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Generalized Random Events

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Abstract

Phenomena in quantum physics motivate studies of mathematical quantum structures and generalized probability. We introduce a new domain of generalized probability which is equivalent to the difference posets (also to effect algebras) of fuzzy sets. It is in terms of a partial operation of addition and it has a natural interpretation as a disjunction in the original spirit of G. Boole. The extension to a binary operation leads to the Łukasiewicz operations, bold algebras and fuzzy probability. We study states on products and mention some applications.

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Acknowledgments

This work was supported by the Slovak Research and Development Agency [contract No. APVV-0178-11]; and Slovak Scientific Grant Agency [VEGA project 2/0031/15].

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovak Republic

    Václav Skřivánek & Roman Frič

  2. Catholic University in Ružomberok, Hrabovská cesta 1, 034 01, Ružomberok, Slovak Republic

    Roman Frič

Authors
  1. Václav Skřivánek
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  2. Roman Frič
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Correspondence to Roman Frič.

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Skřivánek, V., Frič, R. Generalized Random Events. Int J Theor Phys 54, 4386–4396 (2015). https://doi.org/10.1007/s10773-015-2594-2

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  • DOI: https://doi.org/10.1007/s10773-015-2594-2

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