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Type-2 Fuzzy Entropy-Sets

De Miguel, L and Santos, H and Sesma-Sara, M and Bedregal, B and Jurio, A and Bustince, H and Hagras, H (2017) 'Type-2 Fuzzy Entropy-Sets.' IEEE Transactions on Fuzzy Systems. ISSN 1063-6706

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Abstract

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 y Termini. Finally, we present an illustrative example where we use Type-2 Fuzzy Entropy-Sets instead of fuzzy entropies in a classical fuzzy algorithm.

Item Type: Article
Uncontrolled Keywords: Entropy measure, Type-2 Fuzzy Sets, Quasi-entropy measure
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Hani Hagras
Date Deposited: 22 Dec 2016 15:13
Last Modified: 11 Jul 2018 16:15
URI: http://repository.essex.ac.uk/id/eprint/18638

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