Group decision making model and approach based on interval preference orderings

In group decision making under uncertainty, interval preference orderings as a type of simple uncertain preference structure, can be easily and conveniently used to express the experts' evaluations over the considered alternatives. In this paper, we investigate group decision making problems with interval preference orderings on alternatives. We start by fusing all individual interval preference orderings given by the experts into the collective interval preference orderings through the uncertain additive weighted averaging operator. Then we establish a nonlinear programming model by minimizing the divergences between the individual uncertain preferences and the group's opinions, from which we derive an exact formula to determine the experts' relative importance weights. After that, we calculate the distances of the collective interval preference orderings to the positive and negative ideal solutions, respectively, based on which we use a TOPSIS based approach to rank and select the alternatives. All these results are also reduced to solve group decision making problems where the experts' evaluations over the alternatives are expressed in exact preference orderings. A numerical analysis of our model and approach is finally carried out using two illustrative examples.