Pignistic Probability Transforms for Mixes of Low- and High-Probability Events

TL;DR

This paper introduces four new pignistic probability transforms designed to better handle mixes of low- and high-probability events in belief function theory, improving decision-making in time-critical, incomplete information scenarios.

Contribution

The paper proposes novel pignistic probability transforms that incorporate the latest belief measures to enhance decision accuracy, especially for critical systems with risk thresholds.

Findings

New transforms assign probabilities that converge faster to low-probability thresholds.

Transformations adapt probabilities based on Beliefs, Plausibilities, or BBAs.

Introduction of a probability information content (PIC) metric.

Abstract

In some real world information fusion situations, time critical decisions must be made with an incomplete information set. Belief function theories (e.g., Dempster-Shafer theory of evidence, Transferable Belief Model) have been shown to provide a reasonable methodology for processing or fusing the quantitative clues or information measurements that form the incomplete information set. For decision making, the pignistic (from the Latin pignus, a bet) probability transform has been shown to be a good method of using Beliefs or basic belief assignments (BBAs) to make decisions. For many systems, one need only address the most-probable elements in the set. For some critical systems, one must evaluate the risk of wrong decisions and establish safe probability thresholds for decision making. This adds a greater complexity to decision making, since one must address all elements in the set that are above the risk decision threshold. The problem is greatly simplified if most of the probabilities fall below this threshold. Finding a probability transform that properly represents mixes of low- and high-probability events is essential. This article introduces four new pignistic probability transforms with an implementation that uses the latest values of Beliefs, Plausibilities, or BBAs to improve the pignistic probability estimates. Some of them assign smaller values of probabilities for smaller values of Beliefs or BBAs than the Smets pignistic transform. They also assign higher probability values for larger values of Beliefs or BBAs than the Smets pignistic transform. These probability transforms will assign a value of probability that converges faster to the values below the risk threshold. A probability information content (PIC) variable is also introduced that assigns an information content value to any set of probability. Four operators are defined to help simplify the derivations.