This paper is in the continuation of a well-established line of research in multi-criteria decision making, namely, the development of the basic ELECTRE methodology. In the present study, we make an attempt to enhance the influence of the ELECTRE III method, which was conceived in response to the deficiency that existing variants of the ELECTRE method did not provide a full ordering of the alternatives. ELECTRE III has been recently extended so as to make use of information in the form of intuitionistic fuzzy sets. Although this enhancement has been acclaimed by many scholars, it is nonetheless true that further progresses can be made in the quest of generality. In this research, we develop a two-phase Pythagorean fuzzy version of standard ELECTRE III method, called two-phase Pythagorean fuzzy ELECTRE III (PF-ELECTRE III) approach. It takes full advantage of the capabilities of Pythagorean fuzzy sets (PFS); a successful model that generalizes intuitionistic fuzzy sets in a practical and intuitive way. The group decision support system of PF-ELECTRE III first evaluates the performances of the alternatives characterized by Pythagorean fuzzy numbers. The second stage produces a complete ranking of the alternatives from their evaluations in the first phase. We formulate the approach by defining PF indifference threshold, preference threshold and veto threshold functions which provide a more reliable basis to construct outranking relations. The ranking module of the PF-ELECTRE III method is simplified by computing the concordance credibility, discordance credibility and net credibility degrees of each alternative. A diagrammatic representation of the group decision-supporting system is presented to justify the corresponding step-by-step approach for solving problems. Finally, the haze management problem is solved to verify the applicability of the approach proposed in this paper. The investigation of this model and its performance paves the way to additional generalizations by other models like q-rung orthopair fuzzy sets.

本文是在多准则决策中建立完善的研究路线的基础上的，即基本ELECTRE方法的发展。在当前的研究中，我们试图增强ELECTRE III方法的影响，这是对ELECTRE方法的现有变体不能提供替代方案的完整排序这一缺陷的回应。ELECTRE III最近得到了扩展，以便以直觉模糊集的形式使用信息。尽管这种增强得到了许多学者的好评，但确实可以在追求通用性方面取得进一步的进步。在这项研究中，我们开发了标准ELECTRE III方法的两阶段勾股模糊模型，称为两阶段勾股模糊ELECTRE III（PF-ELECTRE III）方法。它充分利用勾股模糊集（PFS）的功能；一个成功的模型，以实用和直观的方式概括直觉模糊集。PF-ELECTRE III的群体决策支持系统首先评估毕达哥拉斯模糊数表征的替代方案的性能。第二阶段从第一阶段的评估中得出对替代方案的完整排名。我们通过定义PF无差异阈值，偏好阈值和否决阈值函数来制定该方法，这为构建排名关系提供了更可靠的基础。通过计算每个替代方案的一致性可信度，不一致可信度和净可信度，简化了PF-ELECTRE III方法的排名模块。提出了小组决策支持系统的图形表示，以证明解决问题的相应分步方法的合理性。最后，解决了雾度管理问题，以验证本文提出的方法的适用性。对这种模型及其性能的研究为其他模型（例如：q阶邻对模糊集。