Although intuitionistic fuzzy preference relations have become powerful techniques to express the decision makers' preference information over alternatives or criteria in group decision making, some limitations of them are pointed out in this paper, then they are overcame by developed the group decision making with Pythagorean fuzzy preference relations (PFPRs). Specially, we provide a partial order on the set of all the PFPRs, based on which, a deviation measure is defined. Then, we check and reach the acceptably multiplicative consistency and consensus of PFPRs associated with the partial order and mathematical programming. Concretely, acceptably multiplicative consistent PRPRs are defined by the deviation between a given PFPR and a multiplicative consistent PFPR constructed by a normal Pythagorean fuzzy priority vector. Then acceptable consensus of a collection of PFPRs is defined by the deviation of each PFPR and the aggregated result from symmetrical Pythagorean fuzzy aggregation operators. Based on which, a method which can simultaneously modify the unacceptable consistency and consensus of PFPRs in a stepwise way is provided. Particularly, we also prove that the collective PFPR obtained by aggregating several individual acceptably consistent PFPRs with various symmetric aggregation operators is still acceptably consistent. Then, a procedure is provided to solve group decision making with PRPRs and a numerical example is given to illustrate the effectiveness of our method.

中文翻译：

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群决策中基于偏序的勾股模糊偏好关系的一致性和一致性研究

尽管直觉模糊偏好关系已经成为在群体决策中表达决策者对备选方案或标准的偏好信息的有力技术，但本文指出了它们的一些局限性，然后通过发展了勾股模糊的群体决策来克服这些局限性。偏好关系 (PFP​​R)。特别地，我们在所有 PFPR 的集合上提供了偏序，在此基础上定义了偏差度量。然后，我们检查并达到与偏序和数学规划相关的 PFPR 的可接受的乘法一致性和共识。具体而言，可接受的乘法一致 PRPR 由给定 PFPR 与由正常勾股模糊优先级向量构造的乘法一致 PFPR 之间的偏差定义。然后通过每个 PFPR 的偏差和对称毕达哥拉斯模糊聚合算子的聚合结果来定义一组 PFPR 的可接受共识。在此基础上，提供了一种可以同时逐步修改PFPRs不可接受的一致性和共识的方法。特别是，我们还证明了通过聚合几个单独的可接受一致的 PFPR 与各种对称聚合算子获得的集体 PFPR 仍然是可接受的一致。然后，提供了用 PRPR 解决群决策问题的程序，并给出了一个数值例子来说明我们方法的有效性。提供了一种可以同时逐步修改 PFPR 不可接受的一致性和共识的方法。特别是，我们还证明了通过聚合几个单独的可接受一致的 PFPR 与各种对称聚合算子获得的集体 PFPR 仍然是可接受的一致。然后，提供了用 PRPR 解决群决策问题的程序，并给出了一个数值例子来说明我们方法的有效性。提供了一种可以同时逐步修改 PFPR 不可接受的一致性和共识的方法。特别是，我们还证明了通过聚合几个单独的可接受一致的 PFPR 与各种对称聚合算子获得的集体 PFPR 仍然是可接受的一致。然后，提供了用 PRPR 解决群决策问题的程序，并给出了一个数值例子来说明我们方法的有效性。