Recently, some fuzzy quantum structures were introduced. We focus on the fuzzy quantum logics arising from the isomorphism of some quantum logics and some systems of fuzzy subsets of the ordering sets of states. In general, a fuzzy quantum logic is equipped with the pointwise-defined fuzzy connectives generated by a common generator g. Stressing the pointwise nature of fuzzy structures and omitting the global properties of quantum elements, we find that only crisp values of elements of a fuzzy quantum logic are allowed. Consequently, fuzzy quantum structures do not exist! However, there exist quantum structures of fuzzy subsets.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Aerts, D., Durt, T., and Vanbogaert, B. (1992).Tatra Mountains Mathematical Publications,1, 5–14.
Beltrametti, E. G., and Cassinelli, G. (1981).The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.
Dvurečenskij, A., and Riečan, B. (1991).International Journal of General Systems,20, 39–54.
Giles, R. (1976).International Journal of Man-Machine Studies,8, 313–327.
Mcaczyňski, M. J. (1974).International Journal of Theoretical Physics,11, 149–156.
Mesiar, R. (1993a).International Journal of Theoretical Physics,32(10), 1933–1940.
Mesiar, R. (1993b).International Journal of Theoretical Physics,32(7), 1143–1151.
Mesiar, R. (1994). h-Fuzzy quantum logics,International Journal of Theoretical Physics,33.
Navara, M. (n.d.). Boolean representations of fuzzy quantum spaces,Fuzzy Sets and Systems, to appear.
Pykacz, J. (1987). Quantum logics as families of fuzzy subsets of the set of physical states, inPreprints of 2nd IFSA Congress, Tokyo, Vol. 2, pp. 437–440.
Pykacz, J. (1992).International Journal of Theoretical Physics,31, 1767–1783.
Pykacz, J. (1994). Fuzzy quantum logics and infinite-valued Lukasiewicz logic,International Journal of Theoretical Physics,33.
Schweizer, B., and Sklar, A. (1983).Probabilistic Metric Spaces, North-Holland, Amsterdam.
Trillas, E. (1979).Stochastica,3, 47–59.
Zadeh, L. A. (1965).Information and Control,8, 338–353.
About this article
Cite this article
Mesiar, R. Do fuzzy quantum structures exist?. Int J Theor Phys 34, 1609–1614 (1995). https://doi.org/10.1007/BF00676273
- Field Theory
- Elementary Particle
- Quantum Field Theory
- Global Property
- Common Generator