further demonstrate the performance of the proposed method, we apply this method to solve some practical problems such as pattern recognition, medical diagnosis, and cluster analysis. In addition, we also list a series of the existing methods which are used to compare with the proposed method to prove the effectiveness and superiority. The experimental results confirm that the performance of the proposed method exceeds most of the existing methods.