{"title":"Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals","authors":"M. Hamidi","doi":"10.18778/0138-0680.2023.20","DOIUrl":null,"url":null,"abstract":"This paper introduces the concept of single-valued neutrosophic hyper \\(BCK\\)-subalgebras as a generalization and alternative of hyper \\(BCK\\)-algebras and on any given nonempty set constructs at least one single-valued neutrosophic hyper \\(BCK\\)-subalgebra and one a single-valued neutrosophic hyper \\(BCK\\)-ideal. In this study level subsets play the main role in the connection between single-valued neutrosophic hyper \\(BCK\\)-subalgebras and hyper \\(BCK\\)-subalgebras and the connection between single-valued neutrosophic hyper \\(BCK\\)-ideals and hyper \\(BCK\\)-ideals. The congruence and (strongly) regular equivalence relations are the important tools for connecting hyperstructures and structures, so the major contribution of this study is to apply and introduce a (strongly) regular relation on hyper \\(BCK\\)-algebras and to investigate their categorical properties (quasi commutative diagram) via single-valued neutrosophic hyper \\(BCK\\)-ideals. Indeed, by using the single-valued neutrosophic hyper \\(BCK\\)-ideals, we define a congruence relation on (weak commutative) hyper \\(BCK\\)-algebras that under some conditions is strongly regular and the quotient of any (single-valued neutrosophic)hyper \\(BCK\\)-(sub)algebra via this relation is a (single-valued neutrosophic)(hyper \\(BCK\\)-subalgebra) \\(BCK\\)-(sub)algebra.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Section of Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18778/0138-0680.2023.20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 1
Abstract
This paper introduces the concept of single-valued neutrosophic hyper \(BCK\)-subalgebras as a generalization and alternative of hyper \(BCK\)-algebras and on any given nonempty set constructs at least one single-valued neutrosophic hyper \(BCK\)-subalgebra and one a single-valued neutrosophic hyper \(BCK\)-ideal. In this study level subsets play the main role in the connection between single-valued neutrosophic hyper \(BCK\)-subalgebras and hyper \(BCK\)-subalgebras and the connection between single-valued neutrosophic hyper \(BCK\)-ideals and hyper \(BCK\)-ideals. The congruence and (strongly) regular equivalence relations are the important tools for connecting hyperstructures and structures, so the major contribution of this study is to apply and introduce a (strongly) regular relation on hyper \(BCK\)-algebras and to investigate their categorical properties (quasi commutative diagram) via single-valued neutrosophic hyper \(BCK\)-ideals. Indeed, by using the single-valued neutrosophic hyper \(BCK\)-ideals, we define a congruence relation on (weak commutative) hyper \(BCK\)-algebras that under some conditions is strongly regular and the quotient of any (single-valued neutrosophic)hyper \(BCK\)-(sub)algebra via this relation is a (single-valued neutrosophic)(hyper \(BCK\)-subalgebra) \(BCK\)-(sub)algebra.