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In this paper, fuzzy neural network (FNN) can be trained with crisp and fuzzy data. The work of this paper is an expansion of the research of fuzzy linear Fredholm integro-differential equations. In this work, we interpret a fuzzy integro-differential equations. In this paper, a novel hybrid method based on FNN and Newton–Cotes methods with positive coefficient for the solution of system of fuzzy linear Fredholm integro-differential equations of the second kind with fuzzy initial values is presented. The problem formulation of the proposed UA is quite straightforward. To obtain the "best-approximated" solution of system of fuzzy linear Fredholm integro-differential equations, the adjustable parameters of PFNN are systematically adjusted by using the learning algorithm. Within this paper, the fuzzy neural network model is used to obtain an estimate for the fuzzy parameters in a statistical sense. Based on the extension principle, a simple algorithm from the cost function of the fuzzy neural network is proposed, in order to find the approximate parameters. We propose a learning algorithm from the cost function for adjusting of fuzzy weights. Here neural network is considered as a part of a larger field called neural computing or soft computing. Finally, we illustrate our approach by some numerical examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy linear programming problems. Recently, fuzzy linear systems are considered by Kumar et al. . In this paper, we employ linear programming (abbreviated to LP) with equality constraints to find a non-negative fuzzy number matrix which satisfies , where and are two fuzzy number matrices. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed. [Copyright &y& Elsevier]

In this paper, a new approach to solve the fuzzy linear system of differential equations based on pseudo-inverse is presented. In this work, we discuss the minimal solution of a system of linear fuzzy differential equations such as $$A\dot{x}(t)=B\dot{x}(t)+Cx(t), x(0)=x_0$$ where A, B, and C are three real m × n matrices and the initial condition x is described by a vector made up of n fuzzy numbers. In this paper, we investigated a necessary and sufficient conditions for the existence fuzzy derivative $$\dot{x}(t)$$ of a fuzzy process x( t) and a necessary and sufficient conditions for the minimal solution vector to be a fuzzy vector, given arbitrary input fuzzy vector x. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a novel hybrid method based on fuzzy neural network for approximate solution of fuzzy linear systems of the form Ax = Bx + d, where A and B are two square matrices of fuzzy coefficients, x and d are two fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution, a simple and fast algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples. [Copyright &y& Elsevier]