{"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}
引用次数: 1
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.
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