Fuzzy set theory and fuzzy logics are the powerful mathematical tools to model the imprecision and vagueness. In this research, the novel concept of complex Pythagorean fuzzy relation (CPFR) is introduced. Furthermore, the types of CPFRs are explained with appropriate examples such as CPF composite relation, CPF equivalence relation, CPF order relation, and CPF equivalence classes. Moreover, numerous results and interesting properties of CPFRs are discussed in detail. Furthermore, the impacts of economic parameters over each other are studied through the proposed concepts of CPFRs. In addition, the application also discusses the effects of economic parameters of one country over the other countries’ economic parameters.

中文翻译：

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用复杂勾股模糊信息概念分析经济关系

模糊集合论和模糊逻辑是对不精确性和模糊性进行建模的有力数学工具。在这项研究中，引入了复杂勾股模糊关系（CPFR）的新概念。此外，通过CPF复合关系、CPF等价关系、CPF阶关系、CPF等价类等适当的例子对CPFR的种类进行了说明。此外，还详细讨论了 CPFR 的众多结果和有趣的特性。此外，通过提议的 CPFR 概念研究了经济参数对彼此的影响。此外，该申请还讨论了一国经济参数对其他国家经济参数的影响。