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In this work an accurate and efficient method is suggested to solve the Fredholm fuzzy integral equations of the second kind. The orthogonal triangular function (TF) based method is first applied to transform the fuzzy Fredholm integral equations to a coupled system of matrix algebraic equations. An iterative algorithm of finite nature is then applied to solve the coupled system to obtain the coefficients used to obtain the form of approximate solution of the unknown functions of the integral problems. Finally, an algorithm is presented to solve the fuzzy integral equation by using the trapezoidal rule. This algorithm is implemented on some numerical examples by using software MATLAB. The obtained numerical results are compared with other numerical method and the exact solutions. The main purpose of this paper is to approximate the solution of linear dimensional fuzzy Fredholm integral equations of the second kind (1D-FFIE-2). We use fuzzy triangular functions (1D-TFs) to replace the Fredholm fuzzy integral with a coupled system of matrix algebraic equations. An iterative algorithm of finite nature is then applied to solve the coupled system to obtain the coefficients used to obtain the form of approximate solution of the unknown functions of the integral problems. Moreover, we prove the convergence of the method. Finally we illustrate this method with some numerical examples to demonstrate the validity and applicability of the technique. In this work an accurate and efficient hybrid technique is suggested to solve the Fredholm fuzzy integral equations of the second kind. First, a two msets of orthogonal triangular basis functions (TFs) method is first used to replace the Fredholm fuzzy integral with a coupled system of matrix algebraic equations. An iterative algorithm of finite nature is then applied to solve the coupled system to obtain the coefficients used to obtain the form of approximate solution of the unknown functions of the integral problems. To illustrate the accuracy and the efficiency of the proposed method, set of numerical examples are solved where obtained numerical results are compared with other numerical method and the exact solutions.

An Accurate and Efficient Technique for Approximating Fuzzy Fredholm Integral Equations of the Second Kind Using Triangular Functions