A novel similarity degree of intuitionistic fuzzy sets induced by triangular norm and its application in pattern recognition

Measuring the similarity between images is an essential problem in various image processing and pattern recognition applications. In pattern recognition problems, it is indispensable to give formulas for calculating similarity between different patterns. But it is very difficult to find a certain measure that can be successfully applied to all kinds of pattern recognition problems. Intuitionistic fuzzy sets have been successfully applied to various areas such as pattern recognition and medical diagnostics. In intuitionistic fuzzy sets theory, the calculation of the similarity between intuitionistic fuzzy sets is a significant technique for distinguishing the similarity degree between intuitionistic fuzzy sets. The existing similarity measures almost are obtained in the sense of distance. In this paper, we present a novel way to obtain the similarity measure between intuitionistic fuzzy sets from a new perspective. Our main purpose is to show that according to the membership and non-membership functions of intuitionistic fuzzy sets, a triangular norm can induce an inclusion degree. Using this triangular norm and the induced inclusion degree, a similarity measure of intuitionistic fuzzy sets can be obtained. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy sets. As the applications of similarity degree proposed in this paper, we first present an intuitionistic fuzzy clustering algorithm based on similarity degree. Then, the similarity degree proposed in this paper is applied to pattern recognition. At the same time, the numerical examples are employed to illustrate the effectiveness of proposed method.