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, ∞[ , bipolar scales [-1, 1] and R =] - ∞, ∞[ , 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.

Ordered Weighted Averaging (OWA) operators, a family of aggregation functions, are widely used in human decision-making schemes to aggregate data inputs of a decision maker's choosing through a process known as OWA aggregation. The weight allocation mechanism of OWA aggregation employs the principle of linear ordering to order data inputs after the input variables have been rearranged. Thus, OWA operators generally cannot be used to aggregate a collection of n inputs obtained from any given convex partially ordered set (poset). This poses a problem since data inputs are often obtained from various convex posets in the real world. To address this problem, this paper proposes methods that practitioners can use in real-world applications to aggregate a collection of n inputs from any given convex poset. The paper also analyzes properties related to the proposed methods, such as monotonicity and weighted OWA aggregation on convex posets.