1. Different Types of Entropy Measures for Type-2 Fuzzy Sets
- Author
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Luis Magdalena, Carmen Torres-Blanc, Susana Cubillo, and Jesus Martinez-Mateo
- Subjects
uncertainty ,fuzziness ,non-probabilistic fuzzy entropy ,type-2 fuzzy set ,Mathematics ,QA1-939 - 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.
- Published
- 2024
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