A physical example of quantum fuzzy sets, and the classical limit

Rok, strany: 1992, 5 - 14

We present an explicit physical example of an experimental situation on a physical entity that gives rise to a fuzzy set. The fuzziness in the example is due to fluctuations of the experimental apparatus, and not to an indetermination about the states of the physical entity, and is described by a varying parameter $varepsilon$. For zero value of the parameter (no fluctuations), the example reduces to a classical mechanics situation, and the corresponding fuzzy set is a quasi-crisp set. For maximal value (maximal fluctuations), the example gives rise to a quantum fuzzy set, more precisely a spin-model. In between, we have a continuum of fuzzy situations, neither classical. nor quantum. We believe that the example can make us understand the nature of the quantum mechanical fuzziness and probability, and how these are related to the classical situation.

ISO 690:

Aerts, D., Durt, T., Van Bogaert, B. 1992. A physical example of quantum fuzzy sets, and the classical limit. In Tatra Mountains Mathematical Publications, vol. 1, no.1, pp. 5-14. 1210-3195.

APA:

Aerts, D., Durt, T., Van Bogaert, B. (1992). A physical example of quantum fuzzy sets, and the classical limit. Tatra Mountains Mathematical Publications, 1(1), 5-14. 1210-3195.