{"title":"A set theory within fuzzy logic","authors":"P. Hájek, Z. Haniková","doi":"10.1109/ISMVL.2001.924590","DOIUrl":null,"url":null,"abstract":"This paper proposes a possibility of developing an axiomatic set theory, as first-order theory within the framework of fuzzy logic in the style of Hajek's Basic fuzzy logic BL. In classical Zermelo-Fraenkel set theory, we use an analogy of the construction of a Boolean-valued universe-over a particular algebra of truth values-we show the nontriviality of our theory. We present a list of problems and research tasks.","PeriodicalId":297353,"journal":{"name":"Proceedings 31st IEEE International Symposium on Multiple-Valued Logic","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 31st IEEE International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2001.924590","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 20
Abstract
This paper proposes a possibility of developing an axiomatic set theory, as first-order theory within the framework of fuzzy logic in the style of Hajek's Basic fuzzy logic BL. In classical Zermelo-Fraenkel set theory, we use an analogy of the construction of a Boolean-valued universe-over a particular algebra of truth values-we show the nontriviality of our theory. We present a list of problems and research tasks.
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