A Novel Score Function Determined by the Residual Sector Area on PFNs Space and Its Application in Fuzzy Decision-Making

Intelligent computing has distinct cognitive characteristics, especially when dealing with some multi-attribute group decision-making questions, it is regarded as a human behavior based on cognition. Pythagorean fuzzy set (PFS) is not only an extension of intuitionistic fuzzy set (IFS), but also can handle some fuzzy decision-making problems of multi-attribute information on a larger scale, especially some new methods have been rapidly spread and developed in decision-making science. In this paper, some defects in the existing ranking criteria for Pythagorean fuzzy numbers (PFNs) were pointed out through some counterexamples, the main reasons of these flaws are analyzed, so that all IFNs are unified into PFNs space through coordinate transformation. Secondly, a novel improved score formula and ranking method are proposed by the residual sector area (RSA) and hesitancy degree of PFNs in a geometric background, and the rationality of this ranking criterion is further demonstrated through rigorous mathematical methods, and then the fundamental properties of the score function are discussed. Finally, the superiority of the novel score function was interpreted through comparison and analysis with other existing seven score formulas, and the new score formula was applied to multi-attribute group decision-making problems through an example, and the superiority of the novel method was fully displayed. In fact, the proposed method achieves a perfect ranking of all PFNs, especially for the equivalent PFNs, it can be achieved precise comparison or ranking, which overcomes some flaws of other methods, and ending the confusion caused by the independent ranking of IFNs and PFNs.