0497410 20240103221026.020181203235959.9 85056628809 000450480200002 10.1007/s00012-018-0569-x 26 s. P cav_un_epca*02506650002-524079Springer MV-algebra Riesz space positive operator cav_un_auth*0101141 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 100 Kroupa Tomáš UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2018/MTR/kroupa-0497410.pdf cav_un_auth*0349495 GA17-04630S GA ČR Probability maps are additive and normalised maps taking values in the unit interval of a lattice ordered Abelian group. They appear in theory of affine representations and they are also a semantic counterpart of Hajek’s probability logic. In this paper we obtain a correspondence between probability maps and positive operators of certain Riesz spaces, which extends the well-known representation theorem of real-valued MV-algebraic states by positive linear functionals. When the codomain algebra contains all continuous functions, the set of all probability maps is convex, and we prove that its extreme points coincide with homomorphisms. We also show that probability maps can be viewed as a collection of states indexed by maximal ideals of a codomain algebra, and we characterise this collection in special cases. WOS BA 10000 10100 10101 2019 1 RVO:67985556 http://hdl.handle.net/11104/0290640 1 S 86 3+4 Article Mathematics MATHEMATICS 0.681 0.189 17.5 0.00144 0.432 846 0.436 0.405 90 Q3 35.823 41.2 Q3 Q4 0.78 Q2 41.242 2018 85056628809 SCOPUS PUBMED 000450480200002 WOS cav_un_epca*0250665 Algebra Universalis 0002-5240 1420-8911 Roč. 79 č. 4 2018 Springer