A distance-based aggregation approach for group decision making with interval preference orderings

• A result is further study for Xu’s method.
• A distance-based method is proposed to aggregate interval preference orderings.
• A formula is proposed to compare two interval preference orderings.

Xu (2013) proposed a nonlinear programming model to derive an exact formula to determine the experts’ relative importance weights for the group decision making (GDM) with interval preference orderings. However, in this study, we show that the exact formula to determine the weight vector which always equals to w = (1/m, 1/m, … , 1/m)T (m is the number of experts). In this paper, we propose a distance-based aggregation approach to assess the relative importance weights for GDM with interval preference orderings. Relevant theorems are offered to support the proposed approach. After that, by using the weighted arithmetic averaging operator, we obtain the aggregated virtual interval preference orderings. We propose a possibility degree formula to compare two virtual interval preference orderings, then rank and select the alternatives. The proposed method is tested by two numerical examples. Comparative analysis are provided to show the advantages and effectiveness of the proposed method.