en عمومى General پژوهشي Research paper <div style="text-align: justify;">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&rsquo;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.</div> MCE-Product, GH-differentiability, Fuzzy differential equation, Analytical solution. 1 16 http://ijmsi.ir/browse.php?a_code=A-10-6214-1&slc_lang=en&sid=1 Masoumeh Zeinali zeinali@tabrizu.ac.ir 100319475328460011770 100319475328460011770 Yes Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Fariba Maheri maherival@gmail.com 100319475328460011771 100319475328460011771 No Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Stefania Tomasiello stefania.tomasiello@ut.ee 100319475328460011772 100319475328460011772 No Institute of Computer Science, University of Tartu, Estonia