Practical extension of MACBETH methodology to deal with sophisticated preferences’ models

When solving complex and critical decision problems involving several aspects, collecting decision-maker (DM) preferences remains a delicate issue. Indirect parameter identification procedures are more adequate in such situations than procedures consisting to ask directly the DM to provide preferences. In the case of methods based on additive models such as MACBETH, disaggregation procedures are implemented to handle this problem. In case of sophisticated non-additive model, e.g. Choquet integral based fuzzy measure, most of the existing indirect procedures assume a 2-additive fuzzy measure and the DM is asked to change her/his preferences if they do not match this model. This paper proposes an approach to determine preferences model that achieves a trade-off between model sophistication and the fastidious MACBETH questioning procedure when considering interactions between more than two attributes. First, it proposes a practical approach to solve a real case of multiple criteria decision problem while considering sophistical model of preferences. On one hand, particular binary alternatives are selected for a first questioning procedure to determine the fuzzy measure parameters. In order to make the later procedure as simple as possible to handle, some simplifications are introduced to reduce both the amount of information and the cognitive effort requested from the DM. Our proposition consists in fixing several non-linear optimization problems until reaching the first k for which the k-additive fuzzy measure match the DM preferences. On the other hand, starting from a decision matrix and the answers to a second questioning procedure, value functions are determined. The second contribution is a theoretical one and consists in proving the existence of a k-additive fuzzy measure matching the DM preferences. Finally, the approach is applied to a real world case that concerns the comparison of some electrical and thermal vehicles regarding their environmental impacts.