The Relationship Between The Solutions Of Fuzzy Differential Equations Under Different Meaning

Fuzzy numbers, calculus theory of fuzzy number valued functions, and fuzzy differential equations are important parts of fuzzy mathematics.We study the following problems in this dissertation: two kinds of special fuzzy numbers. Furthermore, the concepts and basic theories of H-differentiability and integral of fuzzy-number-valued functions are added.Then, we intrudact the calculus theory of fuzzy number valued functions.Especially we introduce the concept of relative derivative,and obtain the similar methods of differentiation and integration by parts.Then we can study fuzzy differential equations(systems)under this new frame.In this paper, we research the relation of fuzzy differential equations about the solutions via extension principle and the solutions via differential inclusions. Recently, M. T. Mizukoshi find out the solutions via extension principle of fuzzy differential equations with fuzzy coefficient and initial condition is equal to the solutions via differential inclusions.But T. Allahviranloo research the solutions is not equal under the two meaning in the two dimensional condition, and they give an counter example.But we find that the two solutions are equal under the one dimensional condition, and give the example. We also proof that in the two point boundary value problem of undamped uncertain dynamical systems.