This paper presents a new approach to solve multi-objective decision-making (DM) problems based on neural networks (NN). The utility evaluation function is estimated using the proposed group method of data handling (GMDH) NN. A series of training data is obtained based on a limited number of initial solutions to train the NN. The NN parameters are adjusted based on the error propagation training method and unscented Kalman filter (UKF). The designed DM is used in solving the practical problem, showing that the proposed method is very effective and gives favorable results, under limited fuzzy data. Also, the results of the proposed method are compared with some similar methods.