Fuzzy sets and fuzzy logics are used to model events with imprecise, incomplete, and uncertain information. Researchers have developed numerous methods and techniques to cope with fuzziness or uncertainty. This research intends to introduce the novel concepts of complex neutrosophic relations (CNRs) and its types based on the idea of complex neutrosophic sets (CNSs). In addition, these concepts are supported by suitable examples. A CNR discusses the quality of a relationship using the degree of membership, the degree of abstinence, and the degree of nonmembership. Each of these degrees is a complex number from the unit circle in a complex plane. The real part of complex-valued degrees represents the amplitude term, while the imaginary part represents the phase term. This property empowers CNRs to model multidimensional variables. Moreover, some interesting properties and useful results have also been proved. Furthermore, the practicality of the proposed concepts is verified by an application, which discusses the use of the proposed concepts in statistical decision-making. Additionally, a comparative analysis between the novel concepts of CNRs and the existing methods is carried out.

中文翻译：

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复杂中智环境下基于统计决策的经济关系评价

模糊集和模糊逻辑用于对具有不准确，不完整和不确定信息的事件进行建模。研究人员已经开发出许多方法和技术来应对模糊性或不确定性。本研究旨在基于复杂中智集合（CNSs）的思想介绍复杂中智关系（CNRs）的新概念及其类型。此外，适当的示例可支持这些概念。CNR使用隶属度，禁欲度和非隶属度来讨论关系的质量。这些度数中的每一个都是从复数平面中的单位圆开始的复数。复数值度的实部表示幅度项，而虚部表示相位项。此属性使CNR可以对多维变量进行建模。而且，还证明了一些有趣的特性和有用的结果。此外，提出的概念的实用性由一个应用程序验证，该应用程序讨论了提出的概念在统计决策中的使用。另外，对CNR的新概念和现有方法进行了比较分析。