Different Types of Entropy Measures for Type-2 Fuzzy Sets

Abstract

In this work, we consider De Luca and Termini’s notion of non-probabilistic entropy, and we extend some entropy-like measures of the degree of fuzziness to type-2 fuzzy sets. With this aim, we first study different entropy measures proposed in the frameworks of fuzzy, intuitionistic, and interval-valued fuzzy sets. Then, we propose three possible novel axiomatizations for entropy in type-2 fuzzy sets. The proposed types of entropy measures evaluate how much a type-2 fuzzy set is non-crisp, non-fuzzy, and non-interval-valued fuzzy. This can also be interpreted as how far a type-2 fuzzy set is from a crisp, fuzzy, or interval-valued fuzzy set. The present contribution is also novel, since we considered the interpretation of type-2 fuzzy sets that is closest to Zadeh’s original conception.

Keywords

• uncertainty
• fuzziness
• non-probabilistic fuzzy entropy
• type-2 fuzzy set