A Vector Valued Similarity Measure Based on the Choquet Integral for Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

Abstract

The concept of Choquet integral that a special ordered weighted averaging operator (OWA) is an aggregation function and it generalizes the concepts of arithmetic and the weighted mean. This concept allows us to model interaction between criteria with the help of a fuzzy measure. Our aim is to combine fuzzy set theory and fuzzy measure theory by using the concept of Choquet integral. In this study, we propose a vector valued similarity measure for intuitionistic fuzzy sets (IFSs) based on the Choquet integral. This vector valued similarity measure consists of a pair of a similarity measure which is obtained from a distance measure for IFSs and an uncertainty measure. In this context, we provide a more effective tool by introducing the interaction between criteria with the help of fuzzy measure. Finally, we support the efficiency of our work with explanatory numerical examples.