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    An incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting
    (Elsevier b.v., 2025) Li, Zhuolin; Zhang, Zhen; Pedrycz, Witold
    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 inactive 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.
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    Integrating machine learning models to learn potentially non-monotonic preferences for multi-criteria sorting from large-scale assignment examples
    (Elsevier Ltd., 2025) Li, Zhuolin; Zhang, Zhen; Pedrycz, Witold
    Learning preferences from assignment examples has attracted considerable attention in the field of multi-criteria sorting (MCS). However, traditional MCS methods, designed to infer decision makers’ preferences from small-scale assignment examples, encounter limitations when confronted with large-scale data sets. Additionally, the presence of decision makers’ non-monotonic preferences for certain criteria in MCS problems necessitates accounting for potential non-monotonicity when devising preference learning methods. To address this, this paper proposes some new models to learn potentially non-monotonic preferences for MCS problems from large-scale assignment examples by leveraging machine learning models. Specifically, we first introduce the Piecewise-Linear Neural Network (PLNN) model, which leverages the threshold-based value-driven sorting procedure as the underlying sorting model and integrates a perceptron-based model to establish piecewise-linear marginal value functions to approximate real ones. On this basis, we address MCS problems with criteria interactions and extend the PLNN model to develop the Piecewise-Linear Factorization Machine-based Neural Network (PLFMNN) model by incorporating the factorization machine to factorize interaction coefficients. Training these models allows us to learn potentially non-monotonic preferences of decision makers. To illustrate the proposed models, we apply them to a red wine quality classification problem. Furthermore, we assess the performance of the proposed models through computational experiments on both artificial and real-world data sets. Additionally, we conduct statistical tests to ascertain the significance of the performance differences. Experimental results reveal that the proposed models are comparable to the multilayer perceptron model and outperform other baseline models on most data sets, thus affirming their efficacy. Finally, we conduct some sensitivity analysis to assess the impact of certain parameters on the performance of the proposed models and compare them with existing studies from a theoretical perspective, further demonstrating their effectiveness. © 2024 Elsevier Ltd