One of the most powerful tools to operate imprecision is bipolar complex fuzzy sets (BCFSs), which is an enlargement of bipolar fuzzy sets (BFSs) as well as complex fuzzy sets (CFSs). This paper deals with an integrated MULTIMOORA (multi-objective optimization on the basis of ratio analysis plus full multiplicative form) framework as a generalization of fuzzy MULTIMOORA procedure to assess the multi-criteria decision-making (MCDM) problems with BCFSs. We develop BCF-Archimedean power weighted (ordered weighted) arithmetic and geometric aggregation operators (AOs) and discuss their properties from this point of view. The proposed Archimedean power-weighted AOs can eliminate the influence of extreme evaluating criteria values from some biased experts with different preference attitudes under the BCF setting. Afterward, we put forward an integrated MULTIMOORA algorithm based on the proposed AOs, where criteria weights are estimated using the CRITIC (criteria importance through inter-criteria correlation) method, which is a well-known objective weighting method based on aggregated score values of options, intensity contrast of every criteria and conflict among attributes. In the proposed methodology, criteria values are aggregated based on the MULTIMOORA method that involves three sub-methods: the ‘ratio system’, the ‘reference point’ and the ‘full multiplicative form’ and thus takes less computational time, minimum mathematical evaluations and bears good stability. In the following, third-party reverse logistics providers' (3PRLP) selection problem is brought into consideration to manifest the sufficiency of the developed methodology. At the end of this study, we draw attention to a comparison between the proposed decision-making approach with the corresponding BCF-CRITIC-TOPSIS and BCF-CRITIC-WASPAS methods.

处理不精确性的最强大工具之一是双极复杂模糊集 (BCFS)，它是双极模糊集 (BFS) 和复杂模糊集 (CFS) 的扩展。本文将综合 MULTIMOORA（基于比率分析加全乘法形式的多目标优化）框架作为模糊 MULTIMOORA 程序的推广，以评估 BCFS 的多标准决策 (MCDM) 问题。我们开发了 BCF-阿基米德幂加权（有序加权）算术和几何聚合算子 (AO)，并从这个角度讨论了它们的属性。所提出的阿基米德幂加权 AOs 可以消除 BCF 设置下一些具有不同偏好态度的偏见专家的极端评估标准值的影响。之后，我们提出了基于所提出的 AOs 的集成 MULTIMOORA 算法，其中使用 CRITIC（通过标准间相关性的标准重要性）方法来估计标准权重，这是一种众所周知的基于选项、强度的聚合得分值的客观加权方法每个标准的对比和属性之间的冲突。在提议的方法中，标准值基于涉及三个子方法的 MULTIMOORA 方法聚合：“比率系统”、“参考点”和“完全乘法形式”，因此需要更少的计算时间、最少的数学评估和具有良好的稳定性。在下文中，第三方逆向物流供应商（3PRLP）的选择问题被考虑在内，以证明所开发方法的充分性。