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 (α,ε)-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 (α,ε)-Lukasiewicz fuzzy subalgebras is discussed, and the conditions under which the ε-Lukasiewicz fuzzy set to be an (α,ε)-Lukasiewicz fuzzy subalgebra are explored. The characterizations of (α,ε)-Lukasiewicz fuzzy subalgebras are exam ined. Conditions under which Lukasiewicz ∈-set, Lukasiewicz q-set and Lukasiewicz O-set can be subalgebras are handled.