{"title":"Representation by cuts in the framework of relational valued fuzzy sets","authors":"B. Seselja, A. Tepavčević","doi":"10.1109/FUZZY.2009.5277357","DOIUrl":null,"url":null,"abstract":"Generalized or relational-valued fuzzy sets are mappings from a set X to a relational system S = (S, p). Representation of collections of subsets by relational-valued fuzzy sets in the cutworthy framework is presented. It is proved that for every collection F of subsets of a set X there is a relational system S = (S, p) and a fuzzy set μ : X → S, such that the collection of cuts of μ coincides with F.","PeriodicalId":117895,"journal":{"name":"2009 IEEE International Conference on Fuzzy Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2009-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 IEEE International Conference on Fuzzy Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZY.2009.5277357","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Generalized or relational-valued fuzzy sets are mappings from a set X to a relational system S = (S, p). Representation of collections of subsets by relational-valued fuzzy sets in the cutworthy framework is presented. It is proved that for every collection F of subsets of a set X there is a relational system S = (S, p) and a fuzzy set μ : X → S, such that the collection of cuts of μ coincides with F.
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