The concept of Pythagorean fuzzy (PF) sets represents a superior tool to model complex uncertainties in an ambiguous and equivocal decision‐making framework. In consideration of the significant capacity for exhibiting the uncertainty of subjective appraisals and estimations under the aegis of the PF theory, this paper presents a simple‐to‐operate decision‐making approach that is grounded in some beneficial concepts of original likelihood functions and measurements of dominating and dominated characters. On the strength of beta distributions, this paper seeks to propound new notions of PF likelihood functions and likelihood‐oriented dominating/dominated characters and to launch an exploitable multiple criteria evaluation method by means of a dominance ordering model for treating decision analysis within PF environments. This paper initiates an efficient beta distribution‐based approach to the construction of novel PF likelihood functions that can quantify the possibility degrees of outranking and outranked relationships between Pythagorean membership grades. The applicable satisfaction and dissatisfaction estimations are established on the likelihood‐oriented dominating and dominated characters, respectively. Furthermore, this paper formulates a straightforward dominance ordering model to obtain the ultimate dominance ranking orders of candidate alternatives and accomplish multiple criteria decision‐making issues involving complicated uncertainty. A financing decision‐making problem concerning working capital requirements is investigated to validate the application results using the advanced methodology. The real‐world application is implemented to examine the reasonableness and efficacy of the established techniques. Moreover, comparative studies through the utility of a sensitivity analysis are performed to demonstrate the efficacy and merits of the dominance ordering model. The comparison results manifest that the initiated methodology is an advantageous and reliable decision‐making technique that can enhance the methodological development regarding the multiple criteria evaluation model under PF uncertainty. Finally, recommendations for future research directions are also presented in the conclusions.

中文翻译：

---

不确定多准则决策支持框架中基于β分布的毕达哥拉斯模糊似然函数及其优势排序模型

毕达哥拉斯模糊（PF）集的概念代表了一种在模棱两可的决策框架中对复杂不确定性进行建模的高级工具。考虑到在PF理论的支持下具有表现主观评估和估计不确定性的强大能力，本文提出了一种简单易行的决策方法，该方法基于一些原始的似然函数和度量的有益概念。支配和支配的角色。关于贝塔分布的强度，本文试图提出PF似然函数和面向似然性的主导/主导特征的新概念，并借助优势排序模型来启动可利用的多准则评估方法，以处理PF环境中的决策分析。本文提出了一种基于Beta分布的有效方法来构造新颖的PF似然函数，该函数可以量化勾股隶属度等级之间排名过高和排名过高的关系的可能性程度。分别在面向似然性的主导和主导特征上建立适用的满意度和不满意估计。此外，本文提出了一种简单的优势排序模型，以获取候选替代方案的最终优势排名顺序，并完成涉及复杂不确定性的多准则决策问题。研究了与营运资金需求有关的融资决策问题，以使用高级方法论验证应用结果。实际应用程序用于检查已建立技术的合理性和有效性。此外，通过敏感性分析的实用性进行了比较研究，以证明优势排序模型的有效性和优点。比较结果表明，所提出的方法学是一种有利且可靠的决策技术，可以在PF不确定性条件下促进多准则评价模型的方法学发展。最后，结论中还提出了对未来研究方向的建议。比较结果表明，所提出的方法学是一种有利且可靠的决策技术，可以在PF不确定性条件下促进多准则评价模型的方法学发展。最后，结论中还提出了对未来研究方向的建议。比较结果表明，所提出的方法学是一种有利且可靠的决策技术，可以在PF不确定性条件下促进多准则评价模型的方法学发展。最后，结论中还提出了对未来研究方向的建议。