Introducing Interpolative Boolean algebra into Intuitionistic fuzzy sets

Abstract

In this paper, we introduce Interpolative Boolean algebra (IBA) as a suitable algebra for intuitionistic fuzzy sets (IFSs). IBA is [0,1]-valued realization of Boolean algebra, consistent with Boolean axioms and theorems. IFS theory takes into account both membership and non-membership function, so it can be viewed as a generalization of the traditional fuzzy set theory. We propose a realization of IFS conjunction and disjunction operations based on IBA. This may be viewed as a generalized framework for IFS-IBA calculus. Finally, we investigate the validity of the laws of contradiction and excluded middle in our approach.