We first establish some necessary and sufficient conditions for solvability of fuzzy LR linear systems. We then propose a concept for an approximate solution when a fuzzy LR linear system lacks a solution. Recently, we have proposed an approximate solution for a fuzzy LR linear system under the condition t hat a corresponding crisp linear system was solvable. Here, we remove this condition by presenting a more general concept of an approximate solution based on a least squares model. We also develop the conditions for t he uniqueness of t he approximate solution. To compute an approximate solution, we propose an algorithm based on a quadratic programming model with bound constraints on some variables. Finally, we s how numerically the appropriateness of our proposed approximate solution f or large scale problems i n comparison with other recently pro-posed approximate solutions. The numerical results show that our proposed algorithm produces significantly more accurate solutions

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