{"title":"O-Fuzzy ideals in distributive lattices","authors":"Wondwosen Zemene Norahun","doi":"10.1080/27684830.2023.2266902","DOIUrl":null,"url":null,"abstract":"In this paper, we study the concept of O-fuzzy ideals in distributive lattices with the least element 0 as a generalization of δ-fuzzy ideals. We investigate the properties of O-fuzzy ideals and establishes their relationships with other types of fuzzy ideals. We observe that χ{0} may not be an O-fuzzy ideal. Hence, we derive a necessary and sufficient condition for χ{0} to become an O-fuzzy ideal. It is proved that the class of O-fuzzy is a distributive lattice. Moreover, we establish a necessary and sufficient condition for the class of O-fuzzy ideals to be a complete distributive lattice.","PeriodicalId":45396,"journal":{"name":"Research in Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-10-17","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/10.1080/27684830.2023.2266902","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the concept of O-fuzzy ideals in distributive lattices with the least element 0 as a generalization of δ-fuzzy ideals. We investigate the properties of O-fuzzy ideals and establishes their relationships with other types of fuzzy ideals. We observe that χ{0} may not be an O-fuzzy ideal. Hence, we derive a necessary and sufficient condition for χ{0} to become an O-fuzzy ideal. It is proved that the class of O-fuzzy is a distributive lattice. Moreover, we establish a necessary and sufficient condition for the class of O-fuzzy ideals to be a complete distributive lattice.
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