Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process

Complex intuitionistic fuzzy set (CIFS) is a distinctive intuitionistic fuzzy set (IFS) in which the membership degrees are determined on the unit disc of the complex plane and can more clearly express the imprecision and ambiguity in the data. The prevailing studies on IFS deal with the data over the subset of a real number and hence there is a sacrifice of some information during the method under certain conditions. As an alteration to these, CIFS characterized with supplementary terms in membership degrees called as phase terms and hence examine two-dimensional data concurrently in a single set. To get full utilization of these assets, in this paper, the aim of the practice is classified into two turns: (i) to define the possibility degree measure to order the numbers, and (ii) to define some novel operational laws and aggregation operators (AOs) to aggregate the various choices over CIFS environment. The beneficial features of the proposed weighted averaging and geometric AOs are addressed. Finally, a decision-making approach is extended for the multicriteria decision-making problem with complex intuitionistic fuzzy information, in which weights are managed objectively. A practical illustration is furnished to address the availability and advantages of the proposed method by comparison with some existing methods.