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This research has been partially supported by the Government of Spain (grants PID2021-122905NB-C22 and PID2020-112502RB-C41), Comunidad de Madrid (Convenio Plurianual con la Universidad Politecnica de Madrid en la linea de actuacion Programa de Excelencia para el Profesorado Universitario).

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Magdalena, Luis; Torres-Blanc, Carmen; Cubillo, Susana; Martinez-Mateo, Jesus;

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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.

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