0576517 20240402214531.220231017235959.9 10 s. E cav_un_epca*05765161-10Osaka, JapanOsaka Metropolitan University2023YoshifumiKusunokiVáclavKratochvílMasahiroInuiguchiOndřejČepek belief functions conditioning composition conditional independence cav_un_auth*0101118 Jiroušek Radim UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0216188 Kratochvíl Václav UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0275452 Shenoy P. P. US PDF dokument http://library.utia.cas.cz/separaty/2023/MTR/kratochvil-0576517.pdf GA21-07494S GA ČR CZ cav_un_auth*0430801 As in probability theory, graphical and compositional models in the Dempster-Shafer (D-S) belief function theory handle multidimensional belief functions applied to support inference for practical problems. Both types of models represent multidimensional belief functions using their low-dimensional marginals. In the case of graphical models, these marginals are usually conditionals, for compositional models, they are unconditional. Nevertheless, one must introduce some conditioning to compose unconditional belief functions and avoid double-counting knowledge. Thus, conditioning is crucial in processing multidimensional compositional models for belief functions. This paper summarizes some important open problems, the solution of which should enable a trouble-free design of computational processes employing D-S belief functions in AI. For some of them, we discuss possible solutions. The problems considered in this paper are of two types. There are still some gaps that should be filled to get a mathematically consistent uncertainty theory. Other problems concern the computational tractability of procedures arising from the super-exponential growth of the space and time complexity of the designed algorithms. cav_un_auth*0456493 Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty 20232 /23./ 20230916 20230920 Matsuyama JP BA 10000 10100 10103 2024 3 PR RVO:67985556 https://hdl.handle.net/11104/0346458 S 2023 SCOPUS PUBMED WOS PDF dokument cav_un_epca*0576516 Proceedings of the 23rd Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty Osaka Metropolitan University 2023 Osaka, Japan 1 10 Yoshifumi Kusunoki 340 Václav Kratochvíl 340 Masahiro Inuiguchi 340 Ondřej Čepek 340