Entropy and similarity measure of Atanassov's intuitionistic fuzzy sets and their application to pattern recognition based on fuzzy measures

In this study, we first examine entropy and similarity measure of Atanassov's intuitionistic fuzzy sets, and define a new entropy. Meanwhile, a construction approach to get the similarity measure of Atanassov's intuitionistic fuzzy sets is introduced, which is based on entropy. Since the independence of elements in a set is usually violated, it is not suitable to aggregate the values for patterns by additive measures. Based on the given entropy and similarity measure, we study their application to Atanassov's intuitionistic fuzzy pattern recognition problems under fuzzy measures, where the interactions between features are considered. To overall reflect the interactive characteristics between them, we define three Shapley-weighted similarity measures. Furthermore, if the information about the weights of features is incompletely known, models for the optimal fuzzy measure on feature set are established. Moreover, an approach to pattern recognition under Atanassov's intuitionistic fuzzy environment is developed.