Group decision-making based on complex spherical fuzzy VIKOR approach

The main objective of this study is to set up the foundations of a new model, namely, complex spherical fuzzy (CSF) model that is highly proficient to express the two dimensional ambiguous information. The absence of neutral membership in complex Pythagorean fuzzy sets to express abstinence part of opinion and limitation of spherical fuzzy sets to capture the two dimensional data motivated us to build up the theory of complex spherical fuzzy sets. To establish the ground-breaking CSF model, we elaborate the essential and rudimentary concepts including score degree, accuracy degree and comparison rule. Further, we define the primary operations that serve as helping tools to found four new aggregation operators, namely, complex spherical fuzzy weighted average (CSFWA) operator, complex spherical fuzzy ordered weighted average (CSFOWA) operator, complex spherical fuzzy weighted geometric (CSFWG) operator and complex spherical fuzzy ordered weighted geometric (CSFOWG) operator. These operators are of vital importance in aggregation of complex spherical fuzzy numbers (CSFNs). Moreover, we present a multi-skilled and high potential multi-criteria group decision-making (MCGDM) technique, namely, complex spherical fuzzy VIKOR (CSF-VIKOR) method using the grounds of VIKOR method and motivation of CSF model which is adequate to deal with two dimensional data. The working rule of the proposed technique emphasizes to propose a compromise solution depending upon two focal properties, namely, group utility and individual regret of opponent. We sort the alternatives via the ranking measure by the dint of ascending order. We accomplish the proposed MCGDM strategy by the means of a numerical example in the field of business to rank the objectives of an advertisement on Facebook. We validate the precision and veracity of the proposed strategy by comparing the results with spherical fuzzy VIKOR (SF-VIKOR) method. Finally, we analyze the proposed method to unfold its edge and dominance over the existing approaches.