New Ways Of Study For Fuzzy Complex Analysis

Fuzzy analysis is a very important component of fuzzy mathematics, which includes fuzzy real analysis and fuzzy complex analysis. In recent decades, the study of fuzzy analysis have had both the rapid development of the deep-rooted. However, the operations of complex fuzzy numbers and complex fuzzy set-valued function are based on the extension principle in fuzzy complex analysis. And differential and integral of complex fuzzy set-valued function are also based on interval-valued function of the corresponding results of the use of representation theorem given in the form. The common features of these operations are all the results of traversing the corresponding demand, or union operation on all the results which are thatλtraverses the interval of [0 , 1]. These operations to traverse the process have brought a lot of inconvenience. To a certain extent, they also limits the application of fuzzy mathematics. So it is necessary to find other simple and effective calculations. We with the aid in fuzzy structured element that Guo Sicong proposed am examined of complex fuzzy numbers complex fuzzy set-valued function and its calculus in fuzzy complex analysis in detail. It simplifies the calculation of fuzzy complex analysis. And it provides a new way for fuzzy complex analysis, theory and application. The organization of this dissertation is as follows:1) We improve the basic theory of fuzzy numbers and fuzzy-valued function based on the fuzzy structured element. We give the definition of the size of the comparison of fuzzy numbers. And we discusse the nature of the fuzzy number Q -distance and limit. We obtain several new concepts and theorems of analysis mathematics, and prove with the intuitive and easy methods.2) We study the basic theory of the complex fuzzy numbers based on fuzzy structured element. We give the manifestations of the complex fuzzy numbers based on fuzzy structured element. We construct the complex fuzzy number Q-distance formula and study its properties. And we give the concept of the complex fuzzy number depending on the Q -distance and study the nature of its limits. Finally we discuss the divergence of a series of complex fuzzy number. It is determined by the divergence of four series of ordinary numbers entirely.3) We study the basic theory of the complex fuzzy set-valued function based on fuzzy structure element. We give the manifestations of the complex fuzzy set-valued function based on fuzzy structured element. And we study the calculus of the complex fuzzy set-valued function. We establish a new bridge between the calculus of the complex fuzzy set-valued function and real function.