| bibtype |
J -
Journal Article
|
| ARLID |
0497410 |
| utime |
20240103221026.0 |
| mtime |
20181203235959.9 |
| SCOPUS |
85056628809 |
| WOS |
000450480200002 |
| DOI |
10.1007/s00012-018-0569-x |
| title
(primary) (eng) |
Ordered group-valued probability, positive operators, and integral representations |
| specification |
| page_count |
26 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0250665 |
| ISSN |
0002-5240 |
| title
|
Algebra Universalis |
| volume_id |
79 |
| publisher |
|
|
| keyword |
MV-algebra |
| keyword |
Riesz space |
| keyword |
positive operator |
| author
(primary) |
| ARLID |
cav_un_auth*0101141 |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept (eng) |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department (eng) |
MTR |
| full_dept |
Department of Decision Making Theory |
| share |
100 |
| name1 |
Kroupa |
| name2 |
Tomáš |
| institution |
UTIA-B |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| source |
|
| cas_special |
| project |
| ARLID |
cav_un_auth*0349495 |
| project_id |
GA17-04630S |
| agency |
GA ČR |
|
| abstract
(eng) |
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,\nand 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. |
| result_subspec |
WOS |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10101 |
| reportyear |
2019 |
| num_of_auth |
1 |
| inst_support |
RVO:67985556 |
| permalink |
http://hdl.handle.net/11104/0290640 |
| mrcbC61 |
1 |
| confidential |
S |
| article_num |
86 |
| mrcbC86 |
3+4 Article Mathematics |
| mrcbT16-e |
MATHEMATICS |
| mrcbT16-j |
0.432 |
| mrcbT16-s |
0.436 |
| mrcbT16-B |
35.823 |
| mrcbT16-D |
Q3 |
| mrcbT16-E |
Q4 |
| arlyear |
2018 |
| mrcbU14 |
85056628809 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
000450480200002 WOS |
| mrcbU63 |
cav_un_epca*0250665 Algebra Universalis 0002-5240 1420-8911 Roč. 79 č. 4 2018 Springer |
|