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

Zhuolin Li, Zhen Zhang, Witold Pedrycz

TL;DR

This work addresses learning potentially non-monotonic preferences in multi-criteria sorting under inconsistent incremental inputs by introducing a max-margin model that tolerates inconsistencies while maximizing discriminative power. The approach leverages information-amount and uncertainty-sampling-based question strategies to select the most informative alternatives, and proposes two termination criteria to balance stopping time against accuracy. Two optimization-based pipelines yield marginal utilities and category thresholds, which are then used in a threshold-based MCS to obtain complete rankings, all validated through a credit-rating case and extensive artificial and real-world experiments. The results show improved accuracy and reduced labeling effort compared to monotonic or benchmark strategies, highlighting practical impact for decision support in complex, real-time preference elicitation settings.

Abstract

This paper introduces a novel incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting (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 credit 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.

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

TL;DR

This work addresses learning potentially non-monotonic preferences in multi-criteria sorting under inconsistent incremental inputs by introducing a max-margin model that tolerates inconsistencies while maximizing discriminative power. The approach leverages information-amount and uncertainty-sampling-based question strategies to select the most informative alternatives, and proposes two termination criteria to balance stopping time against accuracy. Two optimization-based pipelines yield marginal utilities and category thresholds, which are then used in a threshold-based MCS to obtain complete rankings, all validated through a credit-rating case and extensive artificial and real-world experiments. The results show improved accuracy and reduced labeling effort compared to monotonic or benchmark strategies, highlighting practical impact for decision support in complex, real-time preference elicitation settings.

Abstract

This paper introduces a novel incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting (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 credit 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.
Paper Structure (26 sections, 1 theorem, 26 equations, 19 figures, 4 tables, 6 algorithms)

This paper contains 26 sections, 1 theorem, 26 equations, 19 figures, 4 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. The threshold-based MCS model
  3. Problem description and resolution framework
  4. The proposed approach
  5. Inconsistent assignment example preference information modeling method
  6. Termination criteria
  7. Question selection strategies
  8. Information amount measurement methods
  9. Identifying the most informative alternative
  10. Obtaining the sorting result for non-reference alternatives
  11. Incremental preference elicitation-based algorithms
  12. Numerical results
  13. Illustrative example
  14. Comparisons and parameter analysis
  15. Comparisons with the approach considering monotonic preferences
  16. ...and 11 more sections

Key Result

Theorem 1

Let $\gamma_{jl}=\left|\frac{u_j(\beta_j^{l+1})-u_j(\beta_j^l)}{\beta_j^{l+1} - \beta_j^l} - \frac{u_j(\beta_j^l) - u_j(\beta_j^{l-1})}{\beta_j^l - \beta_j^{l-1}} \right|$, the model m:min_slope0 can be converted into the following linear programming model,

Figures (19)

  • Figure 1: A simple resolution framework of the proposed approach
  • Figure 2: The flowchart of the proposed incremental preference elicitation-based approach
  • Figure 3: The sorting result for all firms
  • Figure 4: The marginal utility functions in the UTA-like functional space
  • Figure 5: The marginal utility functions in the UTA-like functional space of the approach considering monotonic preferences
  • ...and 14 more figures

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Remark 3
  • Definition 1
  • Remark 4
  • Remark 5
  • Remark 6
  • Theorem 1
  • Definition 2