An Augmented Classical Least Squares Method for Solving Fuzzy Systems with Linear Equations

Abstract Fuzzy sets theory is a newly emerging mathematical framework to deal with uncertainty problems. Thus, systems of linear equations with vagueness of some parameters play a major role in a large proportion of areas including economics, finance, engineering science and physics. The main purpose of this paper is to compute an approximate solution for the fuzzy systems of linear equations (FSLE) using the least squares method. For simplifying the presentation of the proposed approach, the triangular fuzzy numbers are considered both in algebraic and the parametric forms. According to the first form, the proposed method consists to transform a $n\times n$ fuzzy linear into $3n\times 3n$. Next, the second form requires a transformation into $2n\times 2n$.\\Finally, we illustrate our results via numerical experiments. Effectively, we provide an application of FSLE in economic field. Secondly, we investigate the same fuzzy model in a circuit analysis.