Similarity measure between generalized intuitionistic fuzzy sets with three kinds of negation

Abstract

 The similarity measure of intuitionistic fuzzy sets is a primary method for dealing with uncertainty and fuzzy problems and is commonly used in fuzzy decision-making and pattern recognition. The current mainstream similarity measure is based on the classical fuzzy set with only one negation, which often violates the intuitionistic problem in applications because the actual semantics of multiple negations are not considered. To solve the inconsistency and irrationality problems in the classical similarity methods, we introduce three negations (contradiction negation, opposition negation, and mediation negation) in the intuitionistic fuzzy set to obtain the generalized intuitionistic fuzzy set and prove its related property theorem. On this basis, our similarity measure adopts a mediational negation to represent non-membership, which fully utilizes the multiple negation information of non-membership and hesitancy and avoids the loss of fuzzy information. We verify the method’s rationality, validity, and originality through pattern recognition experiments and numerical examples, which improves the performance of intuitionistic fuzzy set similarity in practical applications and provides a new approach for future research on intuitionistic fuzzy inference.