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The purpose of this paper is twofold. Firstly, a general conclusion about fuzzy entropy induced by distance measure is presented based on the axiom definitions of fuzzy entropy and distance measure. Secondly, some fuzzy entropy formulas which relate to the fuzzy entropy formula defined by De Luca and Termini (Inform. Control 20 (1972) 301) are given.
Based on the axiom definition of distance measure, some new formulas of fuzzy entropy induced by distance measure and some new properties of distance measure are given. A characterization of a σ-distance measure is a metric defined on all fuzzy sets is obtained.
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