Makgeolli Structures and Its Application in BCK/BCI-Algebras

Sun Shin Ahn, Seok-Zun Song, Young Bae Jun and Hee Sik Kim
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Sun Shin Ahn: Department of Mathematics Education, Dongguk University, Seoul 04620, Korea
Seok-Zun Song: Department of Mathematics, Jeju National University, Jeju 63243, Korea
Young Bae Jun: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
Hee Sik Kim: Research Institute for Natural Science, Department of Mathematics, Hanyang University, Seoul 04763, Korea

Mathematics, 2019, vol. 7, issue 9, 1-20

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.

Keywords: BCK/BCI-soft universe; makgeolli structure; makgeolli algebra; makgeolli ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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