L. Behounek, P. Cintula, Ulrich Bodenhofer, Susanne Saminger-Platz, Peter Sarkoci
{"title":"论t-范数和优势的分级概念","authors":"L. Behounek, P. Cintula, Ulrich Bodenhofer, Susanne Saminger-Platz, Peter Sarkoci","doi":"10.1109/ISMVL.2010.21","DOIUrl":null,"url":null,"abstract":"The paper studies graded properties of MTL_Delta-valued binary connectives, focusing on conjunctive connectives such as t-norms, uninorms, aggregation operators, or quasicopulas. The graded properties studied include monotony, a generalized Lipschitz property, unit and null elements, commutativity, associativity, and idempotence. Finally, a graded notion of dominance is investigated and applied to transmission of graded properties of fuzzy relations. The framework of Fuzzy Class Theory (or higher-order fuzzy logic) is employed as a tool for easy derivation of graded theorems on the connectives.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On a Graded Notion of t-Norm and Dominance\",\"authors\":\"L. Behounek, P. Cintula, Ulrich Bodenhofer, Susanne Saminger-Platz, Peter Sarkoci\",\"doi\":\"10.1109/ISMVL.2010.21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper studies graded properties of MTL_Delta-valued binary connectives, focusing on conjunctive connectives such as t-norms, uninorms, aggregation operators, or quasicopulas. The graded properties studied include monotony, a generalized Lipschitz property, unit and null elements, commutativity, associativity, and idempotence. Finally, a graded notion of dominance is investigated and applied to transmission of graded properties of fuzzy relations. The framework of Fuzzy Class Theory (or higher-order fuzzy logic) is employed as a tool for easy derivation of graded theorems on the connectives.\",\"PeriodicalId\":447743,\"journal\":{\"name\":\"2010 40th IEEE International Symposium on Multiple-Valued Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 40th IEEE International Symposium on Multiple-Valued Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2010.21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 40th IEEE International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2010.21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The paper studies graded properties of MTL_Delta-valued binary connectives, focusing on conjunctive connectives such as t-norms, uninorms, aggregation operators, or quasicopulas. The graded properties studied include monotony, a generalized Lipschitz property, unit and null elements, commutativity, associativity, and idempotence. Finally, a graded notion of dominance is investigated and applied to transmission of graded properties of fuzzy relations. The framework of Fuzzy Class Theory (or higher-order fuzzy logic) is employed as a tool for easy derivation of graded theorems on the connectives.
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