Interval-valued intuitionistic fuzzy ideals of B-algebras

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-algebras and investigate some interesting properties. We characterize Artinian and Noetherian K-algebras by considering IIFIs of a K-algebra K. Characterization theorems of fully invariant and characteristic IIFIs are also discussed. Key–Words: K-algebras; Interval-valued intuitionistic fuzzy sets; Equivalence relations; Artinian and Noetherian K-algebras; Fully invariant; Characteristic.