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Ideals of BCK-algebras and BCI-algebras based on a new form of fuzzy setopen access
- Authors
- Roh, Eun Hwan; Yang, Eunsuk; Jun, Young Bae
- Issue Date
- Oct-2023
- Publisher
- New York Business Global
- Keywords
- (closed) Y ϵ J -fuzzy ideal; ideal; J-operator; nonconstant factor; subalgebra; Y ϵ J -fuzzy subalgebra
- Citation
- European Journal of Pure and Applied Mathematics, v.16, no.4, pp 2009 - 2024
- Pages
- 16
- Indexed
- SCOPUS
ESCI
- Journal Title
- European Journal of Pure and Applied Mathematics
- Volume
- 16
- Number
- 4
- Start Page
- 2009
- End Page
- 2024
- ISSN
- 1307-5543
- Abstract
- Ideals in BCK/BCI algebra based on Y ϵ J -fuzzy sets are studied. The fundamental properties of the level set of Y ϵ J -fuzzy sets are investigate first. The concept of (closed) Y ϵ J -fuzzy ideals in BCK/BCI-algebras is introduces, and several properties are investigated. The relationship between Y ϵ J -fuzzy ideal and Y ϵ J -fuzzy subalgebra are discussed, and also the relationship between Y ϵ J -fuzzy ideal and fuzzy ideal is identified. The characterization of (closed) Y ϵ J -fuzzy ideal using the Y-level set is established. The necessary and sufficient conditions for Y ϵ J -fuzzy ideal to be closed is explored, and conditions for Y ϵ J -fuzzy subalgebra to be Y ϵ J -fuzzy ideal are provided. © 2023 EJPAM.
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