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Linguistic Fuzzy Information Evolution with Random Leader Election Mechanism for Decision-Making Systems

Qianlei Jia, Witold Pedrycz

TL;DR

Three new models of linguistic fuzzy information dynamics are proposed: the per-round random leader election mechanism-based DeGroot model (PRRLEM-DeGroot), the PRRLEM-based homogeneous HK model (PRRLEM-HOHK), and the PRRLEM-based heterogeneous HK model (PRRLEM-HEHK).

Abstract

Linguistic fuzzy information evolution is crucial in understanding information exchange among agents. However, different agent weights may lead to different convergence results in the classic DeGroot model. Similarly, in the Hegselmann-Krause bounded confidence model (HK model), changing the confidence threshold values of agents can lead to differences in the final results. To address these limitations, this paper proposes three new models of linguistic fuzzy information dynamics: the per-round random leader election mechanism-based DeGroot model (PRRLEM-DeGroot), the PRRLEM-based homogeneous HK model (PRRLEM-HOHK), and the PRRLEM-based heterogeneous HK model (PRRLEM-HEHK). In these models, after each round of fuzzy information updates, an agent is randomly selected to act as a temporary leader with more significant influence, with the leadership structure being reset after each update. This strategy increases the information sharing and enhances decision-making by integrating multiple agents' evaluation information, which is also in line with real life (\emph{Leader is not unchanged}). The Monte Carlo method is then employed to simulate the behavior of complex systems through repeated random tests, obtaining confidence intervals for different fuzzy information. Subsequently, an improved golden rule representative value (GRRV) in fuzzy theory is proposed to rank these confidence intervals. Simulation examples and a real-world scenario about space situational awareness validate the effectiveness of the proposed models. Comparative analysis with the other models demonstrate our ability to address the echo chamber and improve the robustness.

Linguistic Fuzzy Information Evolution with Random Leader Election Mechanism for Decision-Making Systems

TL;DR

Three new models of linguistic fuzzy information dynamics are proposed: the per-round random leader election mechanism-based DeGroot model (PRRLEM-DeGroot), the PRRLEM-based homogeneous HK model (PRRLEM-HOHK), and the PRRLEM-based heterogeneous HK model (PRRLEM-HEHK).

Abstract

Linguistic fuzzy information evolution is crucial in understanding information exchange among agents. However, different agent weights may lead to different convergence results in the classic DeGroot model. Similarly, in the Hegselmann-Krause bounded confidence model (HK model), changing the confidence threshold values of agents can lead to differences in the final results. To address these limitations, this paper proposes three new models of linguistic fuzzy information dynamics: the per-round random leader election mechanism-based DeGroot model (PRRLEM-DeGroot), the PRRLEM-based homogeneous HK model (PRRLEM-HOHK), and the PRRLEM-based heterogeneous HK model (PRRLEM-HEHK). In these models, after each round of fuzzy information updates, an agent is randomly selected to act as a temporary leader with more significant influence, with the leadership structure being reset after each update. This strategy increases the information sharing and enhances decision-making by integrating multiple agents' evaluation information, which is also in line with real life (\emph{Leader is not unchanged}). The Monte Carlo method is then employed to simulate the behavior of complex systems through repeated random tests, obtaining confidence intervals for different fuzzy information. Subsequently, an improved golden rule representative value (GRRV) in fuzzy theory is proposed to rank these confidence intervals. Simulation examples and a real-world scenario about space situational awareness validate the effectiveness of the proposed models. Comparative analysis with the other models demonstrate our ability to address the echo chamber and improve the robustness.

Paper Structure

This paper contains 17 sections, 14 equations, 9 figures, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Models and Definitions
  3. PRRLEM-DeGroot
  4. PRRLEM-HOHK
  5. PRRLEM-HEHK
  6. Illustrate Examples and Analysis
  7. Example 1 for PRRLEM-DeGroot
  8. Example 2 for PRRLEM-HOHK
  9. Example 3 for PRRLEM-HEHK
  10. Real-World Example about Space Situational Awareness
  11. Robustness Analysis and Comparison Analysis
  12. Robustness Analysis
  13. Comparison Analysis
  14. Comparison with Traditional DeGroot Model
  15. Comparison with Traditional Homogeneous HK Bounded Confidence Model
  16. ...and 2 more sections

Figures (9)

  • Figure 1: Opinion Evolution of All Agents.
  • Figure 2: Confidence Intervals and Representative Values of Each Opinion after Monte Varlo Tests.
  • Figure 3: Confidence Intervals and Maximum Representative Values of Each Agent after Monte Varlo Tests.
  • Figure 4: Opinion Results Based on PRRLEM-HEHK.
  • Figure 5: Results Based on the Three Proposed Models for the Example about Space Situational Awareness.
  • ...and 4 more figures