The Modified MCE-product: An Efficient Approach to Treat Fuzzy Coefficients in Differential Equations

In this paper, first, we modify the recently introduced MCEproduct to include the property of shape-preserving. This product has attractive properties. For example, it is distributive with respect to the addition and it doesn’t depend on the signs of multiplied fuzzy numbers. Then, the effectiveness and applicability of the modified MCE-product are investigated in treating differential equations with fuzzy multiplications. Due to the complexity of fuzzy multiplication, differential equations with fuzzy coefficients are one of the most challenging topics in the field of fuzzy differential equations. In this paper, as an example of these equations, the first-order linear differential equation with fuzzy variable coefficients is solved by using the modified MCE-product. This equation was chosen because it has been recently solved by Zadeh extension principle-based product and cross-product and we can compare our results with them. The results show the priority of the MCE-product over the mentioned methods.