Affiliations: School of Economics and Management, Beihang University, Beijing, China | School of Reliability and Systems Engineering, Beihang University, Beijing, China
Note: [] Corresponding author. Meilin Wen, School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China. E-mail: [email protected]
Abstract: A complex stochastic process is a fundamental connection between two-dimensional stochastic processes. Similarly, a complex fuzzy process will connect two fuzzy processes to describe the spacial dynamic fuzzy phenomena. In this paper, we first give the formal definitions of complex fuzzy process and complex Liu process. And then the complex differential and complex Liu integral of complex Liu process are also studied in this paper. Especially, some properties of analytic functions of complex Liu process are proved. Finally, complex fuzzy differential equations are proposed as the extension of general fuzzy differential equation. The obtained results provide fundamentals and promote the development of fuzzy calculus.
Keywords: Fuzzy process, credibility measure, fuzzy variable, complex Liu process, Liu process
