Introducing Uncertainty-Based Dynamics in MADM Environments

Abstract

One of the main problems faced by the literature on Multi-Attribute Decision-Making (MADM) methods, which constitutes an inherent assumption that remains undiscussed through the different publications, is the fact that rankings are definitive. As a result, these models do not account for any of the consequences derived from the uncertainty inherent to the evaluations or the potentially strategic reports delivered by the experts. That is, once the ranking is computed, the decision makers (DMs) should select the first alternative, concluding the applicability and contribution of the corresponding model. There are no potential regret or uncertainty interactions triggered by the quality of the reports or their credibility. However, the results of the ranking are not always those preferred by the DMs, who may have to proceed through several alternatives, particularly if the evaluations provided by the experts fail to convey the actual value of the corresponding characteristics. This problem has not been considered in the MADM literature, which has incorporated fuzziness and imprecision to its models, but not accounted for the consequences of credibility in terms of regrettable choices and the combinatorial framework that arises as soon as this possibility is incorporated into the analysis. We define a MADM setting designed to demonstrate the ranking differences arising as DMs incorporate the potential realizations from an uncertain evaluation environment in their choices. We illustrate the substantial ranking modifications triggered by the subsequent dynamic and regret considerations while introducing important potential extensions within standard MADM techniques.