Complex Number Representation of Intuitionistic Fuzzy Sets

Complex numbers can capture compound features and convey multifaceted information; thereby providing means for solving complicated problems. In this paper, we combine the degree of membership and a degree of non-membership of members of Intuitionistic Fuzzy Sets via complex numbers to characterize these fuzzy sets. This approach enables extending several concepts such as classical fuzzy sets, Pythagorean fuzzy sets, and complex fuzzy sets. We discuss complex numbers-based set theoretic operations such as union, intersection, and complement. We define the No-Man-Zone (NMZ) set and establish the relation of NMZ characterization with complex numbers. Further, we introduce athematic complex numbers-based operations of intuitionistic fuzzy sets. We show that the square of the absolute of an intuitionistic fuzzy set becomes a Pythagorean fuzzy set. The polar form of an intuitionistic fuzzy set is reduced to a complex fuzzy set.