Study On Initial Value Problem Of Fuzzy Linear Differential Algebraic System

Now,fuzzy mathmatics is widely used in many fields such as physics dynamics,engineering technology,electric power system and so on,many complex fuzzy problems that can not be described by linear differential algebraic system can be described by fuzzy linear differential algebraic system.From the point of view of theory and application,fuzzy linear differential algebraic system has important research value and significance.In this paper,we use the generalized Hukuhara derivative,the extension principle and the structured element method to solve the initial value problem of fuzzy linear differential algebraic system.First,fuzzy valued function is direct defined by the generalized Hukuhara derivative.Based on the generalized Hukuhara derivative,the n dimensional fuzzy linear differential algebraic system is equivalently transformed into 2~n deterministic linear differential algebraic systems with the same solution,a numerical example is given to illustrate the effectiveness of the proposed method.Second,extension principle does not involve the derivative of fuzzy valued function in the process of solving the system.The fuzzy solution of fuzzy linear differential algebraic system is obtained by extending the exact solution of the linear differential algebraic system,and discusses the relationship between the fuzzy solution of extension principle and the fuzzy solution of generalized Hukuhara derivative,points out under certain conditions,the solutions are consistent based on these two methods.The above two methods for solving the system is not the analytic representation of fuzzy solutions.Finally,the analytic solution of fuzzy solution of fuzzy linear differential algebraic system is given by means the fuzzy structured element method.The examples is given to show the effectiveness and feasibility of the fuzzy structured element method for solving the system.