Preference disaggregation analysis with criteria selection in a regularization framework

Limited by cognitive abilities, decision-makers (DMs) may struggle to evaluate decision alternatives based on all criteria in multiple criteria decision-making problems. This paper proposes an embedded criteria selection method derived from preference disaggregation technique and regularization theory. The method aims to infer the criteria and value functions used by the DM to evaluate decision alternatives. It measures the quality of criteria subsets by investigating both the empirical error (fitting ability of value functions to preference information) and generalization error (complexity of value functions). Unlike existing approaches that consider only the deviation from linearity as a measure of complexity, we argue that the number of marginal value functions also affects complexity. To address this, we use 0–1 variables to indicate whether a criterion is selected in the value function or not, and construct a criteria selection model with the trade-off between empirical and generalization errors as the objective function. If the criteria are sufficiently discriminative, we identify all supporting criteria sets that can restore preference information without unnecessary criteria. We further analyze the likelihood of criteria being selected by the DM. Finally, the effectiveness of the proposed method is demonstrated by applying it to an example of the green supplier selection problem.