Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations: Research Articles

Authors:
Wenyi Zeng;Hongxing Li
Affiliations:
Department of Mathematics, Beijing Normal University, Beijing, 100875, P.R. China and Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, SE171 77, Sweden;Department of Mathematics, Beijing Normal University, Beijing, 100875, P.R. China
Venue:
International Journal of Intelligent Systems
Year:
2006

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Abstract

The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures, similarity measures, and the fuzziness of fuzzy sets can be transformed by each other based on their axiomatic definitions, and propose some new formulas to calculate inclusion measures, similarity measures, and the fuzziness of fuzzy sets. These results can be applied in many fields, such as pattern recognition, image processing, fuzzy neural networks, fuzzy reasoning, and fuzzy control. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 639–653, 2006.