| Title:
|
Entropy on effect algebras with Riesz decomposition property II: MV-algebras (English) |
| Author:
|
Di Nola, Antonio |
| Author:
|
Dvurečenskij, Anatolij |
| Author:
|
Hyčko, Marek |
| Author:
|
Manara, Corrado |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
[161]-176 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes. (English) |
| Keyword:
|
effect algebra |
| Keyword:
|
Riesz decomposition property |
| Keyword:
|
MV-algebra |
| Keyword:
|
state |
| Keyword:
|
entropy |
| MSC:
|
03B50 |
| MSC:
|
03G12 |
| MSC:
|
06D35 |
| MSC:
|
28A20 |
| MSC:
|
37B40 |
| idZBL:
|
Zbl 1249.03116 |
| idMR:
|
MR2138766 |
| . |
| Date available:
|
2009-09-24T20:07:56Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135648 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/135647 |
| . |
| Reference:
|
[1] Butnariu D., Klement P.: Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Kluwer Academic Publishers, Dordrecht 199. |
| Reference:
|
[2] Nola A. Di, Dvurečenskij A., Hyčko, M., Manara C.: Entropy of effect algebras with the Riesz decomposition property I: Basic properties.Kybernetika 41 (2005), 143–160 MR 2138765 |
| Reference:
|
[3] Nola A. Di, Dvurečenskij, A., Jakubík J.: Good and bad infinitesimals, and states on pseudo MV-algebras, submitte. |
| Reference:
|
[4] Dvurečenskij A.: Loomis–Sikorski theorem for $\sigma $-complete MV-algebras and $\ell $-groups.J. Austral. Math. Soc. Ser. A 68 (2000), 261–277 Zbl 0958.06006, MR 1738040, 10.1017/S1446788700001993 |
| Reference:
|
[5] Dvurečenskij A.: MV-observables and MV-algebras.J. Math. Anal. Appl. 259 (2001), 413–428 Zbl 0992.03081, MR 1842068, 10.1006/jmaa.2000.7409 |
| Reference:
|
[6] Dvurečenskij A.: Central elements and Cantor–Bernstein’s theorem for pseudo-effect alegbras.J. Austral. Math. Soc. 74 (2003), 121–143 MR 1948263, 10.1017/S1446788700003177 |
| Reference:
|
[7] Dvurečenskij A.: Perfect effect algebras are categorically equivalent with Abelian interpolation po-groups, submitte. |
| Reference:
|
[8] Dvurečenskij A.: Product effect algebras.Inter. J. Theor. Phys. 41 (2002), 1827–1839 Zbl 1014.81004, MR 1944619 |
| Reference:
|
[9] Dvurečenskij A., Pulmannová S.: New Trends in Quantum Structures, Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava 200. MR 1861369 |
| Reference:
|
[10] Fuchs L.: Partially Ordered Algebraic Systems.Pergamon Press, Oxford – London – New York – Paris 1963 Zbl 0137.02001, MR 0171864 |
| Reference:
|
[11] Goodearl K. R.: Partially Ordered Abelian Groups with Interpolation.(Math. Surveys and Monographs No. 20.) Amer. Math. Society, Providence, RI 1986 Zbl 0589.06008, MR 0845783 |
| Reference:
|
[12] Mundici D.: Tensor products and the Loomis–Sikorski theorem for MV-algebras.Advan. Appl. Math. 22 (1999), 227–248 Zbl 0926.06004, MR 1659410, 10.1006/aama.1998.0631 |
| Reference:
|
[13] Riečan B.: Kolmogorov–Sinaj entropy on MV-algebras, submitte. |
| Reference:
|
[14] Riečan B., Mundici D.: Probability on MV-algebras.In: Handbook of Measure Theory (E. Pap, ed.), Elsevier Science, Amsterdam 2002, Vol. II, pp. 869–909 Zbl 1017.28002, MR 1954631 |
| Reference:
|
[15] Riečan B., Neubrunn T.: Integral, Measure and Ordering, Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava 199. MR 1489521 |
| . |
