The aim of this article is to develop a new and simple technique to determine the approximate fuzzy solution of the fully bipolar fuzzy linear system of equations (BFLSEs) \(\tilde{\mathcal {A}}\tilde{\mathcal {U}}=\tilde{\mathfrak {y}}\) , where \(\tilde{\mathcal {U}}\) and \(\tilde{\mathfrak {y}}\) are the triangular bipolar fuzzy vectors and \(\tilde{\mathcal {A}}\) is either the crisp or fuzzy matrix. The solution of the proposed system is extracted in twofold. First, we obtain the crisp solution of the proposed system. To achieve this, we solve the BFLSEs using \((-1,1)\) -cut expansion. Second, we assign unknown symmetric parameters to each row of this crisp system in \((-1,1)\) -cut expansion. Thus, this system will transform into a system of interval equations. The unknown symmetric parameters corresponding to each element of a bipolar fuzzy vector are obtained by solving such an interval system of equations. Additionally, we demonstrate that the bounded and symmetric solutions (B&SSs) of the fully BFLSEs will reside within the tolerable solution set (TSS) and in the controllable solution set (CSS), respectively. To enhance the novelty of the proposed technique, we present several theorems that serve as a formal foundation for our approach. Furthermore, a numerical example is provided to demonstrate the effectiveness and validity of the proposed technique.
