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Best-Worst Disaggregation: An approach to the preference disaggregation problem

Matteo Brunelli, Fuqi Liang, Jafar Rezaei

TL;DR

The paper tackles inconsistency and cognitive biases in preference disaggregation by introducing Best-Worst Disaggregation (BWD), which fuses the Best-Worst Method with a disaggregation framework and uses a consider-the-opposite elicitation to stabilize judgments. It provides a linear optimization model to recover an additive value function, a reference-set design to ensure comprehensive yet compact elicitation, and both ordinal and cardinal consistency analyses, plus an interval-valued extension to handle uncertainty. A logistics-case study demonstrates that BWD yields reliable rankings aligned with expert preferences and shows how compatibility and stability can be assessed through extreme ranking analysis. The approach offers a practical, bias-reducing, and extensible toolkit for MCDA practitioners, with potential extensions to group decision-making and dynamic environments.

Abstract

Preference disaggregation methods in Multi-Criteria Decision-Making (MCDM) often encounter challenges related to inconsistency and cognitive biases when deriving a value function from experts' holistic preferences. This paper introduces the Best-Worst Disaggregation (BWD) method, a novel approach that integrates the principles of the Best-Worst Method (BWM) into the disaggregation framework to enhance the consistency and reliability of derived preference models. BWD employs the "consider-the-opposite" strategy from BWM, allowing experts to provide two opposite pairwise comparison vectors of alternatives. This approach reduces cognitive load and mitigates anchoring bias, possibly leading to more reliable criteria weights and attribute value functions. An optimization model is formulated to determine the most suitable additive value function to the preferences expressed by an expert. The method also incorporates a consistency analysis to quantify and improve the reliability of the judgments. Additionally, BWD is extended to handle interval-valued preferences, enhancing its applicability in situations with uncertainty or imprecise information. We also developed an approach to identify a reference set, which is used for pairwise comparisons to elicit the value functions and weights. A case study in logistics performance evaluation demonstrates the practicality and effectiveness of BWD, showing that it produces reliable rankings aligned closely with experts' preferences.

Best-Worst Disaggregation: An approach to the preference disaggregation problem

TL;DR

The paper tackles inconsistency and cognitive biases in preference disaggregation by introducing Best-Worst Disaggregation (BWD), which fuses the Best-Worst Method with a disaggregation framework and uses a consider-the-opposite elicitation to stabilize judgments. It provides a linear optimization model to recover an additive value function, a reference-set design to ensure comprehensive yet compact elicitation, and both ordinal and cardinal consistency analyses, plus an interval-valued extension to handle uncertainty. A logistics-case study demonstrates that BWD yields reliable rankings aligned with expert preferences and shows how compatibility and stability can be assessed through extreme ranking analysis. The approach offers a practical, bias-reducing, and extensible toolkit for MCDA practitioners, with potential extensions to group decision-making and dynamic environments.

Abstract

Preference disaggregation methods in Multi-Criteria Decision-Making (MCDM) often encounter challenges related to inconsistency and cognitive biases when deriving a value function from experts' holistic preferences. This paper introduces the Best-Worst Disaggregation (BWD) method, a novel approach that integrates the principles of the Best-Worst Method (BWM) into the disaggregation framework to enhance the consistency and reliability of derived preference models. BWD employs the "consider-the-opposite" strategy from BWM, allowing experts to provide two opposite pairwise comparison vectors of alternatives. This approach reduces cognitive load and mitigates anchoring bias, possibly leading to more reliable criteria weights and attribute value functions. An optimization model is formulated to determine the most suitable additive value function to the preferences expressed by an expert. The method also incorporates a consistency analysis to quantify and improve the reliability of the judgments. Additionally, BWD is extended to handle interval-valued preferences, enhancing its applicability in situations with uncertainty or imprecise information. We also developed an approach to identify a reference set, which is used for pairwise comparisons to elicit the value functions and weights. A case study in logistics performance evaluation demonstrates the practicality and effectiveness of BWD, showing that it produces reliable rankings aligned closely with experts' preferences.

Paper Structure

This paper contains 21 sections, 1 theorem, 34 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Multi-attribute value theory (MAVT)
  4. Best-Worst Method
  5. Preference disaggregation analysis framework
  6. Optimization
  7. Stability
  8. Best-worst disaggregation method
  9. A proposal to select the reference set
  10. Necessary relation from the BWD model
  11. Consistency analysis
  12. Extreme ranking analysis
  13. An interval-valued extension
  14. A case study in logistics performance evaluation
  15. Reference set selection and preference elicitation
  16. ...and 6 more sections

Key Result

Proposition 1

If $a_{Bi} \in [a_{Bi}^{-},a_{Bi}^{+}]$, $a_{iW} \in [a_{iW}^{-},a_{iW}^{+}]$ and the consequence vectors are the same for both models, then, $\xi^{*}_{I} \leq \xi^{*}$.

Figures (4)

  • Figure 1: Compatibility and consistency.
  • Figure 2: Improving ranges, in green, for $A^{BO}$ and $A^{OW}$.
  • Figure 3: Rankings of European countries based on BWD (on the left) and I-BWD (on the right).
  • Figure 4: Necessary ranking $\succ_{\mathcal{N}}$ of European countries obtained with the interval-valued BWD. Countries are labeled using the ISO 3166-1 alpha-2 standard.

Theorems & Definitions (2)

  • Proposition 1
  • proof