Given the problem that the relations among alternatives or criteria cannot be handled well in multicriteria decision making, this paper applies the concept of Pythagorean fuzzy sets to the graph and develops a decision-making approach based on Pythagorean fuzzy graphs (PFGs). First, the weights obtained from the Laplacian energy of PFGs are taken as the subjective weights of criteria. Then, a new Pythagorean fuzzy entropy measure is defined to compute the objective weights of criteria. Meanwhile, a combined weighting method is presented, which makes the criteria weights consist of subjective weights and objective weights. Furthermore, combined weights are applied to the decision-making process and a graph-based Pythagorean fuzzy decision-making method is proposed. Compared with other existing techniques, the proposed approach considers the relations between alternatives and the relations between criteria simultaneously. Finally, an illustrative example is used to verify the approach and demonstrate its effectiveness. The results show that the alternative ranking obtained by the proposed approach is reliable and credible.

中文翻译：

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一种基于毕达哥拉斯模糊集和图论的新型多准则决策方法

针对多准则决策中备选方案或准则之间的关系不能很好处理的问题，本文将毕达哥拉斯模糊集的概念应用到图中，发展了一种基于毕达哥拉斯模糊图（PFGs）的决策方法。首先，将PFG的拉普拉斯能量得到的权重作为标准的主观权重。然后，定义了一个新的毕达哥拉斯模糊熵测度来计算标准的客观权重。同时，提出了一种组合赋权法，使评价指标权重由主观权重和客观权重组成。此外，将组合权重应用于决策过程，并提出了一种基于图的勾股模糊决策方法。与其他现有技术相比，所提出的方法同时考虑备选方案之间的关系和标准之间的关系。最后，一个说明性的例子被用来验证该方法并证明其有效性。结果表明，所提出的方法获得的替代排名是可靠和可信的。