Preference disaggregation within the regularization framework for sorting problems with multiple potentially non-monotonic criteria

We propose a new approach to preference model learning for multiple criteria sorting within the regularization framework traditionally used in the statistical learning theory. It employs an additive piecewise-linear value function as a preference model, and infers the model's parameters from the assignment examples concerning a subset of reference alternatives. As such, our approach belongs to the family of preference disaggregation approaches. We propose a new way of measuring the complexity of the preference model. Moreover, by accounting for the trade-off between model's complexity and fitting ability, the proposed approach avoids the problem of over-fitting and enhances the generalization ability to non-reference alternatives. In addition, it is capable of dealing with potentially non-monotonic criteria, whose marginal value functions can be inferred from the assignment examples without using integer variables. The proposed preference learning approach is formulated as a binary classification problem and addressed using support vector machine. In this way, the respective optimization problems can be solved with some computationally efficient algorithms. Moreover, the prior knowledge about the preference directions on particular criteria are incorporated to the model, and a dedicated algorithm is developed to solve the extended quadratic optimization problem. An example of university classification in China is discussed to illustrate the applicability of proposed method and extensive simulation experiments are conducted to analyze its performance under a variety of problem settings.