Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Do fuzzy quantum structures exist?

  • 38 Accesses

  • 3 Citations

Abstract

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.

References

  1. Aerts, D., Durt, T., and Vanbogaert, B. (1992).Tatra Mountains Mathematical Publications,1, 5–14.

  2. Beltrametti, E. G., and Cassinelli, G. (1981).The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.

  3. Dvurečenskij, A., and Riečan, B. (1991).International Journal of General Systems,20, 39–54.

  4. Giles, R. (1976).International Journal of Man-Machine Studies,8, 313–327.

  5. Mcaczyňski, M. J. (1974).International Journal of Theoretical Physics,11, 149–156.

  6. Mesiar, R. (1993a).International Journal of Theoretical Physics,32(10), 1933–1940.

  7. Mesiar, R. (1993b).International Journal of Theoretical Physics,32(7), 1143–1151.

  8. Mesiar, R. (1994). h-Fuzzy quantum logics,International Journal of Theoretical Physics,33.

  9. Navara, M. (n.d.). Boolean representations of fuzzy quantum spaces,Fuzzy Sets and Systems, to appear.

  10. 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.

  11. Pykacz, J. (1992).International Journal of Theoretical Physics,31, 1767–1783.

  12. Pykacz, J. (1994). Fuzzy quantum logics and infinite-valued Lukasiewicz logic,International Journal of Theoretical Physics,33.

  13. Schweizer, B., and Sklar, A. (1983).Probabilistic Metric Spaces, North-Holland, Amsterdam.

  14. Trillas, E. (1979).Stochastica,3, 47–59.

  15. Zadeh, L. A. (1965).Information and Control,8, 338–353.

Download references

Author information

Rights and permissions

Reprints and Permissions

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

Download citation

Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Global Property
  • Common Generator