Robust ordinal regression for value functions handling interacting criteria

International audienceWe present a new method called UTAGMS–INT for ranking a finite set of alternatives evaluated on multiple criteria. It belongs to the family of Robust Ordinal Regression (ROR) methods which build a set of preference models compatible with preference information elicited by the Decision Maker (DM). The preference model used by UTAGMS–INT is a general additive value function augmented by two types of components corresponding to ‘‘bonus’’ or ‘‘penalty’’ values for positively or negatively interacting pairs of criteria, respectively. When calculating value of a particular alternative, a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria. Similarly, a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria. The preference information elicited by the DM is composed of pairwise comparisons of some reference alternatives, as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference, either comprehensively or on a particular criterion. In UTAGMS–INT, ROR starts with identification of pairs of interacting criteria for given preference information by solving a mixed-integer linear program. Once the interacting pairs are validated by the DM, ROR continues calculations with the whole set of compatible value functions handling the interacting criteria, to get necessary and possible preference relations in the considered set of alternatives. A single representative value function can be calculated to attribute specific scores to alternatives. It also gives values to bonuses and penalties. UTAGMS–INT handles quite general interactions among criteria and provides an interesting alternative to the Choquet integral

Data-driven Preference Learning Methods for Multiple Criteria Sorting with Temporal Criteria

The advent of predictive methodologies has catalyzed the emergence of data-driven decision support across various domains. However, developing models capable of effectively handling input time series data presents an enduring challenge. This study presents novel preference learning approaches to multiple criteria sorting problems in the presence of temporal criteria. We first formulate a convex quadratic programming model characterized by fixed time discount factors, operating within a regularization framework. Additionally, we propose an ensemble learning algorithm designed to consolidate the outputs of multiple, potentially weaker, optimizers, a process executed efficiently through parallel computation. To enhance scalability and accommodate learnable time discount factors, we introduce a novel monotonic Recurrent Neural Network (mRNN). It is designed to capture the evolving dynamics of preferences over time while upholding critical properties inherent to MCS problems, including criteria monotonicity, preference independence, and the natural ordering of classes. The proposed mRNN can describe the preference dynamics by depicting marginal value functions and personalized time discount factors along with time, effectively amalgamating the interpretability of traditional MCS methods with the predictive potential offered by deep preference learning models. Comprehensive assessments of the proposed models are conducted, encompassing synthetic data scenarios and a real-case study centered on classifying valuable users within a mobile gaming app based on their historical in-app behavioral sequences. Empirical findings underscore the notable performance improvements achieved by the proposed models when compared to a spectrum of baseline methods, spanning machine learning, deep learning, and conventional multiple criteria sorting approaches