en Fuzzy Sets and Systems Fuzzy Sets and Systems پژوهشی Original <span style="font-size:11pt"><span style="line-height:normal"><span style="text-autospace:none"><span new="" roman="" style="font-family:" times=""><i><span style="letter-spacing:-.25pt">In this work, we consider a &lrm;multi-objective&lrm; &lrm;minimal &lrm;cost &lrm;flow (MMCF) &lrm;problem where there are several commodities to transport from&lrm; sources &lrm;to &lrm;destinations and there is more than one conveyance for those transporting. We also assume that in each conveyance, there are distinct capacities for each commodity. The obtained model is not necessary balanced, and we introduced a method to solve this model without converting it to a balanced model. Some advantages of the proposed method is discussed.</span></i><span style="letter-spacing:-.15pt"></span></span></span></span></span><br> &nbsp; Fuzzy multi-objective solid minimal cost flow problem, LR flat fuzzy number, multicommodity ‎minimal ‎cost ‎flow ‎problem. 59 75 http://iors.ir/journal/browse.php?a_code=A-10-82-11&slc_lang=en&sid=1 Ali Abbass Hadi alfham1622@gmail.com 00031947532846002950 00031947532846002950 Yes University of Mazandaran Seyed Hadi Nasseri nhadi57@gmail.com 00031947532846002951 00031947532846002951 No