{"title":"基于残差格的模糊变精度粗糙集的公理化表征","authors":"Qiu Jin, Lingqiang Li","doi":"10.1080/03081079.2023.2212849","DOIUrl":null,"url":null,"abstract":"Axiomatization is a lively research direction in fuzzy rough set theory. Fuzzy variable precision rough set (FVPRS) incorporates fault-tolerant factors to fuzzy rough set, so its axiomatic description becomes more complicated and difficult to realize. In this paper, we present an axiomatic approach to FVPRSs based on residuated lattice (L-fuzzy variable precision rough set (LFVPRS)). First, a pair of mappings with three axioms is utilized to characterize the upper (resp., lower) approximation operator of LFVPRS. This is distinct from the characterization on upper (resp., lower) approximation operator of fuzzy rough set, which consists of one mapping with two axioms. Second, utilizing the notion of correlation degree (resp., subset degree) of fuzzy sets, three characteristic axioms are grouped into a single axiom. At last, various special LFVPRS generated by reflexive, symmetric and transitive L-fuzzy relation and their composition are also characterized by axiomatic set and single axiom, respectively.","PeriodicalId":50322,"journal":{"name":"International Journal of General Systems","volume":"52 1","pages":"820 - 841"},"PeriodicalIF":2.4000,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The axiomatic characterization on fuzzy variable precision rough sets based on residuated lattice\",\"authors\":\"Qiu Jin, Lingqiang Li\",\"doi\":\"10.1080/03081079.2023.2212849\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Axiomatization is a lively research direction in fuzzy rough set theory. Fuzzy variable precision rough set (FVPRS) incorporates fault-tolerant factors to fuzzy rough set, so its axiomatic description becomes more complicated and difficult to realize. In this paper, we present an axiomatic approach to FVPRSs based on residuated lattice (L-fuzzy variable precision rough set (LFVPRS)). First, a pair of mappings with three axioms is utilized to characterize the upper (resp., lower) approximation operator of LFVPRS. This is distinct from the characterization on upper (resp., lower) approximation operator of fuzzy rough set, which consists of one mapping with two axioms. Second, utilizing the notion of correlation degree (resp., subset degree) of fuzzy sets, three characteristic axioms are grouped into a single axiom. At last, various special LFVPRS generated by reflexive, symmetric and transitive L-fuzzy relation and their composition are also characterized by axiomatic set and single axiom, respectively.\",\"PeriodicalId\":50322,\"journal\":{\"name\":\"International Journal of General Systems\",\"volume\":\"52 1\",\"pages\":\"820 - 841\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2023-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of General Systems\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1080/03081079.2023.2212849\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of General Systems","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1080/03081079.2023.2212849","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
The axiomatic characterization on fuzzy variable precision rough sets based on residuated lattice
Axiomatization is a lively research direction in fuzzy rough set theory. Fuzzy variable precision rough set (FVPRS) incorporates fault-tolerant factors to fuzzy rough set, so its axiomatic description becomes more complicated and difficult to realize. In this paper, we present an axiomatic approach to FVPRSs based on residuated lattice (L-fuzzy variable precision rough set (LFVPRS)). First, a pair of mappings with three axioms is utilized to characterize the upper (resp., lower) approximation operator of LFVPRS. This is distinct from the characterization on upper (resp., lower) approximation operator of fuzzy rough set, which consists of one mapping with two axioms. Second, utilizing the notion of correlation degree (resp., subset degree) of fuzzy sets, three characteristic axioms are grouped into a single axiom. At last, various special LFVPRS generated by reflexive, symmetric and transitive L-fuzzy relation and their composition are also characterized by axiomatic set and single axiom, respectively.
期刊介绍：
International Journal of General Systems is a periodical devoted primarily to the publication of original research contributions to system science, basic as well as applied. However, relevant survey articles, invited book reviews, bibliographies, and letters to the editor are also published.
The principal aim of the journal is to promote original systems ideas (concepts, principles, methods, theoretical or experimental results, etc.) that are broadly applicable to various kinds of systems. The term “general system” in the name of the journal is intended to indicate this aim–the orientation to systems ideas that have a general applicability. Typical subject areas covered by the journal include: uncertainty and randomness; fuzziness and imprecision; information; complexity; inductive and deductive reasoning about systems; learning; systems analysis and design; and theoretical as well as experimental knowledge regarding various categories of systems. Submitted research must be well presented and must clearly state the contribution and novelty. Manuscripts dealing with particular kinds of systems which lack general applicability across a broad range of systems should be sent to journals specializing in the respective topics.
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