{"title":"BCK codes","authors":"Hashem Bordbar","doi":"10.1007/s43674-021-00018-4","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we initiate the study of the notion of the <i>BCK</i>-function on an arbitrary set <i>A</i>, and providing connections with <i>x</i>-functions and <i>x</i>-subsets for <span>\\(x \\in X\\)</span> where <i>X</i> is a <i>BCK</i>-algebra. Moreover, using the notion of order in a <i>BCK</i>-algebra, the <i>BCK</i>-code <i>C</i> is introduced and besides a new structure of order in <i>C</i> is investigated. Finally, we show that the structure of the <i>BCK</i>-algebra <i>X</i> and the <i>BCK</i>-code <i>C</i> which is generated by <i>X</i>, with their related orders are the same.</p></div>","PeriodicalId":72089,"journal":{"name":"Advances in computational intelligence","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43674-021-00018-4.pdf","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in computational intelligence","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43674-021-00018-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, we initiate the study of the notion of the BCK-function on an arbitrary set A, and providing connections with x-functions and x-subsets for \(x \in X\) where X is a BCK-algebra. Moreover, using the notion of order in a BCK-algebra, the BCK-code C is introduced and besides a new structure of order in C is investigated. Finally, we show that the structure of the BCK-algebra X and the BCK-code C which is generated by X, with their related orders are the same.
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