On conditional belief functions in directed graphical models in the Dempster-Shafer theory

0573509 - ÚTIA 2024 RIV US eng J - Článek v odborném periodiku
Jiroušek, Radim - Kratochvíl, Václav - Shenoy, P. P.
On conditional belief functions in directed graphical models in the Dempster-Shafer theory.
International Journal of Approximate Reasoning. Roč. 160, č. 1 (2023), č. článku 108976. ISSN 0888-613X. E-ISSN 1873-4731
Grant CEP: GA ČR(CZ) GA21-07494S
Institucionální podpora: RVO:67985556
Klíčová slova: Dempster-Shafer theory of belief functions * Conditional belief functions * Smets' conditional embedding * Belief-function directed graphical models
Obor OECD: Applied mathematics
Impakt faktor: 3.9, rok: 2022
Způsob publikování: Open access
http://library.utia.cas.cz/separaty/2023/MTR/jirousek-0573509.pdf https://www.sciencedirect.com/science/article/pii/S0888613X2300107X?via%3Dihub

The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similarly to probability theory's notion of conditional probability tables. Conditional belief functions are necessary for constructing directed graphical belief function models in the same sense as conditional probability tables are necessary for constructing Bayesian networks. We provide examples of conditional belief functions, including those obtained by Smets' conditional embedding. Besides defining conditional belief functions, we state and prove a few basic properties of conditionals. In the belief-function literature, conditionals are defined starting from a joint belief function. Conditionals are then defined using the removal operator, an inverse of Dempster's combination operator. When such conditionals are well-defined belief functions, we show that our definition is equivalent to these definitions.
Trvalý link: https://hdl.handle.net/11104/0344419