Type-2 fuzzy entropy sets

The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with type-2 fuzzy sets. We denote this concept type-2 fuzzy entropy set. However, the construction of the notion of entropy measure on an infinite set, such us [0,1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a fuzzy set on the universe [0,1]. Furthermore, whenever the membership function of the considered fuzzy set in the universe [0,1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca and Termini. Finally, we present an illustrative example, where we use type-2 fuzzy entropy sets instead of fuzzy entropies in a classical fuzzy algorithm.