{"title":"p -代数中的γ -模糊滤波器和γ -模糊滤波器的空间","authors":"Wondwosen Zemene Norahun, Teferi Getachew Alemayehu","doi":"10.1080/27684830.2023.2258591","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the concept of γ−fuzzy filters in a pseudo-complemented distributive lattices. We study the special class of fuzzy filters called γ−fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of boosters. We observe that every γ−fuzzy filters is the intersection of all prime γ−fuzzy filters containing it. We also topologize the set of all prime γ−fuzzy filters of a pseudo-completed distributive lattice. Properties of the space also studied. We show that there is a one to one correspondence between the class of γ−fuzzy filters and the lattice of all open sets in Pγ. It is proved that the space Pγ is a T0 space.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"<i>γ</i> -fuzzy filters and space of <i>γ</i> -- fuzzy filters in P-algebra\",\"authors\":\"Wondwosen Zemene Norahun, Teferi Getachew Alemayehu\",\"doi\":\"10.1080/27684830.2023.2258591\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce the concept of γ−fuzzy filters in a pseudo-complemented distributive lattices. We study the special class of fuzzy filters called γ−fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of boosters. We observe that every γ−fuzzy filters is the intersection of all prime γ−fuzzy filters containing it. We also topologize the set of all prime γ−fuzzy filters of a pseudo-completed distributive lattice. Properties of the space also studied. We show that there is a one to one correspondence between the class of γ−fuzzy filters and the lattice of all open sets in Pγ. It is proved that the space Pγ is a T0 space.\",\"PeriodicalId\":45396,\"journal\":{\"name\":\"Research in Mathematics Education\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Research in Mathematics Education\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/27684830.2023.2258591\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"EDUCATION & EDUCATIONAL RESEARCH\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Research in Mathematics Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/27684830.2023.2258591","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
γ -fuzzy filters and space of γ -- fuzzy filters in P-algebra
In this paper, we introduce the concept of γ−fuzzy filters in a pseudo-complemented distributive lattices. We study the special class of fuzzy filters called γ−fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of boosters. We observe that every γ−fuzzy filters is the intersection of all prime γ−fuzzy filters containing it. We also topologize the set of all prime γ−fuzzy filters of a pseudo-completed distributive lattice. Properties of the space also studied. We show that there is a one to one correspondence between the class of γ−fuzzy filters and the lattice of all open sets in Pγ. It is proved that the space Pγ is a T0 space.
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