Sensitivity Analysis of the OWA Operator

The successful design and application of the ordered weighted averaging (OWA) method as a decision-making tool depend on the efficient computation of its order weights. The most popular methods for determining the order weights are the fuzzy linguistic quantifiers approach and the minimal variability method, which give different behavior patterns for the OWA. These two methods will be first analyzed in detail by using sensitivity analysis on the outputs of the OWA with respect to the optimism degree of the decision maker, and then the two methods will be compared. The fuzzy linguistic quantifiers approach gives more information about the behavior of the OWA outputs in comparison to the minimal variability method. However, in using the minimal variability method, the OWA has a linear behavior with respect to the optimism degree, and, therefore, it has better computation efficiency. Since maximizing the combined goodness measure and minimizing its sensitivity to optimism degree are conflicting objectives, a new composite measure of goodness will be defined to have more reliability in obtaining optimal solutions. The theoretical results will be illustrated in a water resources management problem.