The entropy change of fuzzy numbers with arithmetic operations
type: Item
instance of: scholarly article
title: The entropy change of fuzzy numbers with arithmetic operations
zbMATH Open document ID: 0980.94043
DOI: 10.1016/S0165-0114(97)00406-5
author: Wen-June Wang
author: Chih-Hui Chiu
published in: Fuzzy Sets and Systems
publication date: 2002-03-06T00:00:00Z
review text: The paper discusses some properties of the non-probabilistic entropy of fuzzy quantities as introduced by \textit{A. De Luca} and \textit{S. Termini} [Inform. and Control 20, 301-312 (1972; Zbl 0239.94028)]. The formulation of this entropy, more correctly, of a measure of fuzziness \(H\), is not correct for the authors' next considerations because of its dependence on the underlying universe \(X\), as far as it is not ensured that all discussed fuzzy sets are the fuzzy subsets of \(X\) (especially \(C\) in Theorem 4, \(D_1\) and \(D_2\) in Theorem 5, etc.). Also the relationship of the entropy functions \(h\) and \(H\) is not well clarified (in general, \(h\) may depend on \(x)\). The main results of the paper show that the entropy \(H\) has several properties of linearity on the class of triangular fuzzy numbers. Note that these properties hold for the large class of LR-fuzzy numbers as shown by \textit{A. Kolesárová} and \textit{D. Vivona} [Kybernetika 37, 127-145 (2001)].
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 94C15
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 1437006
zbMATH Keywords: fuzzy set
zbMATH Keywords: non-probabilistic entropy of fuzzy quantities
zbMATH Keywords: entropy functions
zbMATH Keywords: triangular fuzzy numbers
MaRDI profile type: Publication
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Wikidata QID: Q127246682
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description: scientific article; zbMATH DE number 1437006