Isopignistic Canonical Decomposition via Belief Evolution Network
It addresses foundational issues in uncertain information processing for explainable AI, though it appears incremental as it builds on existing theories like the hyper-cautious transferable belief model.
The paper tackles the lack of a clear and interpretable transformation process between Dempster-Shafer theory, probability theory, and possibility theory by proposing an isopignistic transformation and canonical decomposition, resulting in an isopignistic function that reflects information content without specific numerical gains.
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.