Aggregation of OWA Operators

Abstract

Inspired by the real needs of group decision problems, aggregation of ordered weighted averaging (OWA) operators is studied and discussed. Our results can be applied for data acting on any real interval, such as the standard scales $[0,1]$ and $[0,\infty [$ , bipolar scales $[-1,1]$ and $\mathbb {R}=]-\infty, \infty [$ , etc. A direct aggregation is shown to be rather restrictive, allowing the convex combinations to be considered only, except the case of dimension n = 2. More general is the approach based on the aggregation of related cumulative weighting vectors. The piecewise linearity of OWA operators allows us to consider bilinear forms of aggregation of related weighting vectors. Several interesting examples yielding the link between the aggregation of OWA operators and the related ANDness and ORness measures are also included. Some possible applications and generalizations of our results are also discussed.