{"title":"The Best Interval Representation of Fuzzy S-Implications and Automorphisms","authors":"B. Bedregal, R. Santiago, R. Reiser, G. Dimuro","doi":"10.1109/FUZZY.2007.4295636","DOIUrl":null,"url":null,"abstract":"The aim of this work is to analyze interval fuzzy S-implications and interval automorphisms. Starting from any fuzzy S-implication, it is shown how to obtain an interval fuzzy S-implication canonically. We proved that such interval fuzzy S-implications meet the optimality property and preserve the same properties satisfied by fuzzy S-implications. In addition, commutative diagrams are used in order to relate fuzzy S-implications to interval fuzzy S-implications, and to understand how interval automorphisms act on interval S-implications, generating other interval fuzzy S-implications.","PeriodicalId":236515,"journal":{"name":"2007 IEEE International Fuzzy Systems Conference","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 IEEE International Fuzzy Systems Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZY.2007.4295636","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
The aim of this work is to analyze interval fuzzy S-implications and interval automorphisms. Starting from any fuzzy S-implication, it is shown how to obtain an interval fuzzy S-implication canonically. We proved that such interval fuzzy S-implications meet the optimality property and preserve the same properties satisfied by fuzzy S-implications. In addition, commutative diagrams are used in order to relate fuzzy S-implications to interval fuzzy S-implications, and to understand how interval automorphisms act on interval S-implications, generating other interval fuzzy S-implications.
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