Computational and Applied Mathematics Journal 2015; 1(3): 67-71 Published online April 20, 2015 (http://www.aascit.org/journal/camj) Keywords Fuzzy Number, Parametric Form of a Fuzzy Number, Fuzzy Integral Equations, Homotopy Analysis Method, Approximate Solution, Simple Algorithm Received: March 2, 2015 Revised: March 16, 2015 Accepted: March 17, 2015 Solving a System of Fuzzy Integral Equations by an Analytic Method Maryam Mosleh, Mahmood Otadi * Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran Email address Maryammosleh79@yahoo.com (M. Mosleh), mahmoodotadi@yahoo.com (M. Otadi), otadi@iaufb.ac.ir (M. Otadi) Citation Maryam Mosleh, Mahmood Otadi. Solving a System of Fuzzy Integral Equations by an Analytic Method. Computational and Applied Mathematics Journal. Vol. 1, No. 3, 2015, pp. 67-71. Abstract In this paper, we use new parametic formof fuzzy numbers and convert a system of fuzzy integral equations to two system of integral equations in crisp. Then we solve a system of fuzzy integral equations by means of an analytic technique, namely the homotopy analysis method (HAM). Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. The results reveal that the proposed method is very effective and simple. Numerical examples are presented to illustrate the proposed model. 1. Introduction The fuzzy mapping function was introduced by Chang and Zadeh [6]. Later, Dubois and Prade [7] presented an elementary fuzzy calculus based on the extension principle also the concept of integration of fuzzy functions was first introduced by Dubois and Prade [7]. The topics of fuzzy integral equations (FIE) and fuzzy differential equations which growing interest for some time, in particular in relation to fuzzy control, have been rapidly developed in recent years. A few of these equations can be solved explicitly, it is often necessary to resort to numerical techniques which are appropriate combinations of numerical integration and interpolation [5, 22, 21]. There are several numerical methods for solving linear Fredholm fuzzy integral equations of the second kind [3, 4]. In 1992, Liao [8] employed the basic ideas of the homotopy in topology to propose a general analytic method for nonlinear problems, namely homotopy analysis method (HAM), [9, 10]. Abbasbandy [1, 2] applied homotopy perturbation method (HPM), which is a special case of HAM, to solve Riccati differential equation. Also he used HAM for solving quadratic Riccati differential equation [24] and mixed Volterra-Fredholm integral equations [14]. After this, the HAM has been applied to obtain solution to a linear Fredholm fuzzy integral equation of the second [20]. The purpose of this paper is to extend the application of the HAM for solving a nonlinear system of fuzzy integral equations. We shall apply HAM to find the approximate analytical solutions of a system of fuzzy Fredholm integral equations of the second kind. 2. Preliminaries In this section the basic notations used in fuzzy calculus are introduced. We start by defining the fuzzy number. Definition 1 ([18]). A fuzzy number is a fuzzy set [0,1] = : 1 I u → R such that i. u is upper semi-continuous; ii. 0 = ) ( x u outside some interval ] , [ d a ; iii. There are real numbers b and c , , d c b a ≤ ≤ ≤ for which