Study on Entropy and Similarity Measure for Fuzzy Set

Sang-Hyuk LEE  Keun Ho RYU  Gyoyong SOHN  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E92-D   No.9   pp.1783-1786
Publication Date: 2009/09/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E92.D.1783
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Computation and Computational Models
Keyword: 
similarity measure,  distance measure,  fuzzy entropy,  

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Summary: 
In this study, we investigated the relationship between similarity measures and entropy for fuzzy sets. First, we developed fuzzy entropy by using the distance measure for fuzzy sets. We pointed out that the distance between the fuzzy set and the corresponding crisp set equals fuzzy entropy. We also found that the sum of the similarity measure and the entropy between the fuzzy set and the corresponding crisp set constitutes the total information in the fuzzy set. Finally, we derived a similarity measure from entropy and showed by a simple example that the maximum similarity measure can be obtained using a minimum entropy formulation.