On Decision Support Under Risk by the WOWA Optimization

Authors:
Włodzimierz Ogryczak;Tomasz Śliwiński
Affiliations:
Institute of Control & Computation Engineering, Warsaw University of Technology, Warsaw, Poland 00-665;Institute of Control & Computation Engineering, Warsaw University of Technology, Warsaw, Poland 00-665
Venue:
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2007

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Abstract

The problem of averaging outcomes under several scenarios to form overall objective functions is of considerable importance in decision support under uncertainty. The fuzzy operator defined as the so-called Weighted OWA (WOWA) aggregation offers a well-suited approach to this problem. The WOWA aggregation, similar to the classical ordered weighted averaging (OWA), uses the preferential weights assigned to the ordered values (i.e. to the worst value, the second worst and so on) rather than to the specific criteria. This allows one to model various preferences with respect to the risk. Simultaneously, importance weighting of scenarios can be introduced. In this paper we analyze solution procedures for optimization problems with the WOWA objective function. A linear programming formulation is introduced for optimization of the WOWA objective with monotonic preferential weights. Its computational efficiency is analyzed.