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Empathic network learning for multi-expert emergency decision-making under incomplete and inconsistent information

Simin Shen, Zaiwu Gong, Bin Zhou, Roman Słowiński

TL;DR

The paper tackles emergency decision-making under incomplete and inconsistent information by proposing an empathic network learning framework built on robust ordinal regression via preference disaggregation. It first completes incomplete fuzzy judgments to obtain intrinsic utilities, then defines compatible empathic networks through constrained optimization, and finally derives necessary and possible empathic relationships to inform DM interactions. Six target networks (including central, distributed, sparse, and topology-specific designs) are proposed, with models to select the most representative network from the feasible set, ensuring robustness. A numerical example with 10 experts and 5 materials demonstrates how network structure materially affects decision outcomes and illustrates the method’s ability to infer plausible empathic networks and produce scenario-adapted recommendations. The approach offers a scalable, interactive framework for network-structure inference in emergency decision-making that supports consensus-building, risk analysis, and strategy selection under uncertainty.

Abstract

Challenges, such as a lack of information for emergency decision-making, time pressure, and limited knowledge of experts acting as decision-makers (DMs), can result in the generation of poor or inconsistent indirect information regarding DMs' preferences. Simultaneously, the empathic relationship represents a tangible social connection within the context of actual emergency decision-making, with the structure of the empathic network being a significant factor influencing the outcomes of the decision-making process. To deduce the empathic network underpinning the decision behaviors of DMs from incomplete and inconsistent preference information, we introduce an empathic network learning methodology rooted in the concept of robust ordinal regression via preference disaggregation. Firstly, we complete incomplete fuzzy judgment matrices including holistic preference information given in terms of decision examples on some reference alternatives, independently by each DM, and we calculate the intrinsic utilities of DMs. Secondly, we establish constraints for empathic network learning models based on empathic preference information and information about relations between some reference nodes. Then, the necessary and possible empathic relationships between any two DMs are calculated. Lastly, tailored to the specific requirements of different emergency scenarios, we design six target networks and construct models to derive the most representative empathic network.

Empathic network learning for multi-expert emergency decision-making under incomplete and inconsistent information

TL;DR

The paper tackles emergency decision-making under incomplete and inconsistent information by proposing an empathic network learning framework built on robust ordinal regression via preference disaggregation. It first completes incomplete fuzzy judgments to obtain intrinsic utilities, then defines compatible empathic networks through constrained optimization, and finally derives necessary and possible empathic relationships to inform DM interactions. Six target networks (including central, distributed, sparse, and topology-specific designs) are proposed, with models to select the most representative network from the feasible set, ensuring robustness. A numerical example with 10 experts and 5 materials demonstrates how network structure materially affects decision outcomes and illustrates the method’s ability to infer plausible empathic networks and produce scenario-adapted recommendations. The approach offers a scalable, interactive framework for network-structure inference in emergency decision-making that supports consensus-building, risk analysis, and strategy selection under uncertainty.

Abstract

Challenges, such as a lack of information for emergency decision-making, time pressure, and limited knowledge of experts acting as decision-makers (DMs), can result in the generation of poor or inconsistent indirect information regarding DMs' preferences. Simultaneously, the empathic relationship represents a tangible social connection within the context of actual emergency decision-making, with the structure of the empathic network being a significant factor influencing the outcomes of the decision-making process. To deduce the empathic network underpinning the decision behaviors of DMs from incomplete and inconsistent preference information, we introduce an empathic network learning methodology rooted in the concept of robust ordinal regression via preference disaggregation. Firstly, we complete incomplete fuzzy judgment matrices including holistic preference information given in terms of decision examples on some reference alternatives, independently by each DM, and we calculate the intrinsic utilities of DMs. Secondly, we establish constraints for empathic network learning models based on empathic preference information and information about relations between some reference nodes. Then, the necessary and possible empathic relationships between any two DMs are calculated. Lastly, tailored to the specific requirements of different emergency scenarios, we design six target networks and construct models to derive the most representative empathic network.

Paper Structure

This paper contains 28 sections, 11 theorems, 56 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Definitions and notation
  3. Empathic networks
  4. Fuzzy judgment matrix and eigenvector method
  5. Decision information
  6. Introduction of the empathic network learning method
  7. Elicitation of incomplete decision information
  8. Calculation of intrinsic utilities
  9. Constraints and binary empathic relations
  10. Constraints on the empathic network learning model
  11. Necessary and possible empathic relationships
  12. Analysis of inconsistencies
  13. Selection of a representative empathic network
  14. The most discriminating empathic network
  15. The sparse empathic network
  16. ...and 13 more sections

Key Result

Theorem 1

When the empathic centrality of all ${d_j}\in D$ in the empathic network is evenly distributed, that is, the status of nodes is equal, the entropy based on the empathic centrality reaches the maximum value. When the empathic centrality of ${d_k}\in D$ is the largest, that is, the node is the "opinio

Figures (7)

  • Figure 1: The flow chart of the empathic network learning method.
  • Figure 2: Three topologies of empathic networks.
  • Figure 3: Comparison of the two empathic networks.
  • Figure 4: Central, distributed, and highly resilient local empathic networks.
  • Figure 5: Local and corresponding highly resilient global empathic networks.
  • ...and 2 more figures

Theorems & Definitions (28)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • definition 5
  • definition 6
  • Theorem 1
  • definition 7
  • definition 8
  • definition 9
  • ...and 18 more