# zbMATH — the first resource for mathematics

Sum of observables in fuzzy quantum spaces. (English) Zbl 0753.60005
It is introduced the sum of observables in fuzzy quantum space. The existence of this sum is proved. Properties of the defined notion are shown.

##### MSC:
 60A99 Foundations of probability theory 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 03E72 Theory of fuzzy sets, etc.
##### Keywords:
observables in fuzzy quantum space
Full Text:
##### References:
 [1] A. Dvurečenskij, F. Chovanec: Fuzzy quantum spaces and compatibility. Inter. J. Theor. Phys. 27(1988), 1069-1082. · Zbl 0657.60004 [2] A. Dvurečenskij, B. Riečan: On joint observables for F-quantum spaces. Busefal 35 (1988), 10-14. · Zbl 0662.03056 [3] A. Dvurečenskij, B. Riečan: On joint distribution of observables for F-quantum spaces. Fuzzy Sets and Systems 39 (1991), 67-73. · Zbl 0814.03041 [4] W. Guz: Fuzzy $$\sigma$$-algebras of physics. Inter. J. Theor. Phys. 24 (1985), 481-493. · Zbl 0575.46052 [5] A. N. Kolmogorov: Grundebegriffe der Wahrscheinlichkeitsrechnung. Berlin, 1933. [6] J. von Neumann: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin, 1932. · Zbl 0152.46101 [7] K. Piasecki: Probability of fuzzy events defined as denumerable additivity measure. Fuzzy Sets and Systems 17 (1985), 271-284. · 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. · Zbl 0123.01303 [11] P. Suppes: The probability argument for a nonclassical logic of quantum mechanics. Phil. Sc. 33 (1966), 14-21. [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. · Zbl 0174.49002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.