Ananto Adi Nugraha, Fitriani Fitriani, Muslim Ansori, Ahmad Faisol
{"title":"A群结构上粗糙集的实现","authors":"Ananto Adi Nugraha, Fitriani Fitriani, Muslim Ansori, Ahmad Faisol","doi":"10.15642/mantik.2022.8.1.45-52","DOIUrl":null,"url":null,"abstract":"Let be a non-empty set and an equivalence relation on . Then, is called an approximation space. The equivalence relation on forms disjoint equivalence classes. If , then we can form a lower approximation and an upper approximation of . If X⊆U, then we can form a lower approximation and an upper approximation of X. In this research, rough group and rough subgroups are constructed in the approximation space for commutative and non-commutative binary operations.","PeriodicalId":32704,"journal":{"name":"Mantik Jurnal Matematika","volume":"34 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Implementation of Rough Set on A Group Structure\",\"authors\":\"Ananto Adi Nugraha, Fitriani Fitriani, Muslim Ansori, Ahmad Faisol\",\"doi\":\"10.15642/mantik.2022.8.1.45-52\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let be a non-empty set and an equivalence relation on . Then, is called an approximation space. The equivalence relation on forms disjoint equivalence classes. If , then we can form a lower approximation and an upper approximation of . If X⊆U, then we can form a lower approximation and an upper approximation of X. In this research, rough group and rough subgroups are constructed in the approximation space for commutative and non-commutative binary operations.\",\"PeriodicalId\":32704,\"journal\":{\"name\":\"Mantik Jurnal Matematika\",\"volume\":\"34 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mantik Jurnal Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15642/mantik.2022.8.1.45-52\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mantik Jurnal Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15642/mantik.2022.8.1.45-52","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let be a non-empty set and an equivalence relation on . Then, is called an approximation space. The equivalence relation on forms disjoint equivalence classes. If , then we can form a lower approximation and an upper approximation of . If X⊆U, then we can form a lower approximation and an upper approximation of X. In this research, rough group and rough subgroups are constructed in the approximation space for commutative and non-commutative binary operations.
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