The focus of this paper is on the criteria weight approximation in Multiple Criteria Decision Making (MCDM). An approximate weighting method produces the weights that are surrogates for the exact values that cannot be elicited directly from the DM. In this field, a very famous model is Rank Order Centroid (ROC). The paper shows that there is a drawback to the ROC method that could be resolved. The paper gives an idea to develop a revised version of the ROC method called Improved ROC (IROC). The behaviour of the IROC method is investigated using a set of simulation experiments. The IROC method could be employed in situations of time pressure, imprecise information, etc. The paper also proposes a methodology including the application of the IROC method in a group decision making mode, to estimate the weights of the criteria in a tree-shaped structure. The proposed methodology is useful for academics/managers/decision makers who want to deal with MCDM problem. A study case is examined to show applicability of the proposed methodology in a real-world situation. This case is engine/vehicle selection problem, that is one of the fundamental challenges of road transport sector of any country.