Quantitative comparison of similarity measure and entropy for fuzzy sets

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...

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Bibliographic Details
Published in:Journal of Central South University of Technology. Science & technology of mining and metallurgy 2011-12, Vol.18 (6), p.2045-2049
Main Authors: Jung, Dong-yean, Choi, Jung-Wook, Park, Wook-Je, Lee, Sang-Hyuk
Format: Article
Language:English
Subjects:
Engineering
Metallic Materials
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Summary: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.
ISSN:1005-9784
1993-0666
DOI:10.1007/s11771-011-0940-y