{"title":"模糊关系的特征向量和生成","authors":"J. Jacas, J. Recasens","doi":"10.1109/FUZZY.1992.258741","DOIUrl":null,"url":null,"abstract":"A new geometric approach to the study of the eigenvectors is provided. The T-eigenvectors of a T-indistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde (1985). This theorem states that every T-indistinguishability operator on a set X can be generated by a family of fuzzy subsets of X and, reciprocally, every family of fuzzy subsets of X generated a T-indistinguishability operator on X in a natural way. Some concepts related to T-eigenvectors and generators of T-indistinguishabilities are reviewed, and their relation is studied. Some examples are given.<<ETX>>","PeriodicalId":222263,"journal":{"name":"[1992 Proceedings] IEEE International Conference on Fuzzy Systems","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"Eigenvectors and generators of fuzzy relations\",\"authors\":\"J. Jacas, J. Recasens\",\"doi\":\"10.1109/FUZZY.1992.258741\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new geometric approach to the study of the eigenvectors is provided. The T-eigenvectors of a T-indistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde (1985). This theorem states that every T-indistinguishability operator on a set X can be generated by a family of fuzzy subsets of X and, reciprocally, every family of fuzzy subsets of X generated a T-indistinguishability operator on X in a natural way. Some concepts related to T-eigenvectors and generators of T-indistinguishabilities are reviewed, and their relation is studied. Some examples are given.<<ETX>>\",\"PeriodicalId\":222263,\"journal\":{\"name\":\"[1992 Proceedings] IEEE International Conference on Fuzzy Systems\",\"volume\":\"5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-03-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1992 Proceedings] IEEE International Conference on Fuzzy Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FUZZY.1992.258741\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1992 Proceedings] IEEE International Conference on Fuzzy Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZY.1992.258741","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A new geometric approach to the study of the eigenvectors is provided. The T-eigenvectors of a T-indistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde (1985). This theorem states that every T-indistinguishability operator on a set X can be generated by a family of fuzzy subsets of X and, reciprocally, every family of fuzzy subsets of X generated a T-indistinguishability operator on X in a natural way. Some concepts related to T-eigenvectors and generators of T-indistinguishabilities are reviewed, and their relation is studied. Some examples are given.<>
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