Quantitative comparison of similarity measure and entropy for fuzzy sets |
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Authors: | Dong-yean Jung Jung-Wook Choi Wook-Je Park and Sang-Hyuk Lee |
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Affiliation: | [1]Daeho Tech, Changwon, Gyeongnam, 641-773, Korea [2]Institute for Information and Electronics Research, Inha University, 253 Yonghyun-dong, Nam-Gu, Incheon, 402-751, Korea [3]Department of Electrical and Electronic Engineering, Xi'an Jiaotong-Liverpool University, Suzhou 215123, China |
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Abstract: | Comparison and data analysis with the similarity measures and entropy for fuzzy sets were carried out. The distance proportional
value between the fuzzy set and the corresponding crisp set was considered by the fuzzy entropy. The relation between the
similarity measure and the entropy for fuzzy set was also analyzed. The fuzzy entropy was reformulated as the dissimilarity
measure. Furthermore, crisp set having the minimum uncertainty with respect to the corresponding fuzzy set was also proposed.
Finally, derivation of a similarity measure from entropy with the help of total information property was derived. A simple
example shows the relation between similarity measure and fuzzy entropy, in which the summation of similarity measure and
fuzzy entropy represents a constant value. |
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Keywords: | similarity measure fuzzy entropy minimum uncertainty quantitative comparison |
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