WOWA Enhancement of the Preference Modeling in the Reference Point Method

The Reference Point Method (RPM) is an interactive technique formalizing the so-called quasi-satisficing approach to multiple criteria optimization. The DM’s preferences are there specified in terms of reference (target) levels for several criteria. The reference levels are further used to build the scalarizing achievement function which generates an efficient solution when optimized. Typical RPM scalarizing functions are based on the augmented min-max aggregation where the worst individual achievement minimization process is additionally regularized with the average achievement. The regularization by the average achievement is easily implementable but it may disturb the basic min-max model. We show that the OWA regularization allows one to overcome this flaw since taking into account differences among all ordered achievement values. Further, allowing to define importance weights we introduce the WOWA enhanced RPM. Both the theoretical and implementation issues of the WOWA enhanced method are analyzed. Linear Programming implementation model is developed and proven.