Fuzzy sets (FSs) are a flexible and powerful tool for reasoning about uncertain situations that cannot be adequately expressed by classical sets. However, these sets fall short in two areas. The first is the reliability of this tool. Z-numbers are an extension of fuzzy numbers that improve the representation of uncertainty by combining two important components: restriction and reliability. The second is the problems that need to be solved simultaneously. Complex fuzzy sets (CFSs) overcome this problem by adding a second dimension to fuzzy numbers and simultaneously adding connected elements to the solution. However, they are insufficient when it comes to problems involving these two areas. We cannot express real-life problems that need to be solved at the same time and require the reliability of the information given with any set approach given in the literature. Therefore, in this study, we propose the complex fuzzy Z-number set (CFZNS), a generalization of Z-numbers and CFS, which fills this gap. We provide the operational laws of CFZNS along with some properties. Additionally, we define two essential aggregation operators called complex fuzzy Z-number weighted averaging (CFZNWA) and complex fuzzy Z-number weighted geometric (CFZNWG) operators. Then, we present an illustrative example to demonstrate the proficiency and superiority of the proposed approach. Thus, we process multiple fuzzy expressions simultaneously and take into account the reliability of these fuzzy expressions in applications. Furthermore, we compare the results with the existing set operations to confirm the advantages and demonstrate the efficiency of the proposed approach. Considering the simultaneous expression of fuzzy statements, this study can serve as a foundation for new aggregation operators and decision-making problems and can be extended to many new applications such as pattern recognition and clustering.

模糊集 (FS) 是一种灵活而强大的工具，用于推理经典集无法充分表达的不确定情况。然而，这些集合在两个方面存在不足。首先是这个工具的可靠性。 Z 数是模糊数的扩展，它通过结合两个重要组成部分来改进不确定性的表示：限制性和可靠性。二是需要同时解决的问题。复杂模糊集 (CFS) 通过向模糊数添加第二个维度并同时向解添加连接元素来克服此问题。然而，当涉及到这两个领域的问题时，它们是不够的。我们无法同时表达需要解决的现实生活问题，并且需要文献中给出的任何既定方法所提供的信息的可靠性。因此，在本研究中，我们提出了复杂模糊 Z 数集（CFZNS），它是 Z 数和 CFS 的推广，填补了这一空白。我们提供 CFZNS 的运行法则以及一些属性。此外，我们定义了两个基本的聚合算子，称为复杂模糊 Z 数加权平均 (CFZNWA) 和复杂模糊 Z 数加权几何 (CFZNWG) 算子。然后，我们提出一个说明性示例来证明所提出方法的熟练程度和优越性。因此，我们同时处理多个模糊表达式，并考虑这些模糊表达式在应用中的可靠性。此外，我们将结果与现有的集合操作进行比较，以确认所提出方法的优点并证明其效率。 考虑到模糊语句的同时表达，这项研究可以作为新的聚合算子和决策问题的基础，并可以扩展到模式识别和聚类等许多新的应用。