CD-BFT: Canonical Decomposition-Based Belief Functions Transformation in Possibility Theory.

Abstract

Based on subjective possibilistic semantics, an agent's subjective probability mass function is dominated by a qualitative Possibility Mass Function (PossMF), which can also be transformed into a unique consonant mass function. However, the existing transformation method cannot maintain the consistency of combination rules, i.e., fusing PossMFs and consonant mass functions with same information content, respectively, the results no longer maintain the reversible transformation. To address the above issue, a novel belief functions transformation is proposed, which can be interpreted based on both Smets' canonical decomposition and Pichon's canonical decomposition. The proposed method is validated based on consistency of combination rules, the least commitment principle, and its application in the fusion of information. In addition, based on the two canonical decompositions, we extend the transformation to possibilistic belief structure, and offer a new perspective of relationship between possibilistic information and evidential information.