Intuitionistic Fuzzy Ideals of BG-Algebras

Abstract — We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BG-algebras, and investigate some of their properties. Keywords — (Intuitionistic) fuzzy subalgebra, (Intuitionistic) fuzzy ideal, upper (respectively, lower) t-level cut, homomorphism.I. I NTRODUCTION FTER the introduction of the concept of fuzzy sets by Zadeh several researches were conducted on the generalizations of the notion of fuzzy sets. The idea of “ Intuitionistic fuzzy set “ was first published by Atanassov, as a generalization of the notion of the fuzzy set . In this paper, using the Atanssov’s idea, we establish the intuitionistic fuzzification of the concept of subalgebras and ideals in BG-algebras, and investigate some of their properties II. P ERLIMINARIES First we present the fundamental definitions. Definition 2.1. A BG-algebra is a non-empty set X with a constant 0 and a binary operating * satisfying the following axioms: ( )(x ) (0 ) ,for all , .( ) x 0 x,( ) 0,iii y y x x y