Some Properties Of Solutions To Fuzzy Differential Equations On Fuzzy N-cell Number Space

With the booming of modern science, the connection of social science and natural science are getting closer. Compared with the limitation of traditional mathematics which is very certain for one thing. The purpose of fuzzy mathematics is to reflect the characteristics of the material world with uncertainty. In order to use the fuzzy mathematics theory to solve the uncertain model in engineering, control and other fields better, it introduces the idea of fuzzy sets in mathematical modeling, and then it forms the fuzzy differential equations. As an effective tool to describe the uncertain system, the fuzzy differential equations is widely used in many aspects.Domestic and foreign scholars discuss the fuzzy differential equations mainly on ndimensional fuzzy number space and fuzzy number space which has only center. But there is few study involved in the properties of differential equations on fuzzy n-cell number space. As a special kind of n-dimensional fuzzy number, the fuzzy n-cell number is quicker and more convenient compared with other n-dimensional fuzzy number. For the lack of previous study results, this paper mainly studies on the definite solutions problem to fuzzy differential equations on fuzzy n-cell number space, and the work of the paper is as follows:Firstly, this paper studies the initial value problem of autonomous and nonautonomous differential equations on fuzzy n-cell number space. By defining the local Lipschitz condition of the fuzzy value mapping on this space, under this condition, it proves the existence and uniqueness of solutions for the initial value problem to autonomous and non-autonomous fuzzy differential equations respectively by using the contraction mapping. And it defines the concept of maximal extension solution and its domain.Secondly, based on the definition of maximal extension solution for initial value problem and using Gr?nwall Inequality, it proves that the maximal extension solution to non-autonomous fuzzy differential equations is uniformly continuous referring to the initial value under the local Lipschitz condition; and proves that, under the same condition, the maximal extension solution to autonomous fuzzy differential equations on its domain is continuous with two respects when the initial value is zero. Moreover, prove that under certain condition, the maximal extension solution to non-autonomous fuzzy differential equations on its domain is continuous with three respects.Finally, by defining the concept of domain on this space, it proves the connectivity of maximal extension solution domain of initial value problem to autonomous and nonautonomous differential equations on this space.