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Makgeolli Structures and Its Application in BCK/BCI-Algebras

Title
Makgeolli Structures and Its Application in BCK/BCI-Algebras
Author
김희식
Keywords
BCK; BCI-soft universe; makgeolli structure; makgeolli algebra; makgeolli ideal
Issue Date
2019-09
Publisher
MDPI
Citation
MATHEMATICS, v. 7, no. 9, article no. 784
Abstract
A fuzzy set is an extension of an existing set using fuzzy logic. Soft set theory is a generalization of fuzzy set theory. Fuzzy and soft set theory are good mathematical tools for dealing with uncertainty in a parametric manner. The aim of this article is to introduce the concept of makgeolli structures using fuzzy and soft set theory and to apply it to BCK/BCI-algebras. The notion of makgeolli algebra and makgeolli ideal in BCK/BCI-algebras is defined, and several properties are investigated. It deals with the relationship between makgeolli algebra and makgeolli ideal, and several examples are given. Characterization of makgeolli algebra and makgeolli ideal are discussed, and a new makgeolli algebra from old one is established. A condition for makgeolli algebra to be makgeolli ideal in BCK-soft universe is considered, and we give example to show that makgeolli ideal is not makgeolli algebra in BCI-soft universe. Conditions for makgeolli ideal to be makgeolli algebra in BCI-soft universe are provided.
URI
https://www.mdpi.com/2227-7390/7/9/784https://repository.hanyang.ac.kr/handle/20.500.11754/152568
ISSN
2227-7390
DOI
10.3390/math7090784
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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