Some Operations on Complex Atanassov's Intuitionistic Fuzzy Sets

Several innovative uncertainty sets were introduced recently. Complex Atanassov's intuitionistic fuzzy set (CAIFS) is one of these uncertainty sets, where Atanassov's intuitionistic fuzzy membership and non-membership functions take values in the unit circle in the complex plane. In this paper, some operations are generalised to the case of CAIFS. Two main operations square and lozenge are introduced and various properties are investigated. Also, we conclude the advantage from generalising these two operations to the realm of complex numbers, by finding out a relationship between the concepts of CAIFS and complex fuzzy sets (CFS).