In some real-world situations, Pythagorean fuzzy sets are more powerful and effective than intuitionistic fuzzy sets to describe vague and uncertain information, and there are many Pythagorean fuzzy information systems for conflicts in which attitudes of agents on issues are depicted by Pythagorean fuzzy numbers. In this paper, we first provide the concepts of positive, neutral, and negative alliances with two thresholds and employ examples to illustrate how to compute positive, neutral, and negative alliances in Pythagorean fuzzy information systems for conflicts. Then, we focus on three-way conflict analysis based on the Bayesian minimum risk theory and explore examples to show how to compute the positive, neutral, and negative alliances with a Pythagorean fuzzy loss function given by an expert. Finally, we study how to calculate positive, neutral, and negative alliances with group decision theory and take examples to demonstrate how to construct the positive, neutral, and negative alliances with a group of Pythagorean fuzzy loss functions given by more experts.

中文翻译：

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基于毕达哥拉斯模糊集理论的三向群体冲突分析


在一些现实情况下，毕达哥拉斯模糊集比直觉模糊集更强大、更有效地描述模糊和不确定的信息，并且有许多针对冲突的毕达哥拉斯模糊信息系统，其中代理人对问题的态度由毕达哥拉斯模糊数来描述。在本文中，我们首先提供具有两个阈值的正联盟、中立联盟和负联盟的概念，并举例说明如何在毕达哥拉斯模糊信息系统中计算冲突的正联盟、中立联盟和负联盟。然后，我们重点关注基于贝叶斯最小风险理论的三向冲突分析，并探索示例来展示如何使用专家给出的毕达哥拉斯模糊损失函数来计算正联盟、中立联盟和负联盟。最后，我们研究如何用群决策理论计算正联盟、中性联盟和负联盟，并举例说明如何用更多专家给出的一组毕达哥拉斯模糊损失函数来构造正联盟、中性联盟和负联盟。