A heuristic nonlinear operator for the aggregation of incomplete judgment matrices in group decision making

摘要

The weighted-average operator and ordered-weighted-average operators are typically used in group decision making (GDM) problems to aggregate individual expert opinions to a collective opinion. However, the existing aggregation operators pay more attentions on the determination of the weights, and neglect the information about the relationship between the values being fused. In this paper, we develop a heuristic-nonlinear-aggregation (HNA) operator based on two metrics of similarity and consistency for the GDM based on incomplete judgment matrices. The similarity and consistency respectively measure the differences between a collective matrix and two optimum matrices, i.e. the optimum similarity matrix and the optimum consistency matrix, which can be calculated by quadratic programming models and the relationship between the values being fused. The validity and practicability of the HNA operator are illustrated by numerical examples.