M. Kologani, X. Xin, M. M. Takallo, Y. Jun, R. Borzooei
{"title":"Constructing a Heyting semilattice that has Wajesberg property by using fuzzy implicative deductive systems of Hoops","authors":"M. Kologani, X. Xin, M. M. Takallo, Y. Jun, R. Borzooei","doi":"10.30495/JME.V0I0.1861","DOIUrl":null,"url":null,"abstract":"In this paper, we defined the notions of $(\\in,\\in)$ -fuzzy implicative deductive systems and $(\\in,\\in\\vee q)$ -fuzzy implicative deductive systems of hoops and studied some traits and tried to define some definitions that are equivalent to them. Thus by using the notion of $(\\in,\\in)$ -fuzzy deductive system of hoop, we defined a new congruence relation on hoop and show that the algebraic structure that is made by it is a Brouwerian semilattice , Heyting algebra and Wajesberg hoop.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V0I0.1861","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we defined the notions of $(\in,\in)$ -fuzzy implicative deductive systems and $(\in,\in\vee q)$ -fuzzy implicative deductive systems of hoops and studied some traits and tried to define some definitions that are equivalent to them. Thus by using the notion of $(\in,\in)$ -fuzzy deductive system of hoop, we defined a new congruence relation on hoop and show that the algebraic structure that is made by it is a Brouwerian semilattice , Heyting algebra and Wajesberg hoop.
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