Nader Biranvand - Department of Mathematics, Faculty of Basic Sciences Imam Ali University, Tehran, Iran
Somayeh Ezadi - Department of statistics, Tehran North Branch, Islamic Azad University, Tehran, Iran
Ashkan Moradi - Department of Mathematics, Islamic Azad University of Sama Kermanshah Branch, Kermanshah, Iran

In this work, we have the general form of a First-Order differential equation based Z-Valuations. Then a new method for solving these equations using generalized neural networks offer. The proposed method consists of a function is based on Z-Valuations. that s mean, ??(Z Tt)=(?AT?(?t),?BT ?(?t)), The first component,BT(?t), is a restriction (constraint) on the values which a real-valued uncertain variable,AT (?t ), is allowed to take. The second componentis a measure of reliability (certainty) of the first component. Since the function values and are fuzzy. We use the technique of α- cutting, both the above functions will be converted to real functions. that s mean, ?ZT?(t)=((AT1?1(?t),?AT2?2(t)),(BT1(t),B T2(?t))). Then, using the method of least squares error, we trained neural network so that the solution proposed is a convenient approximation of the exact answer. An example is shown in a proposed method, an appropriate method to approximate the original answer.

Fuzzy Numbers, Z-numbers, First-Order differential equation, Neural Network