Interval Information Content of Fuzzy Relation and the Application in the Fuzzy Implication Operators | Zendy

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Interval Information Content of Fuzzy Relation and the Application in the Fuzzy Implication Operators

Author(s) -

Yiying Shi

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/6611367

Subject(s) - mathematics , relation (database) , fuzzy logic , interval (graph theory) , measure (data warehouse) , fuzzy set , type 2 fuzzy sets and systems , ranking (information retrieval) , fuzzy number , data mining , similarity (geometry) , fuzzy set operations , defuzzification , content (measure theory) , fuzzy classification , fuzzy measure theory , mathematical optimization , artificial intelligence , computer science , mathematical analysis , combinatorics , image (mathematics)

In rule optimization, some rule characteristics were extracted to describe the uncertainty correlations of fuzzy relations, but the concrete numbers cannot express correlations with uncertainty, such as “at least 0.1 and up to 0.5.” To solve this problem, a novel definition concerning interval information content of fuzzy relation has been proposed in this manuscript to realize the fuzziness measurement of the fuzzy relation. Also, its definition and expressions have also been constructed. Meanwhile based on the interval information content, the issues of fuzzy implication ranking and clustering were analyzed. Finally, utilizing the combination of possibility’s interval comparison equations and interval value’s similarity measure, the classifications of implication operators were proved to be realizable. The achievements in the presented work will provide a reasonable index to measure the fuzzy implication operators and lay a solid foundation for further research.

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