Subalgebras of Sheffer Stroke BCK-Algebras Illuminated by the New Fuzzy Set Environment

Abstract

For the purpose of dealing with the subalgebras of Sheer stroke BCK-algebras associated with the YJ -fuzzy set, the concept of YJ -fuzzy subalgebras in Sheffer stroke BCK-algebras is introduced and the properties involved are investigated. Conditions for creating a YJ fuzzy subalgebra from a given fuzzy are explored. The relationship between fuzzy subalgebra and the YJ fuzzy subalgebra is discussed, and conditions are given for the YJ -fuzzy subalgebra to be a fuzzy subalgebra. The task of creating a new YJ -fuzzy subalgebra is established using the given fuzzy subalgebra. Two types of level sets are created and the conditions under which they become subalgebras are explored. © World Scientific Publishing Company.