The q-rung orthopair fuzzy set is a powerful and useful tool to deal with uncertainty, but in actual decision-making process, decision-makers are usually required to analyze the actual problem dynamically. Therefore in this paper, we consider the time-series q-rung orthopair fuzzy decision making.First, we introduce the new cosine similarity measure of q-ROFS which combines the cosine similarity measure and the Euclidean distance measure. Then, we combine the advantages of projection method and grey correlation degree, establishing the nonlinear programming model to calculate the weights of attributes. Furthermore, we use the exponential decay model to get the weights formulas of q-ROFS at different times. Then we replace the distance function with grey relational projection and extend TOPSIS method. Based on these, we propose a new MAGDM approach to deal with time-series q-rung orthopair fuzzy problem not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate effectiveness and feasibility of the new method.

中文翻译：

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基于时间序列q-rung orthopair模糊集的多属性群决策方法

q-rung orthopair模糊集是处理不确定性的强大而有用的工具，但在实际决策过程中，通常需要决策者动态地分析实际问题。因此在本文中，我们考虑了时间序列q-rung orthopair模糊决策。首先，我们介绍了结合余弦相似性度量和欧几里德距离度量的q-ROFS新的余弦相似性度量。然后，结合投影法和灰色关联度的优点，建立非线性规划模型来计算属性的权重。此外，我们使用指数衰减模型来获得不同时间 q-ROFS 的权重公式。然后我们用灰色关联投影代替距离函数并扩展TOPSIS方法。基于这些，我们提出了一种新的 MAGDM 方法，不仅从几何的角度而且从代数的角度来处理时间序列 q-rung orthopair 模糊问题。最后，我们给出了一个实际例子来说明新方法的有效性和可行性。