Geodesic
A new approach to representation of observables on fuzzy quantum posets
Applications of Mathematics, Tome 37 (1992) no. 5, pp. 357-368

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR
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.
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.
DOI : 10.21136/AM.1992.104516
Classification : 04A72, 06C15, 81P15
Keywords: fuzzy quantum poset; fuzzy quantum space; $q$-$\sigma$-algebra; observable 
Long, Le Ba. A new approach to representation of observables on fuzzy quantum posets. Applications of Mathematics, Tome 37 (1992) no. 5, pp. 357-368. doi: 10.21136/AM.1992.104516
@article{10_21136_AM_1992_104516,
     author = {Long, Le Ba},
     title = {A new approach to representation of observables on fuzzy quantum posets},
     journal = {Applications of Mathematics},
     pages = {357--368},
     year = {1992},
     volume = {37},
     number = {5},
     doi = {10.21136/AM.1992.104516},
     mrnumber = {1175930},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104516/}
}
TY  - JOUR
AU  - Long, Le Ba
TI  - A new approach to representation of observables on fuzzy quantum posets
JO  - Applications of Mathematics
PY  - 1992
SP  - 357
EP  - 368
VL  - 37
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104516/
DO  - 10.21136/AM.1992.104516
LA  - en
ID  - 10_21136_AM_1992_104516
ER  - 
%0 Journal Article
%A Long, Le Ba
%T A new approach to representation of observables on fuzzy quantum posets
%J Applications of Mathematics
%D 1992
%P 357-368
%V 37
%N 5
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104516/
%R 10.21136/AM.1992.104516
%G en
%F 10_21136_AM_1992_104516

[1] A. Dvurečenskij, F. Chovanec: Fuzzy quantum spaces and compatibility. Inter. J. Theor. Phys. 27 (1988), 1069-1082. | MR

[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

[3] A. Dvurečenskij, L. B. Long: On representation of fuzzy quantum posets. Acta Math. Univ. Comenianae 58-59 (1991), 239-246. | MR

[4] A. Dvurečenskij, L. B. Long: Observables in fuzzy quantum posets. Acta Math. Univ. Comenianae 58-59 (1991), 247-258. | MR

[5] A. Dvurečenskij: On a representation of observables in fuzzy measurable spaces. to appear.

[6] A. Kolesárová: Representation of fuzzy observables. Proc. Sec. Winter School on Meas. Theory, Lipt. Ján, Jan. 7-12 (1990), 117-120. | MR

[7] A. Kolesárová, R. Mesiar: A note on the representation of fuzzy observables. BUSEFAL 43 (1990), 42-47.

[8] L. B. Long: Fuzzy quantum posets and their states. Acta Math. Univ. Comenianae 58-59 (1991), 231-238. | MR | Zbl

[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. | MR | Zbl

[10] T. Neubrunn, B. Riečan: Measure and Integral. Veda, Bratislava (1981). | MR

[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

[12] B. Riečan: A new approach to some notions of statistical quantum mechanics. BUSEFAL 35 (1988), 4-6.

Cité par Sources :