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.