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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:
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 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.


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