322 Copyright © 2017, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 15 DOI: 10.4018/978-1-5225-0914-1.ch015 ABSTRACT In the present chapter, we give an overview of computational iterative schemes for fuzzy system of linear equations. We also consider fully fuzzy linear systems (FFLS) and demonstrate a class of the existing iterative methods using the splitting approach for calculating the solution. Furthermore, the main aim in this work is to design a numerical procedure for improving this algorithm. Some numerical experiments are illustrated to show the applicability of the methods and to show the efciency of proposed algorithm, we report the numerical results of large-scaled fuzzy problems. INTRODUCTION Unfailing real world problems in economics, finance, mechanics etc. can lead to solving a system of linear equations. There are many methods for solving linear systems, see(Barrett et al., 1994; Edalatpa- nah, 2008; Eisenstat, Elman, & Schultz, 1983; Greenbaum, 1997; Martins, Trigo, & Evans, 2007; Saad, 2003; Saberi Najafi & Edalatpanad, 2013a; Saberi Najafi & Edalatpanah, 2013b, 2013c, 2014b; Saberi Najafi & Edalatpanah, 2011; Varga, 2009; Young, 2014; Zhang, Huang, Cheng, & Wang, 2012) and the references therein. Let us consider the following linear systems Ax=b, (1) However, when the estimation of the system coefficients is imprecise and only some vague knowl- edge about the actual values of the parameters is available, it may be convenient to represent some or all of them with fuzzy numbers. Fuzzy data is being used as a natural way to describe uncertain data. Fuzzy concept was introduced by Zadeh (Zadeh, 1965, 1972) and following his work, many papers and books were published in fuzzy system theory; see (Bellman & Zadeh, 1970; Bezdek, 2013; Chen, 2000; Cordón, 2001; Driankov, Hellendoorn, & Reinfrank, 2013; Hájek, 1998; Höppner, 1999; Jang & Sun, Modifed Iterative Methods for Solving Fully Fuzzy Linear Systems S. A. Edalatpanah Ayandegan Institute of Higher Education, Tonekabon, Iran