Fuzzy Sets and Systems ( IF 3.9 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.fss.2020.12.021 Zengtai Gong , Zhiyong Xiao
As a key theoretical basis of fuzzy complex analysis, a new representation of fuzzy complex numbers is proposed in this paper which unifies the exponential form, trigonometric form and algebraic form of fuzzy complex numbers, and some arithmetic operations are investigated. The concepts of strong sum and strong difference are defined in order to simplify the addition and subtraction operations of complex fuzzy numbers and establish the calculus theory of fuzzy complex valued functions. The metric between two fuzzy complex numbers, the derivative, differentiability and analyticity of fuzzy complex-valued functions are defined and characterized. The necessary and sufficient conditions of the analyticity of fuzzy complex-valued functions are investigated. Furthermore, the integral of fuzzy complex-valued functions and Cauchy integral theorem are given and discussed.
中文翻译:
模糊复数:表示,运算及其分析
作为模糊复数分析的重要理论基础,本文提出了模糊复数的一种新表示形式,统一了模糊复数的指数形式,三角形式和代数形式,并研究了一些算术运算。定义了强和和强差的概念,以简化复杂模糊数的加减运算,并建立模糊复杂值函数的演算理论。定义了两个模糊复数之间的度量,模糊复值函数的导数,可微性和解析性。研究了模糊复值函数分析的充要条件。此外,