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.

智能计算具有鲜明的认知特征，特别是在处理一些多属性群体决策问题时，被视为基于认知的人类行为。毕达哥拉斯模糊集（PFS）不仅是直觉模糊集（IFS）的扩展，而且可以在更大范围内处理一些多属性信息的模糊决策问题，特别是一些新方法在国内外得到了迅速传播和发展。决策科学。本文通过反例指出了现有毕达哥拉斯模糊数(PFNs)排序标准的一些缺陷，并分析了这些缺陷的主要原因，从而通过坐标变换将所有的IFNs统一到PFNs空间中。其次，在几何背景下，根据PFN的残差扇区面积（RSA）和犹豫度，提出了一种新颖的改进评分公式和排序方法，并通过严格的数学方法进一步证明了该排序标准的合理性，进而证明了该排序标准的基本性质讨论了评分函数。最后，通过与现有的其他7种评分公式的比较分析，阐释了新评分函数的优越性，并通过实例将新评分公式应用于多属性群决策问题，说明了新方法的优越性。完全显示出来。事实上，该方法实现了所有PFN的完美排序，特别是对于等效的PFN，可以实现精确的比较或排序，克服了其他方法的一些缺陷，结束了IFN和PFN独立排序带来的混乱。