{"title":"有界偏集上的三角范数","authors":"Zhang Kun-lun, Li Dong-hai","doi":"10.1109/KAMW.2008.4810415","DOIUrl":null,"url":null,"abstract":"In this presented note, triangular norms are studied in the general setting of bounded partially ordered sets(posets). The sets of idempotent elements, zero divisors and nilpotent elements associated to a t-norm are introduced and related to each other. The Archimedean of t-norms is discussed, in particular its relationship to the diagonal inequality.","PeriodicalId":375613,"journal":{"name":"2008 IEEE International Symposium on Knowledge Acquisition and Modeling Workshop","volume":"128 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Triangular Norms on a Bounded Posets\",\"authors\":\"Zhang Kun-lun, Li Dong-hai\",\"doi\":\"10.1109/KAMW.2008.4810415\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this presented note, triangular norms are studied in the general setting of bounded partially ordered sets(posets). The sets of idempotent elements, zero divisors and nilpotent elements associated to a t-norm are introduced and related to each other. The Archimedean of t-norms is discussed, in particular its relationship to the diagonal inequality.\",\"PeriodicalId\":375613,\"journal\":{\"name\":\"2008 IEEE International Symposium on Knowledge Acquisition and Modeling Workshop\",\"volume\":\"128 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 IEEE International Symposium on Knowledge Acquisition and Modeling Workshop\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/KAMW.2008.4810415\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 IEEE International Symposium on Knowledge Acquisition and Modeling Workshop","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/KAMW.2008.4810415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this presented note, triangular norms are studied in the general setting of bounded partially ordered sets(posets). The sets of idempotent elements, zero divisors and nilpotent elements associated to a t-norm are introduced and related to each other. The Archimedean of t-norms is discussed, in particular its relationship to the diagonal inequality.