Due to insufficient information in multi-criteria decision-making (MCDM) problems, the decision values given by experts are often fuzzy and uncertain. As an extension of Pythagorean fuzzy set (PFS), interval-valued Pythagorean fuzzy (IPF) set is a more effective and powerful tool to handle fuzzy information in decision problems. But, there are two key issues that needed to be solved: weights of experts in the IPF environment and IPF aggregation operators. For these issues, a two-stage MCDM method is constructed in the IPF environment. In the first stage, a novel method for determining the weights of experts is proposed by introducing IPF set (IPFS) into social networks. To do that, the concepts of trust function (TF) and trust score (TS) in the IPF environment are defined to obtain the objective weights of experts. Meanwhile, the subjective weights of experts are obtained from the number of experts. Afterward, the objective weight and subjective weight of each expert are combined to derive the weight of each expert. In the second stage, a novel weighted sum model (WSM) with novel IPF aggregation operators is constructed to rank alternatives. Considering the psychological behavior of experts, that is, self-confidence level, four IPF aggregation operators with self-confidence levels are defined, namely, the self-confidence interval-valued Pythagorean fuzzy weighted averaging (SC-IPFWA) and ordered weighted averaging (SC-IPFOWA) operator, the self-confidence interval-valued Pythagorean fuzzy weighted geometric (SC-IPFWG) and ordered weighted geometric (SC-IPFOWG) operator. Finally, a numerical case is used to verify the effectiveness of the proposed two-stage MCDM method.

由于多准则决策（MCDM）问题中的信息不足，专家给出的决策值通常是模糊且不确定的。作为勾股勾股模糊集（PFS）的扩展，区间值勾股勾股模糊（IPF）集是处理决策问题中的模糊信息的一种更有效，更强大的工具。但是，有两个关键问题需要解决：IPF环境中的专家和IPF聚合运算符的权重。对于这些问题，在IPF环境中构造了两阶段的MCDM方法。在第一阶段，通过将IPF集（IPFS）引入社交网络，提出了一种确定专家权重的新方法。为此，定义IPF环境中的信任函数（TF）和信任分数（TS）的概念以获得专家的客观权重。与此同时，专家的主观权重是从专家人数中得出的。然后，将每个专家的客观权重和主观权重相加以得出每个专家的权重。在第二阶段，构建具有新颖IPF聚合运算符的新颖加权和模型（WSM）来对替代方案进行排名。考虑到专家的心理行为，即自信心水平，定义了四个具有自信心水平的IPF聚合算子，即自信心区间值勾股勾股模糊加权平均（SC-IPFWA）和有序加权平均（ SC-IPFOWA）运算符，自信区间值毕达哥拉斯模糊加权几何（SC-IPFWG）和有序加权几何（SC-IPFOWG）运算符。最后，通过数值算例验证了所提出的两阶段MCDM方法的有效性。