Previous |  Up |  Next

Article

Keywords:
fuzzy quantum space; observable; sum of observables
Summary:
We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.
References:
[1] A. Dvurečenskij, F. Chovanec: Fuzzy quantum spaces and compatibility. Inter. J. Theor. Phys. 27(1988), 1069-1082. MR 0967421
[2] A. Dvurečenskij, B. Riečan: On joint observables for F-quantum spaces. Busefal 35 (1988), 10-14.
[3] A. Dvurečenskij, B. Riečan: On joint distribution of observables for F-quantum spaces. Fuzzy Sets and Systems 39 (1991), 67-73. DOI 10.1016/0165-0114(91)90066-Y | MR 1089012
[4] W. Guz: Fuzzy $\sigma$-algebras of physics. Inter. J. Theor. Phys. 24 (1985), 481-493. MR 0798920 | Zbl 0575.46052
[5] A. N. Kolmogorov: Grundebegriffe der Wahrscheinlichkeitsrechnung. Berlin, 1933.
[6] J. von Neumann: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin, 1932. MR 0223138
[7] K. Piasecki: Probability of fuzzy events defined as denumerable additivity measure. Fuzzy Sets and Systems 17 (1985), 271-284. DOI 10.1016/0165-0114(85)90093-4 | MR 0819364 | Zbl 0604.60005
[8] J. Pykacz: Quantum logics and soft fuzzy probability spaces. Busefal 32 (1987), 150-157. Zbl 0662.03055
[9] B. Riečan: A new approach to some basic notions of statistical quantum theory. Busefal 35 (1987), 4-6.
[10] R. Sikorski: Boolean algebras. Springer-Verlag, 1964. MR 0126393 | Zbl 0123.01303
[11] P. Suppes: The probability argument for a nonclassical logic of quantum mechanics. Phil. Sc. 33 (1966), 14-21. DOI 10.1086/288067 | MR 0215575
[12] V. S. Varadarjan: Geometry of quantum theory. Van Nostrand, New Jersey, 1968.
[13] L. A. Zadeh: Probability measures on fuzzy events. J. Math. Anal. Appl. 23 (1968), 421-427. DOI 10.1016/0022-247X(68)90078-4 | MR 0230569
Partner of
EuDML logo