Skip to main content

An Enjoyable Research Journey on Uncertainty

  • Chapter
  • First Online:

Part of the book series: Studies in Computational Intelligence ((SCI,volume 892))

Abstract

This is a story of research on uncertainty modeling from information measures without probability to Choquet capacities, possibility measures, fuzzy measures, imprecise probabilities, belief functions and finally, quantum probability. The main part of the paper is devoted, almost entirely, to an invitation to quantum probability for behavioral economics.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. B.E. Baaquie, Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates (Cambridge University Press, Cambridge, 2007)

    MATH  Google Scholar 

  2. A. Bera, S. Park, Optimal portfolio diversification using maximum entropy principle. Econ. Rev. 27, 484–512 (2008)

    Google Scholar 

  3. J.R. Busemeyer, P.D. Bruza, Quantum Models of Cognition and Decision (Cambridge University Press, Cambridge, 2012)

    Book  Google Scholar 

  4. L. Coroianu, R. Fuller, Nguyen type theorem for extension principle based on a joint possibility distribution. Intern. J. Approx. Reason. 95, 22–35 (2018)

    Article  MathSciNet  Google Scholar 

  5. P. Darbyshire, Quantum physics meets classical finance. Phys. World 25–29 (2005)

    Google Scholar 

  6. A. Dempster, Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist. 38, 325–339 (1967)

    Article  MathSciNet  Google Scholar 

  7. P. Diaconis, B. Skyrms, Ten Great Ideas About Chance (Princeton University Press, Princeton and Oxford, 2018)

    Book  Google Scholar 

  8. R. Feynman, The concept of probability in quantum mechanics, in Berkeley Symposium on Mathematical Statistics (1951), pp. 533–541

    Google Scholar 

  9. R. Feynman, A. Hibbs, Quantum Mechanics and Path Integrals (Dover, New York, 1965)

    MATH  Google Scholar 

  10. R. Fuller, T. Keresztfalvi, On generalization of Nguyen’s theorem. Fuzzy Sets Syst. 41(3), 371–374 (1991)

    Article  MathSciNet  Google Scholar 

  11. R. Fuller, On generalization of Nguyen’s theorem: a short survey of recent developments. Adv. Soft Comput. Intell. Robot. Control., 183–190 (2014)

    Google Scholar 

  12. A. Gelman, M. Bethancourt, Does quantum uncertainty have a place in everyday applied statistics. Behav. Brain Sci. 36(3), 285 (2013)

    Article  Google Scholar 

  13. A. Golan, G. Judge, D. Miller, Maximum Entropy Econometrics (Wiley, New York, 1996)

    Google Scholar 

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

    Google Scholar 

  15. S. Hawking, L. Mlodinow, The Grand Design (Bantam Books, London, 2010)

    Google Scholar 

  16. B. Herzog, Quantum models of decision-making in economics. J. Quantum Inf. Sci. 5, 1–5 (2015)

    Article  Google Scholar 

  17. R. Hudson, A short walk in quantum probability. Phil. Trans. R. Soc. A 376, 20170226 (2017)

    Google Scholar 

  18. J.M. Jauch, The quantum probability calculus. Synthese 29, 131–154 (1974)

    Article  Google Scholar 

  19. D. Kahneman, A. Tversky, Prospect theory: an analysis of decision under risk. Econometrica 47, 263–292 (1979)

    Article  MathSciNet  Google Scholar 

  20. D.M. Kreps, Notes on the Theory of Choice (Westview Press, 1988)

    Google Scholar 

  21. J.M. Malley, A. Fletcher, Joint distribution and quantum nonlocal models. Axioms 3, 166–176 (2014)

    Article  Google Scholar 

  22. P.A. Meyer, Quantum Probability for Probabilists (Springer, Berlin, 1995)

    Book  Google Scholar 

  23. H.T. Nguyen, A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64, 369–380 (1978)

    Article  MathSciNet  Google Scholar 

  24. H.T. Nguyen, On conditional possibility distributions. Fuzzy Sets Syst. 1(4), 299–309 (1978)

    Article  MathSciNet  Google Scholar 

  25. H.T. Nguyen, On random sets and belief functions. J. Math. Anal. Appl. 65, 531–542 (1978)

    Article  MathSciNet  Google Scholar 

  26. H.T. Nguyen, On the entropy of random sets and possibility distributions, in The Analysis of Fuzzy Information, ed. by J. Bezdek (CRC Press, 1987), pp. 45–156

    Google Scholar 

  27. H.T. Nguyen, Toward improving models for decision making in economics. Asian J. Econ. Bank. 3(01), 1–19 (2019)

    Google Scholar 

  28. H.T. Nguyen, An Introduction to Random Sets (Chapman and Hall/CRC Press, Boca Raton, 2006)

    Book  Google Scholar 

  29. H.T. Nguyen, C.L. Walker, E.A. Walker, A First Course in Fuzzy Logic, 4th edn. (Chapman and Hall/CRC Press, Boca Raton, 2019)

    MATH  Google Scholar 

  30. K.R. Parthasarathy, An Introduction to Quantum Stochastic Calculus (Springer, Basel, 1992)

    Book  Google Scholar 

  31. L. Pasca, A critical review of the main approaches on financial market dynamics modeling. J. Heterodox Econ. 2(2), 151–167 (2015)

    Article  MathSciNet  Google Scholar 

  32. S. Patra, A quantum framework for economic science: new directions. Economics 2019–20 (2019)

    Google Scholar 

  33. E.W. Piotrowski, J. Sladkowski, Quantum games in finance. Quant. Financ. 4(6), 61–67 (2004)

    Article  MathSciNet  Google Scholar 

  34. S. Segal, I.E. Segal, The Black-Scholes pricing formula in the quantum context. Proc. Nat. Acad. Sci. USA 95, 4072–4075 (1998)

    Article  Google Scholar 

  35. G. Shafer, A Mathematical Theory of Evidence (Princeton University, University Press, Princeton, 1976)

    MATH  Google Scholar 

  36. J. von Neumann, Mathematical Foundations of Quantum Mechanics, New edn. (Princeton University Press, Princeton, 2018)

    Google Scholar 

  37. V. Vukotic, Quantum economics. Panoeconomicus 2, 267–276 (2011)

    Article  Google Scholar 

  38. P. Walley, Statistical Reasoning with Imprecise Probabilities (Chapman and Hall, London, 1991)

    Book  Google Scholar 

  39. V.I. Yukalov, D. Sornette, Quantum probabilities of composite events in quantum measurements with multimode states. Lazer Phys. 23, 105502 (2013)

    Article  Google Scholar 

  40. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hung T. Nguyen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Nguyen, H.T. (2021). An Enjoyable Research Journey on Uncertainty. In: Kreinovich, V. (eds) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas. Studies in Computational Intelligence, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-030-45619-1_1

Download citation

Publish with us

Policies and ethics