The recently proposed q-rung orthopair fuzzy set, which is characterized by a membership degree and a non-membership degree, is effective for handling uncertainty and vagueness. This paper proposes the concept of complex q-rung orthopair fuzzy sets (Cq-ROFS) and their operational laws. A multi-attribute decision making (MADM) method with complex q-rung orthopair fuzzy information is investigated. To aggregate complex q-rung orthopair fuzzy numbers, we extend the Einstein operations to Cq-ROFSs and propose a family of complex q-rung orthopair fuzzy Einstein averaging operators, such as the complex q-rung orthopair fuzzy Einstein weighted averaging operator, the complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator, the generalized complex q-rung orthopair fuzzy Einstein weighted averaging operator, and the generalized complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator. Desirable properties and special cases of the introduced operators are discussed. Further, we develop a novel MADM approach based on the proposed operators in a complex q-rung orthopair fuzzy context. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

最近提出的q-阶邻对模糊集具有隶属度和非隶属度的特征，对于处理不确定性和模糊性是有效的。本文提出了复杂的q-阶邻对模糊集（Cq-ROFS）的概念及其操作律。研究了带有复杂q-阶邻态对模糊信息的多属性决策（MADM）方法。为了聚合复杂的q阶正交对数模糊数，我们将Einstein运算扩展到Cq-ROFS，并提出了一组复杂的q阶正交对模糊爱因斯坦平均算子，例如复杂的q阶邻对模糊爱因斯坦加权平均算子。 q阶正交对对模糊爱因斯坦有序加权平均算子，广义复q阶对对模糊爱因斯坦加权平均算子，广义复阶r-对邻模糊Einstein有序加权平均算子。讨论了引入的运算符的理想属性和特殊情况。此外，我们在复杂的q阶邻位对模糊上下文中基于拟议的算子开发了一种新颖的MADM方法。通过与现有方法的详细比较，提供了数值示例，以证明所提方法的有效性和优越性。