Perfect score function in picture fuzzy set and its applications in decision-making problems

Abstract

The picture fuzzy set (PFS) is a more frequent platform for describing the degree of positive, neutral, and negative membership functions that generalizes the concept of fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). Neutrality is a crucial component of PFS, and the score function plays a crucial role in ranking the alternatives in decision-making situations. In the decision-making process, some researchers concentrate on the various aggregation operators’ development while ignoring the development of score functions. This factor causes several errors in the existing score function. If there are two separate picture fuzzy numbers (PFNs), there should be two different scores or accuracy values. Some researchers failed to rank the alternatives when the score and accuracy values for various PFNs were equal. To overcome the shortcomings, we proposed the perfect score function in this paper for ranking PFNs and introduced strong and weak PFSs. The shortcoming of the existing score function in PFNs has been highlighted in this paper. Furthermore, the decision-making approach has been depicted based on the proposed score function, and real-world applications have been shown by ranking the COVID-19 affected regions to demonstrate its efficacy.