A Method for Group Decision-making with Uncertain Preference Ordinals Based on Probability Matrix

In this paper, a new method to solve the group decision-making problems is proposed, in which the preference information on alternatives provided by decision makers is in the form of uncertain preference ordinals. This paper firstly gives two new definitions on the probability that the alternative is ranked in each position. Then, in order to process uncertain preference ordinals, two new definitions are used respectively to construct a decision matrix in the form of probabilities. On this basis, a weight probability matrix and a collective probability matrix on alternatives with regard to rank positions are constructed. Finally, an optimization model is built based on the collective probability matrix, and the ranking of alternatives can be obtained by solving the model.