| Title:
|
A new approach to representation of observables on fuzzy quantum posets (English) |
| Author:
|
Long, Le Ba |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
5 |
| Year:
|
1992 |
| Pages:
|
357-368 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a representation of an observable on a fuzzy quantum poset of type II by a pointwise defined real-valued function. This method is inspired by that of Kolesárová [6] and Mesiar [7], and our results extend representations given by the author and Dvurečenskij [4]. Moreover, we show that in this model, the converse representation fails, in general. (English) |
| Keyword:
|
fuzzy quantum poset |
| Keyword:
|
fuzzy quantum space |
| Keyword:
|
$q$-$\sigma$-algebra |
| Keyword:
|
observable |
| MSC:
|
04A72 |
| MSC:
|
06C15 |
| MSC:
|
81P15 |
| idMR:
|
MR1175930 |
| DOI:
|
10.21136/AM.1992.104516 |
| . |
| Date available:
|
2008-05-20T18:44:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104516 |
| . |
| Reference:
|
[1] A. Dvurečenskij, F. Chovanec: Fuzzy quantum spaces and compatibility.Inter. J. Theor. Phys. 27 (1988), 1069-1082. MR 0967421 |
| Reference:
|
[2] A. Dvurečenskij F. Chovanec, F. Köpka: On mean valued additivity in fuzzy measurable spaces.Acta Math. Univ. Comenianae 58-59 (1991), 107-117. MR 1120358 |
| Reference:
|
[3] A. Dvurečenskij, L. B. Long: On representation of fuzzy quantum posets.Acta Math. Univ. Comenianae 58-59 (1991), 239-246. MR 1120371 |
| Reference:
|
[4] A. Dvurečenskij, L. B. Long: Observables in fuzzy quantum posets.Acta Math. Univ. Comenianae 58-59 (1991), 247-258. MR 1120372 |
| Reference:
|
[5] A. Dvurečenskij: On a representation of observables in fuzzy measurable spaces.to appear. |
| Reference:
|
[6] A. Kolesárová: Representation of fuzzy observables.Proc. Sec. Winter School on Meas. Theory, Lipt. Ján, Jan. 7-12 (1990), 117-120. MR 1118414 |
| Reference:
|
[7] A. Kolesárová, R. Mesiar: A note on the representation of fuzzy observables.BUSEFAL 43 (1990), 42-47. |
| Reference:
|
[8] L. B. Long: Fuzzy quantum posets and their states.Acta Math. Univ. Comenianae 58-59 (1991), 231-238. Zbl 0733.60007, MR 1120370 |
| Reference:
|
[9] R. Mesiar: Fuzzy Bayes formula and the ill defined elements.Proc. 1st Winter School on Meas. Th., Lipt. Ján., Jan. 10-15, 1988, pp. 82-87. Zbl 0685.60006, MR 1000194 |
| Reference:
|
[10] T. Neubrunn, B. Riečan: Measure and Integral.Veda, Bratislava (1981). MR 0657765 |
| Reference:
|
[11] J. Pykacz: Probability measure in the fuzzy set approach to quantum logics.In Proc. 1st Winter School on Meas. Th., Lipt. Ján., Jan. 10-15 (1988), 124-127. MR 1000203 |
| Reference:
|
[12] B. Riečan: A new approach to some notions of statistical quantum mechanics.BUSEFAL 35 (1988), 4-6. |
| . |
