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

Area of Science:

• Decision Theory
• Artificial Intelligence
• Information Fusion

Background:

• Subjective probability mass functions are often represented by qualitative Possibility Mass Functions (PossMFs).
• Existing transformations between PossMFs and consonant mass functions lack consistency in combination rules, hindering reversible transformations.

Purpose of the Study:

• To propose a novel belief function transformation method.
• To ensure consistency of combination rules between PossMFs and consonant mass functions.
• To extend the transformation to possibilistic belief structures.

Main Methods:

• A new belief function transformation is proposed, interpretable via Smets' and Pichon's canonical decompositions.
• The method is validated using combination rule consistency, the least commitment principle, and information fusion applications.

Main Results:

• The proposed transformation maintains the consistency of combination rules.
• Reversibility is achieved between PossMFs and consonant mass functions.
• The transformation is extended to possibilistic belief structures, clarifying the link between possibilistic and evidential information.

Conclusions:

• The novel transformation addresses limitations in existing methods, enabling reliable information fusion.
• This work provides a new perspective on the relationship between possibilistic and evidential information within belief function frameworks.