{"title":"分配格中的模糊理想","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":"{\"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}","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}
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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