Generalized Similarity Operator for Intuitionistic Fuzzy Sets and its Applications Based on Recognition Principle and Multiple Criteria Decision Making Technique

Abstract

Many complex real-world problems have been resolved based on similarity operators under intuitionistic fuzzy sets (IFSs). Numerous authors have developed intuitionistic fuzzy similarity operators (IFSOs) but with some setbacks, which include imprecise results, omission of hesitation information, misleading interpretations, and outright violations of metric axioms of similarity operator. To this end, this article presents a newly developed similarity operator under IFSs to ameliorate the itemized setbacks noticed with the hitherto similarity operators. To buttress the validity of the new similarity operator, we discuss its properties in alliance with the truisms of similarity. In addition, we discuss some complex decision-making situations involving car purchase selection process, pattern recognition, and emergency management using the new similarity operator based on multiple criteria decision making (MCDM) technique and recognition principle, respectively. Finally, comparative studies are presented to argue the justification of the new similarity operator. In short, the novelty of this work includes the evaluation of the existing IFSOs to isolate their fault lines, development of a new IFSO technique with the capacity to resolve the fault lines in the existing techniques, elaboration of some properties of the newly developed IFSO, and its applications in the solution of disaster control, pattern recognition, and the process of car selection for purchasing purpose based on the recognition principle and MCDM.