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Why Quantum (Wave Probability) Models Are a Good Description of Many Non-quantum Complex Systems, and How to Go Beyond Quantum Models

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Beyond Traditional Probabilistic Methods in Economics (ECONVN 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 809))

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Abstract

In many practical situations, it turns out to be beneficial to use techniques from quantum physics in describing non-quantum complex systems. For example, quantum techniques have been very successful in econometrics and, more generally, in describing phenomena related to human decision making. In this paper, we provide a possible explanation for this empirical success. We also show how to modify quantum formulas to come up with an even more accurate descriptions of the corresponding phenomena.

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References

  1. Baaquie, B.E.: Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates. Camridge University Press, New York (2004)

    Book  Google Scholar 

  2. Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)

    MATH  Google Scholar 

  3. Conway, J.H., Smith, D.A.: On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. A. K. Peters, Natick (2003)

    Book  Google Scholar 

  4. Dick, S.: Towards complex fuzzy logic. IEEE Trans. Fuzzy Syst. 13(3), 405–414 (2005)

    Article  MathSciNet  Google Scholar 

  5. Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge University Press, Cambridge (2013)

    Book  Google Scholar 

  6. Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)

    MATH  Google Scholar 

  7. Kosheleva, O., Kreinovich, V.: Approximate nature of traditional fuzzy methodology naturally leads to complex-valued fuzzy degrees. In: Proceedings of the IEEE World Congress on Computational Intelligence WCCI 2014, Beijing, China, 6–11 July 2014

    Google Scholar 

  8. Kosheleva, O., Kreinovich, V., Ngamsantivong, T.: Why complex-valued fuzzy? Why complex values in general? A computational explanation. In: Proceedings of the Joint World Congress of the International Fuzzy Systems Association and Annual Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS 2013, Edmonton, Canada, pp. 1233–1236, 24–28 June 2013

    Google Scholar 

  9. Kreinovich, V., Nguyen, H.T., Sriboonchitta, S.: Quantum ideas in economics beyond quantum econometrics. In: Anh, L.Y., Dong, L.S., Kreinovich, V., Thach, N.N. (eds.) Econometrics for Financial Applications, pp. 146–151. Springer, Cham (2018)

    Google Scholar 

  10. Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017)

    Book  Google Scholar 

  11. Nguyen, H.T., Kreinovich, V., Shekhter, V.: On the possibility of using complex values in fuzzy logic for representing inconsistencies. Int. J. Intell. Syst. 13(8), 683–714 (1998)

    Article  Google Scholar 

  12. Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2006)

    Google Scholar 

  13. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston, Dordrecht (1999)

    Book  Google Scholar 

  14. Servin, C., Kreinovich, V., Kosheleva, O.: From 1-D to 2-D fuzzy: a proof that interval-valued and complex-valued are the only distributive options. In: Proceedings of the Annual Conference of the North American Fuzzy Information Processing Society NAFIPS’2015 and 5th World Conference on Soft Computing, Redmond, Washington, 17–19 August 2015

    Google Scholar 

  15. Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton (2011)

    MATH  Google Scholar 

  16. Svítek, M.: Quantum System Theory: Principles and Applications. VDM Verlag, Saarbrucken (2010)

    Google Scholar 

  17. Svítek, M.: Towards complex system theory. Neural Netw. World 15(1), 5–33 (2015)

    Article  Google Scholar 

  18. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Project AI & Reasoning CZ.02.1.01/0.0/0.0/15003/0000466 and the European Regional Development Fund. It was also supported in part by the US National Science Foundation grant HRD-1242122 (Cyber-ShARE Center). This work was performed when M. Svítek was a Visiting Professor at the University of Texas at El Paso.

The authors are thankful to Vladimir Marik and Hung T. Nguyen for their support and valuable discussions.

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Correspondence to Vladik Kreinovich .

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Svítek, M., Kosheleva, O., Kreinovich, V., Nguyen, T.N. (2019). Why Quantum (Wave Probability) Models Are a Good Description of Many Non-quantum Complex Systems, and How to Go Beyond Quantum Models. In: Kreinovich, V., Thach, N., Trung, N., Van Thanh, D. (eds) Beyond Traditional Probabilistic Methods in Economics. ECONVN 2019. Studies in Computational Intelligence, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-030-04200-4_13

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