The Properties Of Complex Fuzzy Process And Complex Fuzzy Calculus

In the field of fluid dynamics, information technology, electrical science and so on, some physical quantities are often expressed in complex number, such as the current, cycle and two-dimensional potential flow etc. Because of experimental conditions and the methods of measure, some physical quantities cannot be accurately quantified indeed. However in the actual research they can only be estimated by subjective experience. In the current study complex random variable has been used to describe these quantities. However through many research and practice scholars realized probability theory does not solve all the problems. Sometimes the complex random does not conform to the actual situation. In 2007, Liu put forward credibility theory which is a new tool for researching subjective fuzzy phenomena. On the basis of this, Yang defined complex fuzzy variable; Qin came up with some properties of complex fuzzy process. But the nature of complex fuzzy process is not perfect enough and the properties of complex fuzzy calculus also need further research. In order to lay a better mathematical theory foundation for fluid dynamics, information technology, electrical science, under the framework of the credibility theory and complex fuzzy theory this paper studies the convergence and dependence of complex fuzzy variable, the properties of complex fuzzy calculus and the concept of complex index process is proposed.The structure of this paper is as follows: Firstly, the basic concepts of fuzzy process and complex fuzzy process are given. Secondly the convergences of complex fuzzy variable are raised. The properties of complex fuzzy process are proposed. At last the properties of complex fuzzy calculus are put forward.