Relationship between s -entropy and s -similarity measure of fuzzy sets

ISSN： 0368-492X

Source： Kybernetes: The International Journal of Systems & Cybernetics, Vol.35, Iss.9, 2006-10, pp. : 1382-1392

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Abstract

Purpose ? To provide a simplified proof for Liu's results concerning the relationship between s-entropy and s-similarity measure. Design/methodology/approach ? First obtains Liu's clear and simple functional expression of s-similarity measures based on the structure of s-entropy by using expressions of equivalent functions of s-entropy. Then, by employing the general expression of equivalent functions of s-similarity measure of fuzzy sets, provides a different proof of Liu's results. Findings ? Here, the proof is much simpler than the original one provided by Liu. And, on the basis of Shannon's probability entropy as introduced by De Luca and Termini, a s-similarity measure is constructed, on which a No answer to an open question as proposed by Liu is provided. Originality/value ? Constructs a new approach to some known results and provides a definite answer to an open question.