Model and Algorithm based on Sum of Deviation Squares for Multi-criteria Decision-making

With regard to the multi-criteria decision making (MCDM) problems that the criteria weights are unknown and the decision maker (DM) has avail preference information on alternatives. Firstly, a quadratic programming model is established by using the minimum sum of deviation squares between the subjective and objective decision-making preference information on alternatives. Secondly, the existent condition of solution is given and the calculated formula of the criteria weights are obtained by solving the model, thus the overall values of the alternatives are gained. Based on these values, the ranking priorities on alternatives are processed. Finally, a practical example is illustrated to show the feasibility and availability of the developed model and method.