Generalizing TOPSIS for Multi-criteria Group Decision-making with Weighted Ordinal Preferences

Decision-making problems were addressed in which all decision makers just gave ordinal preferences of the alternatives with respect to each criterion. The concepts of individual ideal solution and group's ideal solution under ordinal preferences were proposed and thus the technique for preference by similarity to ideal solution (TOPSIS) was generalized for the ordinal preferences environment. At first, the individual ordinal preferences of each alternative under all criteria were integrated to the comprehensive evaluation of it in the view of each decision maker by TOPSIS. After the weights of all decision-makers were considered, then, the final ranking results of the alternatives in the opinion of the group were derived from the comprehensive evaluations of them above by TOPSIS again. Finally, a decision-making example was presented to illustrate the procedure of the method. The comparisons of the results have demonstrated this proposed method is rational, practical and simple in computation.