Q-rung orthopair fuzzy (q-ROF) set is one of the powerful tools for handling the uncertain multi-criteria decision-making (MCDM) problems, various MCDM methods under q-ROF environment have been developed in recent years. However, most existing studies merely concerned about the relationship between the criteria but they have not investigated the interactions between membership function and non-membership function. To explore the multiple heterogeneous relationships among membership functions and criteria, we propose a novel decision algorithm based on q-ROF set to deal with these using interactive operators and Maclaurin symmetric mean (MSM) operators. Specifically, the new interaction laws in the membership pairs of q-ROF sets are explained, and their properties are analyzed as the initial stage. Then, taking into account the influence of two or more factors on decision analysis, a q-ROF interaction Maclaurin symmetry mean (q-ROFIMSM) operator is formed based on the proposed interaction law to identify these factors’ interrelationship. Thirdly, based on the proposed operator with q-ROF information, a MCDM algorithm is developed and illustrated by numerical examples. An analysis of the feasibility, sensitivity, and superiority of the proposed framework is provided to validate our proposed method.

Q阶邻对模糊（q-ROF）集是处理不确定的多准则决策（MCDM）问题的强大工具之一，近年来开发了各种在q-ROF环境下的MCDM方法。然而，大多数现有研究仅关注准则之间的关系，而没有研究隶属函数和非隶属函数之间的相互作用。为了探索隶属函数和准则之间的多种异构关系，我们提出了一种基于q-ROF集的新颖决策算法，以使用交互式算子和Maclaurin对称均值（MSM）算子来处理这些问题。具体来说，解释了q-ROF集成员对中的新交互定律，并分析了它们的性质作为初始阶段。然后，考虑到两个或两个以上因素对决策分析的影响，基于拟议的相互作用定律形成了q-ROF相互作用麦克劳林对称均值（q-ROFIMSM）算子，以识别这些因素的相互关系。第三，基于提出的具有q-ROF信息的算子，开发了MCDM算法，并通过数值实例进行了说明。对所提出框架的可行性，敏感性和优越性进行了分析，以验证我们提出的方法。