A new approach to representation of observables on fuzzy quantum posets

Le Ba Long

Applications of Mathematics (1992)

  • Volume: 37, Issue: 5, page 357-368
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Long, Le Ba. "A new approach to representation of observables on fuzzy quantum posets." Applications of Mathematics 37.5 (1992): 357-368. <http://eudml.org/doc/15721>.

@article{Long1992,
abstract = {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.},
author = {Long, Le Ba},
journal = {Applications of Mathematics},
keywords = {fuzzy quantum poset; fuzzy quantum space; $q$-$\sigma $-algebra; observable; fuzzy quantum poset; representation; quantum logic; orthomodular poset},
language = {eng},
number = {5},
pages = {357-368},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new approach to representation of observables on fuzzy quantum posets},
url = {http://eudml.org/doc/15721},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Long, Le Ba
TI - A new approach to representation of observables on fuzzy quantum posets
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 5
SP - 357
EP - 368
AB - 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.
LA - eng
KW - fuzzy quantum poset; fuzzy quantum space; $q$-$\sigma $-algebra; observable; fuzzy quantum poset; representation; quantum logic; orthomodular poset
UR - http://eudml.org/doc/15721
ER -

References

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  1. A. Dvurečenskij, F. Chovanec, Fuzzy quantum spaces and compatibility, Inter. J. Theor. Phys. 27 (1988), 1069-1082. (1988) MR0967421
  2. A. Dvurečenskij F. Chovanec, F. Köpka, On mean valued additivity in fuzzy measurable spaces, Acta Math. Univ. Comenianae 58-59 (1991), 107-117. (1991) MR1120358
  3. A. Dvurečenskij, L. B. Long, On representation of fuzzy quantum posets, Acta Math. Univ. Comenianae 58-59 (1991), 239-246. (1991) MR1120371
  4. A. Dvurečenskij, L. B. Long, Observables in fuzzy quantum posets, Acta Math. Univ. Comenianae 58-59 (1991), 247-258. (1991) MR1120372
  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. (1990) MR1118414
  7. A. Kolesárová, R. Mesiar, A note on the representation of fuzzy observables, BUSEFAL 43 (1990), 42-47. (1990) 
  8. L. B. Long, Fuzzy quantum posets and their states, Acta Math. Univ. Comenianae 58-59 (1991), 231-238. (1991) Zbl0733.60007MR1120370
  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. (1988) Zbl0685.60006MR1000194
  10. T. Neubrunn, B. Riečan, Measure and Integral, Veda, Bratislava (1981). (1981) MR0657765
  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. (1988) MR1000203
  12. B. Riečan, A new approach to some notions of statistical quantum mechanics, BUSEFAL 35 (1988), 4-6. (1988) 

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