New parametric identification method for a preference model

Abstract

This article presents a contribution to multi-criteria decision support intended for industrial decision-makers in order to determine the best compromise between design criteria when working on risky or innovative products. In (RENAUD et al. 2008) we used the OWA operator (Ordered Weighted Average), a well-known multi-criteria analysis technique introduced by (YAGER 1988). The interest of this aggregation method is, beyond its ease of use, its ability to evaluate a product according to a single scale. When using the OWA method, the choice of criterion weights and their values remains an important and delicate operation. Indeed, the weights are not fixed by criterion but according to a level of utility (FISHBURN 1967). The weights can, in addition, be determined using different methods. A traditional approach consists in estimating the weights from an a priori selection of the most representative samples by an expert. We propose a new approach based on applied D-Optimality to determine the best sample. The results of the two approaches are compared. Indeed, in some multi-criteria decision problems, it is difficult to choose the method that best describes the behavior of the decision maker. As said above, the first part of this paper presents an original method based on D-optimality to determine the most representative set of samples to determine the decision parameters. This method has been applied and validated in an OWA approach. It has been shown that the accuracy and reliability of the method have been improved. Since the OWA application has been improved, the other goal of this paper is to verify whether the real decision maker has an OWA-based behavior or not. To achieve this, the D-optimality approach is applied to the MAUT (Multi-Attribute Utility Theory) approach to find the best set of samples. The results of the two methods are compared. Both approaches show that, while OWA better simulates the decision maker's behavior, there is still a gap between its scores and that of OWA. The question here is how to improve the accuracy of the score estimated by OWA compared to those given by the expert. Subsequently, a hybrid approach is tested, such as a linear combination of the MAUT and OWA approaches. The results obtained with this combination were found to be more accurate than those of OWA. However, we also tested the CHOQUET discrete integral approach. In other words, it is possible to find a model capable of better describing the decision maker's behavior.