GENERALIZED LUKASIEWICZ FUZZY SUBALGEBRAS OF BCI-ALGEBRAS AND BCK-ALGEBRAS

Abstract

The aim of this paper is to generalize Lukasiewicz fuzzy subalgebras in BCK/BCI-algebras. First, the concept of (alpha, epsilon)-Lukasiewicz fuzzy subalgebras using fuzzy points is defined and examples to explain it are given, and then several properties are investigated. The relationship between Lukasiewicz fuzzy subalgebras and (alpha, epsilon)-Lukasiewicz fuzzy subalgebras is discussed, and the conditions under which the epsilon- Lukasiewicz fuzzy set to be an (alpha, epsilon)-Lukasiewicz fuzzy subalgebra are explored. The characterizations of (alpha, epsilon)-Lukasiewicz fuzzy subalgebras are examined. Conditions under which Lukasiewicz is an element of-set, Lukasiewiczqset and Lukasiewicz is an element of-set can be subalgebras are handled.