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 [Formula: see text]-fuzzy set, the concept of [Formula: see text]-fuzzy subalgebras in Sheffer stroke BCK-algebras is introduced and the properties involved are investigated. Conditions for creating a [Formula: see text] fuzzy subalgebra from a given fuzzy are explored. The relationship between fuzzy subalgebra and the [Formula: see text] fuzzy subalgebra is discussed, and conditions are given for the [Formula: see text]-fuzzy subalgebra to be a fuzzy subalgebra. The task of creating a new [Formula: see text]-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.