A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. (February 2019) - Jiang, Qian; Jin, Xin; Lee, Shin-Jye; Yao, Shaowen
Highlights: We proposed a new similarity/distance measure between intuitionistic fuzzy sets. The given IFSs are transformed into the corresponding isosceles triangles. The transformed isosceles triangles of IFS are placed in different axes. This measure is defined by the intersections of the transformed isosceles triangles. This measure is applied to pattern recognition problems to verify its rationality. Abstract: Intuitionistic fuzzy set (IFS) is a representative model of fuzzy theory, and it is widely used to deal with fuzzy and uncertain problems in many practical applications. In IFS theory, the calculation of the distance and similarity between IFSs are significant techniques that are effective measurement methods for distinguishing the similarity degree between IFSs, and the two measures can be used in pattern recognition, decision-making and so on. In this paper, a novel similarity/distance measure between IFSs is proposed according to the intersections of the transformed isosceles triangles from IFSs, and the isosceles triangles are placed in a square area; furthermore, the properties of the proposed measure are also analyzed to prove whether the measure satisfies the definition of the similarity/distance measure for IFSs or not. The numerical experiments are implemented to test the validity of the proposed measure; in addition, several pattern recognition and clustering problems are also employed to further demonstrate its effectiveness. The experimental results show that the proposed measure is an accurate and superior measure that can avoid the shortcomings of most existing measures. Finally, the directions for future research of this work are also represented in the conclusion.