A family of OWA operators based on Faulhaber's formulas

TL;DR

This paper introduces a new family of OWA operators using Faulhaber's formulas to efficiently compute weight vectors based on desired orness, resulting in a fast, robust, and near-optimal method compared to existing procedures.

Contribution

It presents a novel approach to derive OWA weights directly from Faulhaber's formulas, simplifying computation and improving robustness.

Findings

The proposed method is faster and more robust than previous algorithms.

The weight vectors are close to the maximum entropy optimal solutions.

Comparative analysis shows advantages over existing procedures.

Abstract

In this paper we develop a new family of Ordered Weighted Averaging (OWA) operators. Weight vector is obtained from a desired orness of the operator. Using Faulhaber's formulas we obtain direct and simple expressions for the weight vector without any iteration loop. With the exception of one weight, the remaining follow a straight line relation. As a result, a fast and robust algorithm is developed. The resulting weight vector is suboptimal according with the Maximum Entropy criterion, but it is very close to the optimal. Comparisons are done with other procedures.