Indonesian Journal of Electrical Engineering and Computer Science Vol. 11, No. 3, September 2018, pp.1228∼1235 ISSN: 2502-4752, DOI:10.11591/ijeecs.v11.i3.pp1228-1235  1228 A Study of Some Iterative Methods for Solving Fuzzy Volterra-Fredholm Integral Equations Ahmed A. Hamoud 1 , Ali Dhurgham Azeez 2 , and Kirtiwant P. Ghadle 3 1,3 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004 (M.S.) India. 1 Department of Mathematics, Taiz University, Taiz, Yemen. 2 Master of Mathematics, Thi Qar Directorates of Education, Iraq Article Info Article history: Received May 9, 2018 Revised July 3, 2018 Accepted July 16, 2018 Keyword: Adomian Decomposition Method Variational Iteration Method Homotopy Analysis Method Fuzzy Volterra-Fredholm Integral Equation. ABSTRACT This paper mainly focuses on the recent advances in the some approximated methods for solving fuzzy Volterra-Fredholm integral equations, namely, Adomian decomposition method, variational iteration method and homotopy analysis method. We converted fuzzy Volterra-Fredholm integral equation to a system of Volterra-Fredholm integral equations in crisp case. The approximated methods using to find the approximate solutions of this system and hence obtain an approximation for the fuzzy solution of the fuzzy Volterra-Fredholm integral equation. To assess the accuracy of each method, algorithms with Mathematica 6 according is used. Also, numerical example is included to demonstrate the validity and applicability of the proposed techniques. Copyright c  2018 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: Ahmed A. Hamoud Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004 (M.S.) India. Email: drahmed985@yahoo.com 1. INTRODUCTION Recently, the topics of fuzzy integral equations which attracted increasing interest, in particular in relation to fuzzy control, have been rapidly developed. The concept of fuzzy numbers and arithmetic operations firstly in- troduced by Zadeh [1], and then by Dubois and Prade [2]. Also, they have introduced the concept of integration of fuzzy functions. The fuzzy mapping function was introduced by Cheng and Zadeh [1]. Moreover, [3] presented an elementary fuzzy calculus based on the extension principle. Later, Goetschel and Voxman [4] preferred a Riemann integral type approach. Kaleva [5] chose to define the integral of fuzzy function, using the Lebesgue-type concept for integration. One of the first applications of the fuzzy integral equation was given by Ma and Wu who investigated the fuzzy Fredholm integral equation of the second kind. Recently, some mathematicians have studied fuzzy integral and integro-differential equation by numerical techniques [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. As we know the fuzzy integral and differential equations are one of the important parts of the fuzzy analysis theory that play a main role in the numerical analysis. In this work, we will suggests recent advances in the some approximated methods for solving fuzzy Volterra- Fredholm integral equations of the second kind, namely, Adomian decomposition method, variational iteration method and homotopy analysis method. 2. FUZZY VOLTERRA-FREDHOLM INTEGRAL EQUATION The fuzzy Volterra-Fredholm integral equation of the second kind is as follows: ˜ u(x)= ˜ f (x)+ µ 1  x a K 1 (x, t)G 1 (t, ˜ u(t))dt + µ 2  b a K 2 (x, t)G 2 (t, ˜ u(t))dt, (1) Journal Homepage: http://iaesjournal.com/online/index.php/IJECE