0525114 20240103224152.220200618235959.9 85086260553 10.1007/978-3-030-50143-3_29 12 s. P cav_un_epca*0525113978-3-030-50142-61865-0929382-393ChamSpringer2020 Marginal problem Extension Product extension cav_un_auth*0101223 Vejnarová Jiřina 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. http://library.utia.cas.cz/separaty/2020/MTR/vejnarova-0525114.pdf GA19-04579S GA ČR CZ cav_un_auth*0380558 Recently introduced marginal problem – which addresses the question of whether or not a common extension exists for a given set of marginal basic assignments – in the framework of evidence theory is recalled. Sets of solutions are studied in more detail and it is shown, by a simple example, that their structure is much more complicated (i.e. the number of extreme vertices of the convex set of solutions is substantially greater) than that in an analogous problem in probabilistic framework. The concept of product extension of two basic assignments is generalized (via operator of composition) to a finite sequence of basic assignments. This makes possible not only to express the extension, if it exists, in a closed form, but also enables us to find the sufficient condition for the existence of an extension of evidential marginal problem. Presented approach is illustrated by a simple example. cav_un_auth*0393126 IPMU 2020 /18./ 20200615 20200620 Lisabon PT BA 10000 10100 10102 2021 4 A sml 4as 20231122144954.1 PR RVO:67985556 http://hdl.handle.net/11104/0309420 S Consent to Publish 20200405 2020 Soubory v repozitáři: vejnarova-0525114-copyright.pdf 85086260553 SCOPUS PUBMED WOS cav_un_epca*0525113 Information Processing and Management of Uncertainty in Knowledge-Based Systems : 18th International Conference, IPMU 2020 978-3-030-50142-6 1865-0929 382 393 Cham Springer 2020