{"title":"直觉模糊偏好关系的因子化","authors":"J. Mordeson, T. Clark, Karen E. Albert","doi":"10.1142/S179300571450001X","DOIUrl":null,"url":null,"abstract":"The proofs of many factorization results for an intuitionistic fuzzy binary relation 〈ρμ,ρν〉 involve dual proofs, one for ρμ with respect to a t-conorm ⊕ and one for ρν with respect to a t-norm ⊗. In this paper, we show that one proof can be obtained from the other by considering ⊕ and ⊗ dual under an involutive fuzzy complement. We provide a series of singular proofs for commonly defined norms and conorms.","PeriodicalId":44835,"journal":{"name":"New Mathematics and Natural Computation","volume":"10 1","pages":"1-25"},"PeriodicalIF":0.7000,"publicationDate":"2014-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S179300571450001X","citationCount":"1","resultStr":"{\"title\":\"Factorization of intuitionistic fuzzy preference relations\",\"authors\":\"J. Mordeson, T. Clark, Karen E. Albert\",\"doi\":\"10.1142/S179300571450001X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The proofs of many factorization results for an intuitionistic fuzzy binary relation 〈ρμ,ρν〉 involve dual proofs, one for ρμ with respect to a t-conorm ⊕ and one for ρν with respect to a t-norm ⊗. In this paper, we show that one proof can be obtained from the other by considering ⊕ and ⊗ dual under an involutive fuzzy complement. We provide a series of singular proofs for commonly defined norms and conorms.\",\"PeriodicalId\":44835,\"journal\":{\"name\":\"New Mathematics and Natural Computation\",\"volume\":\"10 1\",\"pages\":\"1-25\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2014-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1142/S179300571450001X\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"New Mathematics and Natural Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/S179300571450001X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"New Mathematics and Natural Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S179300571450001X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Factorization of intuitionistic fuzzy preference relations
The proofs of many factorization results for an intuitionistic fuzzy binary relation 〈ρμ,ρν〉 involve dual proofs, one for ρμ with respect to a t-conorm ⊕ and one for ρν with respect to a t-norm ⊗. In this paper, we show that one proof can be obtained from the other by considering ⊕ and ⊗ dual under an involutive fuzzy complement. We provide a series of singular proofs for commonly defined norms and conorms.
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