Summary: Classic linear assignment method is a multi-criteria decision-making approach in which criteria are weighted and each rank is assigned to a choice. In this study, to abandon the requirement of calculating the weight of criteria and use decision attributes prioritizing and also to be able to assign a rank to more than one choice, a multi-objective linear programming (MOLP) method is suggested. The objective function of MOLP is defined for each attribute and MOLP is solved based on absolute priority and comprehensive criteria methods. For solving the linear programming problems we apply a recurrent neural network (RNN). Indeed, the Lyapunov stability of the proposed model is proved. Results of comparing the proposed method with TOPSIS, VICOR, and MORA methods which are the most common multi-criteria decision schemes show that the proposed approach is more compatible with these methods.