Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations | Zendy

Zeng Wenyi | Zendy; Li Hongxing | Zendy

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

Author(s) -

Zeng Wenyi,

Li Hongxing

Publication year - 2006

Publication title -

international journal of intelligent systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.291

H-Index - 87

eISSN - 1098-111X

pISSN - 0884-8173

DOI - 10.1002/int.20152

Subject(s) - mathematics , fuzzy set , similarity (geometry) , fuzzy classification , axiom , fuzzy set operations , defuzzification , fuzzy measure theory , fuzzy number , fuzzy logic , similarity measure , measure (data warehouse) , type 2 fuzzy sets and systems , artificial intelligence , data mining , pattern recognition (psychology) , image (mathematics) , computer science , geometry

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.

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