{"title":"Rough logic system RSL and fuzzy logic system Luk","authors":"Xiao-hong Zhang, Feng Zhu","doi":"10.3969/J.ISSN.1001-0548.2011.02.028","DOIUrl":null,"url":null,"abstract":"From the description of the pairs (low approximation,upper approximation) of rough sets,a new rough implication operator is introduced by modifying the method by Ref.[1],some algebraic properties of this rough implication operator are investigated,and these results are generalized to regular double Stone algebras and the following important result is proved: the regular double Stone algebra with the new rough implication operator is an MV-algebra.Further more a rough logic system RSL is constructed,its schematic is rough sets and extensional regular double Stone algebras.The completeness theorem of RSL is proved by introducing the notion of RSL-algebra.Finally,the relationship between rough logic RSL and fuzzy logic Luk(continuous-valued tukasiewicz logic system) is discussed.","PeriodicalId":35864,"journal":{"name":"电子科技大学学报","volume":"40 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"电子科技大学学报","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.3969/J.ISSN.1001-0548.2011.02.028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 6
Abstract
From the description of the pairs (low approximation,upper approximation) of rough sets,a new rough implication operator is introduced by modifying the method by Ref.[1],some algebraic properties of this rough implication operator are investigated,and these results are generalized to regular double Stone algebras and the following important result is proved: the regular double Stone algebra with the new rough implication operator is an MV-algebra.Further more a rough logic system RSL is constructed,its schematic is rough sets and extensional regular double Stone algebras.The completeness theorem of RSL is proved by introducing the notion of RSL-algebra.Finally,the relationship between rough logic RSL and fuzzy logic Luk(continuous-valued tukasiewicz logic system) is discussed.