Ideals of BCK-algebras and BCI-algebras based on a new form of fuzzy set

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.