An extension of Ordered Weighted Averaging over intervals with application to optimization under risk

TL;DR

This paper extends the Ordered Weighted Averaging (OWA) operator to continuous cases using distortion risk measures, enabling optimization under uncertainty with new solution methods and computational analysis.

Contribution

It introduces a continuous extension of OWA via distortion risk measures and develops approximation algorithms with verified computational performance.

Findings

Proposed a continuous OWA extension using distortion risk measures.

Analyzed the computational complexity of the new optimization problem.

Developed and tested approximation algorithms with guarantees.

Abstract

The Ordered Weighted Averaging (OWA) operator is a traditional and commonly used criterion for aggregating discrete values of uncertain quantities. In this paper, it is shown that the discrete OWA naturally extends to the continuous case by using the concept of a distortion risk measure. It is shown how to apply the distortion risk measure to optimization problems with a linear objective function, whose coefficients are random variables with continuous distribution functions supported on intervals. The case where these coefficients are independent, uniformly distributed random variables is explored in more detail. The computational complexity of the resulting optimization problem is analyzed, and solution methods with approximation guarantees are proposed. These methods are also verified through computational experiments.