Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Imprecise Belief Fusion Facing a DST benchmark problem

Francisco Aragão, João Alcântara

TL;DR

The paper addresses the Dempster-Shafer belief fusion anomaly (Dempster paradox) where equal-expertise sources can be unfairly discounted by the DS combination rule. It establishes an isomorphism between DST and probabilistic logic and replaces the DS rule with a Fusion Method based on a Combined Alternative Measure, applied to the DST paradox benchmark such as the Two Doctors problem. A key result is a theorem showing that the fused measure $\mu_{XX}$ cannot replica input BBAs $m_1$ or $m_2$ for all hypotheses, thereby avoiding the traditional anomalies; this is supported by a contradiction-based proof outline. The approach yields a robust imprecise-data fusion framework that remains informative under conflict and highlights the potential for broader AI applications, albeit with considerations of computational complexity.

Abstract

When we merge information in Dempster-Shafer Theory (DST), we are faced with anomalous behavior: agents with equal expertise and credibility can have their opinion disregarded after resorting to the belief combination rule of this theory. This problem is interesting because belief fusion is an inherent part of dealing with situations where available information is imprecise, as often occurs in Artificial Intelligence. We managed to identify an isomorphism betwin the DST formal apparatus into that of a Probabilistic Logic. Thus, we solved the problematic inputs affair by replacing the DST combination rule with a new fusion process aiming at eliminating anomalies proposed by that rule. We apply the new fusion method to the DST paradox Problem.

Imprecise Belief Fusion Facing a DST benchmark problem

TL;DR

The paper addresses the Dempster-Shafer belief fusion anomaly (Dempster paradox) where equal-expertise sources can be unfairly discounted by the DS combination rule. It establishes an isomorphism between DST and probabilistic logic and replaces the DS rule with a Fusion Method based on a Combined Alternative Measure, applied to the DST paradox benchmark such as the Two Doctors problem. A key result is a theorem showing that the fused measure cannot replica input BBAs or for all hypotheses, thereby avoiding the traditional anomalies; this is supported by a contradiction-based proof outline. The approach yields a robust imprecise-data fusion framework that remains informative under conflict and highlights the potential for broader AI applications, albeit with considerations of computational complexity.

Abstract

When we merge information in Dempster-Shafer Theory (DST), we are faced with anomalous behavior: agents with equal expertise and credibility can have their opinion disregarded after resorting to the belief combination rule of this theory. This problem is interesting because belief fusion is an inherent part of dealing with situations where available information is imprecise, as often occurs in Artificial Intelligence. We managed to identify an isomorphism betwin the DST formal apparatus into that of a Probabilistic Logic. Thus, we solved the problematic inputs affair by replacing the DST combination rule with a new fusion process aiming at eliminating anomalies proposed by that rule. We apply the new fusion method to the DST paradox Problem.
Paper Structure (16 sections, 3 theorems, 29 equations, 3 tables)

This paper contains 16 sections, 3 theorems, 29 equations, 3 tables.

Table of Contents

  1. Introduction
  2. The Dempster-Shafer Theory
  3. Basic Definitions
  4. A Combination Rule Counter-example
  5. Information Fusion
  6. The Fusion Problem
  7. A Solution to Dempster Paradox Fusion Problem
  8. Conclusion of Two Doctors Example
  9. Results and Conclusion
  10. Proof outline of the theorem
  11. The hypothesis of contradiction leads to a system of equations
  12. The theorem hypothesis leads to Lemma \ref{['teo:Lema01julhoC']} on inequalities in BBAs
  13. Lemma \ref{['teo:Lema01julhoC']}, Lemma \ref{['teo:Lema01julhoB']} and the constraints of the BBA definition lead to the inconsistency of the system of equations
  14. The system without a solution in the real interval $[0, 1]$ constitutes a contradiction to the hypothesis of contradiction.
  15. Related Work - DST-CR
  16. ...and 1 more sections

Key Result

Theorem 12

Let $\Theta$ be a frame of discernment and $m_1$ and $m_2$ be two BBA over $\Theta$. Let $\mu_1$ and $\mu_2$ be transcripted measures of $m_1$ and $m_2$. There exists $A \in \Theta$ such that $\mu_{XX}(A) \neq m_1(A)$ and $\mu_{XX}(A) \neq m_2(A)$. Where $\mu_{XX}(\cdot)$ is the combined measure of

Theorems & Definitions (16)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Example 5
  • Definition 6
  • Example 7
  • Definition 8
  • Definition 9
  • Definition 10
  • ...and 6 more