Article
Full entry |
PDF
(1.3 MB)
Feedback
PDF
(1.3 MB)
Feedback
Keywords:
fuzzy quantum poset; fuzzy quantum space; $q$-$\sigma$-algebra; observable
fuzzy quantum poset; fuzzy quantum space; $q$-$\sigma$-algebra; observable
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.
References:
[1] A. Dvurečenskij, F. Chovanec: Fuzzy quantum spaces and compatibility. Inter. J. Theor. Phys. 27 (1988), 1069-1082. MR 0967421
[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
[3] A. Dvurečenskij, L. B. Long: On representation of fuzzy quantum posets. Acta Math. Univ. Comenianae 58-59 (1991), 239-246. MR 1120371
[4] A. Dvurečenskij, L. B. Long: Observables in fuzzy quantum posets. Acta Math. Univ. Comenianae 58-59 (1991), 247-258. MR 1120372
[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 1118414
[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 1120370 | Zbl 0733.60007
[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 1000194 | Zbl 0685.60006
[10] T. Neubrunn, B. Riečan: Measure and Integral. Veda, Bratislava (1981). MR 0657765
[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
[12] B. Riečan: A new approach to some notions of statistical quantum mechanics. BUSEFAL 35 (1988), 4-6.
Search
Partner of
