Information Measures in the Intuitionistic Fuzzy Framework and Their Relationships

This contribution first addresses axiomatic definitions of some important information measures of Atanassov's intuitionistic fuzzy sets (AIFSs), such as, distance measure, similarity measure, entropy measure, and recently developed knowledge measure. After that, we study the relationship between similarity measures and knowledge measures, and that between distance measures and knowledge measures for AIFSs. In particular, we investigate the transformations of similarity measures into knowledge measures for AIFSs and vice versa. These transformations can induce more formulae to define the distance measures, the similarity measures, and the knowledge measures for AIFSs. In addition, to support these processes, suitable examples are provided for each of the introduced transformations. The contribution ends by introducing numerical examples with a discussion of results by using several types of knowledge measures and similarity measures.