A TOPSIS-based approach to multiple attribute decision making with interval numbers

In ambiguous decision domain, the evaluation values of alternatives against the attributes would be interval numbers due to the inherent uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the usages of the linear programming models in Bryson and Mobolurin´s approach. Whether the alternatives are comparable is a question because of the different attribute weights. In this paper, a new approach is proposed to overcome the drawbacks of Bryson and Mobolurin´s approach. By determining the positive and negative ideal alternatives and calculating the relative distances between every alternative and the positive ideal one, a new programming model is set up to figure our the attribute weights for conducting alternative ranking.