QUASI-ASSOCIATIVE IDEALS IN BCI-ALGEBRAS BASED ON BIPOLAR-VALUED FUZZY SETS Jun, Young-Bae; Kim, Seon-Yu; Roh, Eun-Hwan;
After the introduction of fuzzy sets by Zadeh, there have been a number of generaizations of this fundamental concept. The notion of bipolar-valued fuzzy sets introduced by Lee is one among them. In this paper, we apply the concept of a bipolar-valued fuzzy set to quasi-associative ideals in BCI-algebras. The notion of a bipolar fuzzy quasi-associative ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of a bipolar fuzzy quasi-associative ideal are given. Extension property for a bipolar fuzzy QA-ideal is established.