Interpolative Boolean Algebra for Generalizations of Intuitionistic Fuzzy Sets

Abstract

The idea of this paper is to investigate intuitionistic fuzzy set (IFS) generalizations and make one step further into that direction by introducing interpolative Boolean algebra (IBA) to Liu's generalized IFS. First, we aim to give an overview of the existing attempts to generalize or alter the definition of IFS and to underline the most general approach. Further, Liu's bipolar I-fuzzy sets (LBIFSs) are introduced as the most universal case of Liu's generalized intuitionistic fuzzy sets. Finally, IBA-based operations are introduced to deal with LBIFS. In the proposed LBIFS-IBA approach, all Boolean laws are fulfilled. The special attention is dedicated to laws of the excluded middle and contradiction.