Isopignistic Canonical Decomposition via Belief Evolution Network

TL;DR

This paper introduces an isopignistic transformation within belief networks to unify and interpret different uncertainty models, enabling better information processing in explainable AI.

Contribution

It proposes a novel isopignistic transformation based on belief evolution networks and integrates it with a hyper-cautious transferable belief model for canonical decomposition.

Findings

Established a reverse mapping between possibility distribution and belief functions.

Reconstructed basic belief assignments using the isopignistic function.

Provided a theoretical foundation linking probability, Dempster-Shafer, and possibility theories.

Abstract

Developing a general information processing model in uncertain environments is fundamental for the advancement of explainable artificial intelligence. Dempster-Shafer theory of evidence is a well-known and effective reasoning method for representing epistemic uncertainty, which is closely related to subjective probability theory and possibility theory. Although they can be transformed to each other under some particular belief structures, there remains a lack of a clear and interpretable transformation process, as well as a unified approach for information processing. In this paper, we aim to address these issues from the perspectives of isopignistic belief functions and the hyper-cautious transferable belief model. Firstly, we propose an isopignistic transformation based on the belief evolution network. This transformation allows for the adjustment of the information granule while retaining the potential decision outcome. The isopignistic transformation is integrated with a hyper-cautious transferable belief model to establish a new canonical decomposition. This decomposition offers a reverse path between the possibility distribution and its isopignistic mass functions. The result of the canonical decomposition, called isopignistic function, is an identical information content distribution to reflect the propensity and relative commitment degree of the BPA. Furthermore, this paper introduces a method to reconstruct the basic belief assignment by adjusting the isopignistic function. It explores the advantages of this approach in modeling and handling uncertainty within the hyper-cautious transferable belief model. More general, this paper establishes a theoretical basis for building general models of artificial intelligence based on probability theory, Dempster-Shafer theory, and possibility theory.