Intuitionisitic Fuzzy B-algebras

In 1966, (Imai and Iseki, 1966) defined a class of algebras of type (2, 0) named BCK-algebras. At the same time, (Iseki, 1966) generalized another class of algebras of type (2, 0) called BCI-algebras. Hu and Li (1983) introduced the concept of BCH-algebras and gave examples of proper BCH-algebras (Hu and Li, 1985). Neggers and Kim (2001) introduced and investigated a class of algebras, viz., the class of B-algebras, which is related to several classes of algebras of interest such as BCH/BCI/BCKalgebras and which seems to have rather nice properties without being excessively complicated otherwise. Xi (1991) applied the notion of fuzzy sets (Zadeh, 1966) to BCK/BCI-algebras. Jun (1993), Meng, (1994) and Jun and Roh (1994) investigated fuzzy ideals of BCK/BCI-algebras. Young et al. (2002) introduced notions of fuzzy B-algebras and investigated its properties. In 1986, (Atanassov, 1986) introduced the concept of intuitionistic fuzzy sets, which is a significant extension of fuzzy set theory by Zadeh (1966).Li and Wang (2000) studied intuitionistic fuzzy group and its homomorphisic image and subsequently discussed the product and extension principle of the intuitionistic fuzzy sets (Li and Wang, 2002). In this study, we introduce notion of intuitionistic fuzzy B-algebras and discuss their properties. Some properties of the homomorphic (isomorphic) image and inverse image of intuitionistic fuzzy B-algebras will be studied, the notions of intuitionistic fuzzy relation, strongest intuitionistic fuzzy relation and Cartesian product of intuitionisitic fuzzy sets will be given, some relations between intuitionistic fuzzy B-algebras and its product B-algebras are exposed.