An incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting

Leveraging assignment example preference information, to determine the shape of marginal utility functions and category thresholds of the threshold-based multi-criteria sorting (MCS) model, has emerged as a focal point of current research within the realm of MCS. Most studies assume decision makers can provide all assignment example preference information in batch and that their preferences over criteria are monotonic, which may not align with practical MCS problems. This paper introduces a novel incremental preference elicitation-based approach to learning potentially non-monotonic preferences in MCS problems, enabling decision makers to progressively provide assignment example preference information. Specifically, we first construct a max-margin optimization-based model to model potentially non-monotonic preferences and inconsistent assignment example preference information in each iteration of the incremental preference elicitation process. Using the optimal objective function value of the max-margin optimization-based model, we devise information amount measurement methods and question selection strategies to pinpoint the most informative alternative in each iteration within the framework of uncertainty sampling in active learning. Once the termination criterion is satisfied, the sorting result for non-reference alternatives can be determined through the use of two optimization models, i.e., the max-margin optimization-based model and the complexity controlling optimization model. Subsequently, two incremental preference elicitation-based algorithms are developed to learn potentially non-monotonic preferences, considering different termination criteria. Ultimately, we apply the proposed approach to a firm financial state rating problem to elucidate the detailed implementation steps, and perform computational experiments on both artificial and real-world data sets to compare the proposed question selection strategies with several benchmark strategies.