Ordered Weighted Averaging Aggregation on Convex Poset

Abstract

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.