Novel similarity measures and multi-expert TOPSIS method using picture m-polar fuzzy sets

Abstract

In this paper, we give a new notion of the picture m-polar fuzzy sets (Pm-PFSs) (i.e, combination between the picture fuzzy sets (PFSs) and the m-polar fuzzy sets (m-PFSs)) and study several of the structure operations including subset, equal, union, intersection, and complement. After that, the basic definitions, theorems, and examples on Pm-PFSs are explained. Also, the certain distance between two Pm-PFSs and a novel similarity measure for Pm-PFSs based on distances are defined. MCDM is animated for Pm-PFS data that take into account the distances for the best alternative (solution) by proposed an application of similarity measure for Pm-PFSs in decision-making. Finally, we construct a new methodology to extend the TOPSIS to Pm-PFS in which capable of different objects recognizing belonging to the same family and illustrate its applicability via a numerical example.