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A Study on Group Decision Making Problem Based on Fuzzy Reasoning and Bayesian Networks

Shui-jin Rong, Wei Guo, Da-qing Zhang

TL;DR

The paper tackles multi-attribute group decision making by marrying fuzzy reasoning with Bayesian networks to handle both linguistic and numerical indicators. It proposes a three-layer hierarchical BN fed by fuzzified inputs, with CPTs dynamically updated via maximum likelihood estimation to adapt to new data. Across synthetic evaluations and eight UCI datasets, the approach yields higher accuracy and F1 scores than traditional weighted methods and shows robustness in high-dimensional and small-sample contexts. This work advances decision-support systems by enabling mixed-input evaluations with adaptive probabilistic reasoning, with potential impact in education, medicine, and finance through improved ranking and uncertainty handling.

Abstract

Aiming at the group decision - making problem with multi - objective attributes, this study proposes a group decision - making system that integrates fuzzy inference and Bayesian network. A fuzzy rule base is constructed by combining threshold values, membership functions, expert experience, and domain knowledge to address quantitative challenges such as scale differences and expert linguistic variables. A hierarchical Bayesian network is designed, featuring a directed acyclic graph with nodes selected by experts, and maximum likelihood estimation is used to dynamically optimize the conditional probability table, modeling the nonlinear correlations among multidimensional indices for posterior probability aggregation. In a comprehensive student evaluation case, this method is compared with the traditional weighted scoring approach. The results indicate that the proposed method demonstrates effectiveness in both rule criterion construction and ranking consistency, with a classification accuracy of 86.0% and an F1 value improvement of 53.4% over the traditional method. Additionally, computational experiments on real - world datasets across various group decision scenarios assess the method's performance and robustness, providing evidence of its reliability in diverse contexts.

A Study on Group Decision Making Problem Based on Fuzzy Reasoning and Bayesian Networks

TL;DR

The paper tackles multi-attribute group decision making by marrying fuzzy reasoning with Bayesian networks to handle both linguistic and numerical indicators. It proposes a three-layer hierarchical BN fed by fuzzified inputs, with CPTs dynamically updated via maximum likelihood estimation to adapt to new data. Across synthetic evaluations and eight UCI datasets, the approach yields higher accuracy and F1 scores than traditional weighted methods and shows robustness in high-dimensional and small-sample contexts. This work advances decision-support systems by enabling mixed-input evaluations with adaptive probabilistic reasoning, with potential impact in education, medicine, and finance through improved ranking and uncertainty handling.

Abstract

Aiming at the group decision - making problem with multi - objective attributes, this study proposes a group decision - making system that integrates fuzzy inference and Bayesian network. A fuzzy rule base is constructed by combining threshold values, membership functions, expert experience, and domain knowledge to address quantitative challenges such as scale differences and expert linguistic variables. A hierarchical Bayesian network is designed, featuring a directed acyclic graph with nodes selected by experts, and maximum likelihood estimation is used to dynamically optimize the conditional probability table, modeling the nonlinear correlations among multidimensional indices for posterior probability aggregation. In a comprehensive student evaluation case, this method is compared with the traditional weighted scoring approach. The results indicate that the proposed method demonstrates effectiveness in both rule criterion construction and ranking consistency, with a classification accuracy of 86.0% and an F1 value improvement of 53.4% over the traditional method. Additionally, computational experiments on real - world datasets across various group decision scenarios assess the method's performance and robustness, providing evidence of its reliability in diverse contexts.
Paper Structure (17 sections, 10 equations, 3 figures, 7 tables, 1 algorithm)

This paper contains 17 sections, 10 equations, 3 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Fuzzy reasoning mechanism
  4. Introduction of Bayesian networks
  5. Group decision system
  6. Data fuzzy processing
  7. Structure design of Bayesian network
  8. Comprehensive evaluation with Bayesian network
  9. Experimental study
  10. Data generation and segmentation
  11. Model training and parameter optimization
  12. Fuzzy rules of input layer in the model
  13. Decision Results of the Output Layer in the Model
  14. Evaluation indicators and comparative analysis
  15. Validation Experiments on UCI Datasets
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Fuzzy Inference System Structure
  • Figure 2: Bayesian Network Structure
  • Figure 3: Flowchart of System Algorithm