{"title":"模糊关系单调性的等级及其在模糊规则库中的应用","authors":"M. Daňková, M. Štěpnička, B. Baets","doi":"10.1109/FOCI.2011.5949466","DOIUrl":null,"url":null,"abstract":"In this contribution, we will introduce a notion of monotonicity of a fuzzy relation as a graded property. We will study its behavior w.r.t. fuzzy set operations and show relationship between monotone crisp functions and monotone fuzzy relations. Finally, a connection to special models of a monotone fuzzy rule base system will be provided.","PeriodicalId":106271,"journal":{"name":"2011 IEEE Symposium on Foundations of Computational Intelligence (FOCI)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Grades of Monotonicity of Fuzzy Relations and Their Application to Fuzzy Rule Bases\",\"authors\":\"M. Daňková, M. Štěpnička, B. Baets\",\"doi\":\"10.1109/FOCI.2011.5949466\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this contribution, we will introduce a notion of monotonicity of a fuzzy relation as a graded property. We will study its behavior w.r.t. fuzzy set operations and show relationship between monotone crisp functions and monotone fuzzy relations. Finally, a connection to special models of a monotone fuzzy rule base system will be provided.\",\"PeriodicalId\":106271,\"journal\":{\"name\":\"2011 IEEE Symposium on Foundations of Computational Intelligence (FOCI)\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 IEEE Symposium on Foundations of Computational Intelligence (FOCI)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FOCI.2011.5949466\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 IEEE Symposium on Foundations of Computational Intelligence (FOCI)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FOCI.2011.5949466","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Grades of Monotonicity of Fuzzy Relations and Their Application to Fuzzy Rule Bases
In this contribution, we will introduce a notion of monotonicity of a fuzzy relation as a graded property. We will study its behavior w.r.t. fuzzy set operations and show relationship between monotone crisp functions and monotone fuzzy relations. Finally, a connection to special models of a monotone fuzzy rule base system will be provided.
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