CUT SETS, DISTANCE, AND SIMILARITY MEASURES ON TYPE-2 INTUITIONISTIC FUZZY SET

Abstract

Intuitionistic Fuzzy Sets are substantial extensions of fuzzy sets which plays a key factor in describing and providing ease of solving higher complexities in engineering and science. However, certain ambiguous situations cannot be addressed by using fuzzy sets and intuitionistic fuzzy sets. The extension of fuzzy set, namely, Type-2 Fuzzy Sets and Interval Type-2 Fuzzy Sets paved the way for implementing methods and techniques for unanswered problems. In this research, an attempt has been made to represent Type-2 Intuitionistic Fuzzy Set in a refined manner. The concept of cut sets has been modified to suit the requirement of a type-2 intuitionistic fuzzy set and distance formulae namely Euclidean, Normalized Euclidean, Chebyshev, Normalized Chebyshev, Manhattan, Normalized Manhattan, Minkowski, Canberra and Sorensen distances have been redefined for a Type-2 Intuitionistic Fuzzy Set (T2IFS). Also, basic operators and a cosine similarity measure have been described for a T2IFS.