Journal of Soft Computing and Applications 2013 (2013) 1-11 Available online at www.ispacs.com/jsca Volume 2013, Year 2013 Article ID jsca-00012, 11 Pages doi:10.5899/2013/jsca-00012 Research Article The pseudo inverse matrices to solve general fully fuzzy linear systems S. Moloudzadeh 1 ∗ , P. Darabi 1 , H. Khandani 2 (1) Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran. (2) Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran. Copyright 2013 c ⃝ S. Moloudzadeh, P. Darabi and H. Khandani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we present a solution of an arbitrary general fully fuzzy linear systems (FFLS) in the form  A ⊗  x =  b. Where coefficient matrix  A is an m × n fuzzy matrix and all of this system are elements of LR type fuzzy numbers. Our method discuss a general FFLS (square or rectangle fully fuzzy linear systems with trapezoidal or triangular LR fuzzy numbers). To do this, we transform fully fuzzy linear system in to two crisp linear systems, then obtain the solution of this two systems by using the pseudo inverse matrix method. Numerical examples are given to illustrate our method. Keywords: Fully fuzzy linear system (FFLS); Overdetermined linear system; Pseudo inverse matrix; Underdetermined linear system. 1 Introduction Systems of linear equations are used to solve many problems in various areas such as structural mechanic appli- cations in civil and mechanical structures, heat transport, fluid flow, electromagnetic and etc. In many applications, at least one of the system’s parameters and measurements are vague or imprecise and we can present them with fuzzy numbers rather than crisp numbers. Hence, it is important to develop mathematical models and numerical procedure that would appropriately treat general fuzzy systems and solve them. Fuzzy linear system A x =  b, where A is a crisp matrix and  b is a fuzzy number vector has been solved by Friedman and his colleagues. Using the embedding approach Friedman et. al. proposed a general model to solving such a fuzzy linear systems (see [9]). Asady et al. [4], who merely discussed the full row rank system, used the same method to solve the m × n fuzzy linear system for m ≤ n. Zheng and wang [12, 13] discussed the solution of the general m × n consistent and inconsistent fuzzy linear system. The system of linear equations  A x =  b where  a ij and  b i are the ele- ments of the matrix A and vector b respectively, and are fuzzy numbers, is called a fully fuzzy linear systems (FFLS). FFLS has been studied by several authors. Dehghan et. al. [5, 6, 7] has studied some methods for solving FFLS. They have represented fuzzy numbers in LR form and applied approximate operators between fuzzy numbers to find positive solutions of FFLS, so finding the solutions of FFLS is transformed to finding the solutions of three crisp systems. Allahviranloo et. al. [2, 3] proposed a new method to obtain symmetric solutions (bounded and symmetric solutions) of a fully fuzzy linear systems (FFLS) based on a 1-cut expansion. The purpose of this paper is to present a solution of an arbitrary general (square or rectangle) FFLS. To do this, the original m × n fully fuzzy linear system ∗ Corresponding author. Email address: saeidmoloudzadeh@gmail.com, Tel:+989143891299