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Canonical decomposition of dichotomous basic belief assignment
Author(s) -
Dezert Jean,
Smarandache Florentin
Publication year - 2020
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22236
Subject(s) - mathematics , canonical form , decomposition , dempster–shafer theory , rule based system , artificial intelligence , computer science , pure mathematics , statistics , ecology , biology
In this paper, we prove that any dichotomous basic belief assignment (BBA) m can be expressed as the combination of two simple belief assignments m p and m c called, respectively, the pros and cons BBAs thanks to the proportional conflict redistribution rule no 5 (PCR5). This decomposition always exists and is unique and we call it the canonical decomposition of the BBA m . We also show that canonical decompositions do not exist in general if we use the conjunctive rule, the disjunctive rule, Dempster's rule, Dubois and Prade's or Yager's rules, or even the averaging rule of combination. We give some numerical examples of canonical decompositions and discuss of the potential interest of this canonical decomposition for applications in information fusion.