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Random Graph Set and Evidence Pattern Reasoning Model

Tianxiang Zhan, Zhen Li, Yong Deng

TL;DR

This work addresses the mismatch between traditional preference-free evidential reasoning and real-world decision tasks by introducing the Evidence Pattern Reasoning Model (EPRM), which integrates BPA, Pattern Operator, and Decision Making Operator to encode user preferences. To capture complex sample relationships beyond simple combinations or permutations, it extends Random Permutation Set with Random Graph Set (RGS), enabling graph-based representations of events and relations. The framework is demonstrated on an aircraft velocity ranking problem, where the Conflict Resolution Decision (CRD) method—an EPRM implementation leveraging RGS—achieves notable improvements over the Mean Velocity Decision baseline in 18.17% of cases and provides a unified approach for evidential decision making under uncertainty. The work suggests that combining preference-aware fusion with graph-based relational modeling offers practical benefits for multi-sensor data fusion and complex decision tasks, with open avenues for broader applications and real-time optimization.

Abstract

Evidence theory is widely used in decision-making and reasoning systems. In previous research, Transferable Belief Model (TBM) is a commonly used evidential decision making model, but TBM is a non-preference model. In order to better fit the decision making goals, the Evidence Pattern Reasoning Model (EPRM) is proposed. By defining pattern operators and decision making operators, corresponding preferences can be set for different tasks. Random Permutation Set (RPS) expands order information for evidence theory. It is hard for RPS to characterize the complex relationship between samples such as cycling, paralleling relationships. Therefore, Random Graph Set (RGS) were proposed to model complex relationships and represent more event types. In order to illustrate the significance of RGS and EPRM, an experiment of aircraft velocity ranking was designed and 10,000 cases were simulated. The implementation of EPRM called Conflict Resolution Decision optimized 18.17\% of the cases compared to Mean Velocity Decision, effectively improving the aircraft velocity ranking. EPRM provides a unified solution for evidence-based decision making.

Random Graph Set and Evidence Pattern Reasoning Model

TL;DR

This work addresses the mismatch between traditional preference-free evidential reasoning and real-world decision tasks by introducing the Evidence Pattern Reasoning Model (EPRM), which integrates BPA, Pattern Operator, and Decision Making Operator to encode user preferences. To capture complex sample relationships beyond simple combinations or permutations, it extends Random Permutation Set with Random Graph Set (RGS), enabling graph-based representations of events and relations. The framework is demonstrated on an aircraft velocity ranking problem, where the Conflict Resolution Decision (CRD) method—an EPRM implementation leveraging RGS—achieves notable improvements over the Mean Velocity Decision baseline in 18.17% of cases and provides a unified approach for evidential decision making under uncertainty. The work suggests that combining preference-aware fusion with graph-based relational modeling offers practical benefits for multi-sensor data fusion and complex decision tasks, with open avenues for broader applications and real-time optimization.

Abstract

Evidence theory is widely used in decision-making and reasoning systems. In previous research, Transferable Belief Model (TBM) is a commonly used evidential decision making model, but TBM is a non-preference model. In order to better fit the decision making goals, the Evidence Pattern Reasoning Model (EPRM) is proposed. By defining pattern operators and decision making operators, corresponding preferences can be set for different tasks. Random Permutation Set (RPS) expands order information for evidence theory. It is hard for RPS to characterize the complex relationship between samples such as cycling, paralleling relationships. Therefore, Random Graph Set (RGS) were proposed to model complex relationships and represent more event types. In order to illustrate the significance of RGS and EPRM, an experiment of aircraft velocity ranking was designed and 10,000 cases were simulated. The implementation of EPRM called Conflict Resolution Decision optimized 18.17\% of the cases compared to Mean Velocity Decision, effectively improving the aircraft velocity ranking. EPRM provides a unified solution for evidence-based decision making.
Paper Structure (25 sections, 31 equations, 12 figures, 5 tables, 1 algorithm)

This paper contains 25 sections, 31 equations, 12 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Dempster-Shafer Theory
  4. Transferable Belief Model and Decision Making
  5. Random Permutation Set
  6. Evidence Pattern Reasoning Model
  7. Confirming Sample Space And Event Space
  8. Confirming Information Sources
  9. Designing basic probability assignment algorithm
  10. Implement Pattern Operator
  11. Pattern Fusion
  12. Reasoning and Decision Making
  13. Random Graph Set
  14. Relation Expression Of Graph
  15. Definition
  16. ...and 10 more sections

Figures (12)

  • Figure 1: Direction of transference in TBM (FOD $\Omega=\{A,B,C\}$)
  • Figure 2: Process flow of belief pattern reasoning model
  • Figure 3: Ambiguous numbers in MNIST
  • Figure 4: Three sources of input information and s
  • Figure 5: Combination and permutation in form of graph
  • ...and 7 more figures