The Theory Of Fuzzy Analytic Geometry And It's Application Based On Structured Element

As we all know, mathematical analysis is based on the theoretical system of analytic geometry. So far, the theory of fuzzy analysis has been studied mature, but for the study of fuzzy analytic geometry is still relatively weak. In order to improve the system of fuzzy analysis theories and understand it better, the paper study the theory of fuzzy analytic geometry and its applications.In the paper, bases on the theory of fuzzy structured element, the nature of fuzzy point and fuzzy curve has been discussed, and the theoretical framework of fuzzy analytic geometry has been build. Further more, this paper introduces the applications of fuzzy analytic geometry. Specifically including the following aspects:First of all, based on the definition of two-dimensional (or three-dimensional) fuzzy structured element, the methods of express the fuzzy point has been given, the fuzzy distance between two fuzzy points has been studied. And the article proved that the Fuzzy point space is a metric space, discusses the convergence form of fuzzy points. The article gives two definitions of fuzzy curve, and also the method how to calculate the fuzzy slope of the fuzzy curve. Further more, the nature of fuzzy line has been discussed in this paper. Through the studying of the intersection of a fuzzy line and a general line, this paper gives the solution method of a class fuzzy constraint equation.In terms of application of fuzzy analytic geometry, this paper correspond the fuzzy points and circular fuzzy vector, gives the methods of seeking the sum, difference, and numerical multiplication of fuzzy vector, and prove that the fuzzy vector space is closed for the operations. Further more, the paper studies the projection of fuzzy vector.Finally, this paper gives the definition of fuzzy-valued function's first form curvilinear integral and the first fuzzy value function surface integral. Based on it, through the studying of the projection of fuzzy vector, the paper gets the methods of calculating the fuzzy vector function's curvilinear and surface Integral. Further more, the nature of the fuzzy vector function's curvilinear and surface Integral has been discussed in this paper.