Computational procedure for solving fuzzy equations

Abstract

The classical methods for solving fuzzy equations are very limited because, often, there are no solutions or very strong conditions for the equations it is placed to have a solution. In addition, the solution’s support obtained in these methods is large. All of this is due to the consideration of operations related to equations based on the principle of extension, which is due to the absence of ineffective members. These high points are our motive for achieving a new approach to solving fuzzy equations. We will solve the fuzzy equations, taking into account the fuzzy operations involved in the equation based on the transmission average by Abbasi et al. (J Intell Fuzzy Syst 29:851–861, 2015). In this paper, a computational procedure is proposed to solve the fuzzy equations that meets the defects of previous techniques, specially reluctant to question whether the answer is valid in the equation. The proposed approach is implemented on the fuzzy equations as $AX+B=C$, $AX^{2}+BX+C=D$, $AX^{3}+BX^{2}=CX$ . At the end, it is shown that the solution of the proposed method in comparison with other methods of solving fuzzy equations are more realistic, that is, they have smaller support.