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Reliability Assessment of Information Sources Based on Random Permutation Set

Juntao Xu, Tianxiang Zhan, Yong Deng

TL;DR

A reliability computation method for RPS sources, based on the RPS probability transformation, is introduced and applied to pattern recognition, and demonstrates that the proposed approach effectively bridges the gap between DST and RPS and achieves superior recognition accuracy in classification problems.

Abstract

In pattern recognition, handling uncertainty is a critical challenge that significantly affects decision-making and classification accuracy. Dempster-Shafer Theory (DST) is an effective reasoning framework for addressing uncertainty, and the Random Permutation Set (RPS) extends DST by additionally considering the internal order of elements, forming a more ordered extension of DST. However, there is a lack of a transformation method based on permutation order between RPS and DST, as well as a sequence-based probability transformation method for RPS. Moreover, the reliability of RPS sources remains an issue that requires attention. To address these challenges, this paper proposes an RPS transformation approach and a probability transformation method tailored for RPS. On this basis, a reliability computation method for RPS sources, based on the RPS probability transformation, is introduced and applied to pattern recognition. Experimental results demonstrate that the proposed approach effectively bridges the gap between DST and RPS and achieves superior recognition accuracy in classification problems.

Reliability Assessment of Information Sources Based on Random Permutation Set

TL;DR

A reliability computation method for RPS sources, based on the RPS probability transformation, is introduced and applied to pattern recognition, and demonstrates that the proposed approach effectively bridges the gap between DST and RPS and achieves superior recognition accuracy in classification problems.

Abstract

In pattern recognition, handling uncertainty is a critical challenge that significantly affects decision-making and classification accuracy. Dempster-Shafer Theory (DST) is an effective reasoning framework for addressing uncertainty, and the Random Permutation Set (RPS) extends DST by additionally considering the internal order of elements, forming a more ordered extension of DST. However, there is a lack of a transformation method based on permutation order between RPS and DST, as well as a sequence-based probability transformation method for RPS. Moreover, the reliability of RPS sources remains an issue that requires attention. To address these challenges, this paper proposes an RPS transformation approach and a probability transformation method tailored for RPS. On this basis, a reliability computation method for RPS sources, based on the RPS probability transformation, is introduced and applied to pattern recognition. Experimental results demonstrate that the proposed approach effectively bridges the gap between DST and RPS and achieves superior recognition accuracy in classification problems.

Paper Structure

This paper contains 12 sections, 2 theorems, 38 equations, 7 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dempster-Shafer evidence theory
  4. Random permutation set theory
  5. Proposed methods
  6. Numerical examples
  7. Application of the proposed method in target classification
  8. Dataset
  9. Comparative models
  10. Implementation
  11. Result and discussion
  12. Conclusion

Key Result

Corollary 13.1

Since the RPS additionally considers the impact of order compared to DST, for different $A \in PES(\Theta)$, if they contain the same number of elements, their order support satisfies: where $g$ denotes the number of elements contained in $A$.

Figures (7)

  • Figure 1: An illustration of the subdivision of PEs for the given FOD
  • Figure 2: Different distance under different A.
  • Figure 3: The reliability factor of information source under different $\eta$.
  • Figure 4: The reliability factor of information source under different $\eta$.
  • Figure 5: Overview of the proposed method's diagrams: (a) Calculation of decision contribution, (b) Calculation of evidence reliability, and (c) Classification problem-solving process based on the proposed method.
  • ...and 2 more figures

Theorems & Definitions (25)

  • Definition 1: Frame of discernment
  • Definition 2: Basic probability assignment
  • Definition 3: Pignistic probability transformation
  • Definition 4: Discounting rules
  • Definition 5: Permutation Event Space
  • Definition 6: Random permutation set
  • Definition 7: Intersection of permutation events
  • Definition 8: Orthogonal sum of permutation mass functions
  • Definition 9: Ordered probability transformation
  • Definition 10: RPS discounting rule
  • ...and 15 more