IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Regular Section
Study on Entropy and Similarity Measure for Fuzzy Set
Sang-Hyuk LEEKeun Ho RYUGyoyong SOHN
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2009 Volume E92.D Issue 9 Pages 1783-1786

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Abstract

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.

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© 2009 The Institute of Electronics, Information and Communication Engineers
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