Sum of observables in fuzzy quantum spaces

Anatolij Dvurečenskij; Anna Tirpáková

Applications of Mathematics (1992)

  • Volume: 37, Issue: 1, page 40-50
  • ISSN: 0862-7940

Abstract

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We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.

How to cite

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Dvurečenskij, Anatolij, and Tirpáková, Anna. "Sum of observables in fuzzy quantum spaces." Applications of Mathematics 37.1 (1992): 40-50. <http://eudml.org/doc/15699>.

@article{Dvurečenskij1992,
abstract = {We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.},
author = {Dvurečenskij, Anatolij, Tirpáková, Anna},
journal = {Applications of Mathematics},
keywords = {fuzzy quantum space; observable; sum of observables; observables in fuzzy quantum space},
language = {eng},
number = {1},
pages = {40-50},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sum of observables in fuzzy quantum spaces},
url = {http://eudml.org/doc/15699},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Dvurečenskij, Anatolij
AU - Tirpáková, Anna
TI - Sum of observables in fuzzy quantum spaces
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 1
SP - 40
EP - 50
AB - We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.
LA - eng
KW - fuzzy quantum space; observable; sum of observables; observables in fuzzy quantum space
UR - http://eudml.org/doc/15699
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, B. Riečan, On joint observables for F-quantum spaces, Busefal 35 (1988), 10-14. (1988) 
  3. A. Dvurečenskij, B. Riečan, 10.1016/0165-0114(91)90066-Y, Fuzzy Sets and Systems 39 (1991), 67-73. (1991) MR1089012DOI10.1016/0165-0114(91)90066-Y
  4. W. Guz, Fuzzy σ -algebras of physics, Inter. J. Theor. Phys. 24 (1985), 481-493. (1985) Zbl0575.46052MR0798920
  5. A. N. Kolmogorov, Grundebegriffe der Wahrscheinlichkeitsrechnung, Berlin, 1933. (1933) 
  6. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932. (1932) MR0223138
  7. K. Piasecki, 10.1016/0165-0114(85)90093-4, Fuzzy Sets and Systems 17 (1985), 271-284. (1985) Zbl0604.60005MR0819364DOI10.1016/0165-0114(85)90093-4
  8. J. Pykacz, Quantum logics and soft fuzzy probability spaces, Busefal 32 (1987), 150-157. (1987) Zbl0662.03055
  9. B. Riečan, A new approach to some basic notions of statistical quantum theory, Busefal 35 (1987), 4-6. (1987) 
  10. R. Sikorski, Boolean algebras, Springer-Verlag, 1964. (1964) Zbl0123.01303MR0126393
  11. P. Suppes, 10.1086/288067, Phil. Sc. 33 (1966), 14-21. (1966) MR0215575DOI10.1086/288067
  12. V. S. Varadarjan, Geometry of quantum theory, Van Nostrand, New Jersey, 1968. (1968) 
  13. L. A. Zadeh, 10.1016/0022-247X(68)90078-4, J. Math. Anal. Appl. 23 (1968), 421-427. (1968) MR0230569DOI10.1016/0022-247X(68)90078-4

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