Some remarks on axiomatic definition of entropy measure

Article type: Research Article

Authors: Piasecki, Krzysztof^{; *}

Affiliations: Department of Investment and Real Estate, Poznan University of Economics and Business, al. Niepodległości, Poznan, Poland

Correspondence: [*] Corresponding author. Krzysztof Piasecki, Department of Investment and Real Estate, Poznan University of Economics and Business, al. Niepodległości 10, 61-875 Poznan, Poland. Tel.: +48 61 8569473; E-mail: [email protected].

Abstract: The entropy measure is predefined as a mapping, increasing with an increase in the fuzziness of evaluated set. The relation “is less fuzzy than” is strictly modeled by an inequality fulfilled by membership functions. This inequality is systematically repeated across the literature. In this paper we show that it is incorrect. We prove that the relation “is less fuzzy than” should be modeled by an inclusion. Obtained conclusions are applied in a more precise definition of entropy measure.

Keywords: Fuzzy set, intuitionistic fuzzy set, entropy measure, ambiguity, indistinctness, undecidability

DOI: 10.3233/JIFS-15364

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1945-1952, 2017