{"title":"模糊概率集和r-模糊集","authors":"Xuehai Yuan, Hongxing Li, Cheng Zhang","doi":"10.1109/FSKD.2008.100","DOIUrl":null,"url":null,"abstract":"In this paper, a connection between the fuzzy probabilistic set and the r-fuzzy set is established. Firstly, a new concept of r-fuzzy nested set is presented and it is pointed that a fuzzy probabilistic set is an equivalent class of a r-fuzzy nested set. Secondly, the concepts of fuzzy probabilistic subgroup and r-fuzzy subgroup of a group are given respectively, the relations between fuzzy probabilistic subgroups and fuzzy subgroups presented by Rosenfeld and the properties of r-fuzzy subgroups are discussed. Finally, the membership function of fuzzy probabilistic sets and r-fuzzy subgroups are defined, the properties of membership function of r-fuzzy subgroups are studied.","PeriodicalId":208332,"journal":{"name":"2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Fuzzy Probabilistic Sets and r-Fuzzy Sets\",\"authors\":\"Xuehai Yuan, Hongxing Li, Cheng Zhang\",\"doi\":\"10.1109/FSKD.2008.100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a connection between the fuzzy probabilistic set and the r-fuzzy set is established. Firstly, a new concept of r-fuzzy nested set is presented and it is pointed that a fuzzy probabilistic set is an equivalent class of a r-fuzzy nested set. Secondly, the concepts of fuzzy probabilistic subgroup and r-fuzzy subgroup of a group are given respectively, the relations between fuzzy probabilistic subgroups and fuzzy subgroups presented by Rosenfeld and the properties of r-fuzzy subgroups are discussed. Finally, the membership function of fuzzy probabilistic sets and r-fuzzy subgroups are defined, the properties of membership function of r-fuzzy subgroups are studied.\",\"PeriodicalId\":208332,\"journal\":{\"name\":\"2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FSKD.2008.100\",\"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 Fifth International Conference on Fuzzy Systems and Knowledge Discovery","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FSKD.2008.100","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, a connection between the fuzzy probabilistic set and the r-fuzzy set is established. Firstly, a new concept of r-fuzzy nested set is presented and it is pointed that a fuzzy probabilistic set is an equivalent class of a r-fuzzy nested set. Secondly, the concepts of fuzzy probabilistic subgroup and r-fuzzy subgroup of a group are given respectively, the relations between fuzzy probabilistic subgroups and fuzzy subgroups presented by Rosenfeld and the properties of r-fuzzy subgroups are discussed. Finally, the membership function of fuzzy probabilistic sets and r-fuzzy subgroups are defined, the properties of membership function of r-fuzzy subgroups are studied.
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