Skip to main content

On Fuzzy Theory for Econometrics

  • Chapter
  • First Online:
  • 1638 Accesses

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 326))

Abstract

This paper aims mainly at informing statisticians and econometricians of relevant concepts and methods in fuzzy theory that are useful in addressing economic problems. We emphasize three recent significant contributions of fuzzy theory to economics, namely fuzzy games for capital risk allocations, fuzzy rule bases and compositional rule of inference for causal inference, and a statistical setting for fuzzy data based on continuous lattices.

Dedicated to Lotfi Zadeh.

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   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
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. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  2. Haavelmo, T.: The probability approach in econometrics. Econometrica 12, 1–115 (1944)

    Article  MathSciNet  Google Scholar 

  3. Lindley, D.: Scoring rules and the inevitability of probability. Intern. Statist. Review 50, 1–26 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Goodman. I.R., Nguyen, H.T., Rogers, G.S.: On the scoring approach to admissibility of uncertainty measures in expert systems. J. Math. Anal. Appl. 159, 550–594 (1991)

    Google Scholar 

  5. Kolmogorov, A.N.: On logical foundations of probability theory. In: Probability Theory and Mathematical Statistics (Tbilisi, 1982). Volume 1021 of Lecture Notes in Mathematics, pp. 1–5. Springer, Berlin (1983)

    Google Scholar 

  6. Johnson, O.: Information Theory and The Central Limit Theorem. Imperial College Press, London (2004)

    Google Scholar 

  7. Elkans, C.: The paradoxical sucess of fuzzy logic. In: AAAI-93 Proceedings, pp. 698–703 (1993)

    Google Scholar 

  8. Nguyen, H.T., Kosheleva, O., Kreinovich, V.: Is the sucess of fuzzy logic really paradoxical?: toward the actual logic behind expert systems. Int. J. Intell. Syst. 11(5), 295–326 (1996)

    Article  MATH  Google Scholar 

  9. Gehrke, M., Walker, C., Walker, E.: A mathematical setting for fuzzy sets. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 5(3), 223–238 (1997)

    Google Scholar 

  10. Aumann, R.J., Shapley, L.S.: Values on Non-Atomic Games. Princeton University Press, Princeton (1974)

    Google Scholar 

  11. Denault, M.: Coherent allocation of risk capital. J. Risk. 4, 1–34 (2001)

    Article  Google Scholar 

  12. Aubin, J.P.: Optima and Equilibra. Springer, Berlin (1993)

    Google Scholar 

  13. Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)

    Google Scholar 

  14. Robbins, H.E.: On the measure of a random set. Ann. Math. Statist. 14, 70–74 (1944)

    Article  Google Scholar 

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

    Google Scholar 

  16. Fuller, R.: On generalization of Nguyen’s theorem: a short survey of recent developments. In: Advances in Soft Computing, Robotics and Control, pp. 183–190. Springer, New York (2014)

    Google Scholar 

  17. Vorobiev, D., Seikkala, S.: Towards the theory of fuzzy differential equations. Fuzzy Sets Syst. 125, 231–237 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Bzowski, A., Urbanski, M.K.: A note on Nguyen-Fuller-Keresztfalvi theorem and Zadeh’s extension principle. Fuzzy Sets Syst. 213, 91–101 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  19. Goodman. I.R., Nguyen, H.T., Walker, E.A.: Conditional Inference and Logic for Intelligent Systems. North-Holland, Amsterdam (1991)

    Google Scholar 

  20. Milne, P.: Bruno de Finetti and the logic of conditional events. Br. J. Philos. Sci. 48, 195–232 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  21. Milne, P.: Algebras of inytervals and a logic of conditional assertions. J. Philos. Logic. 33(5), 497–548 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Pelessoni, R., Vicig, P.: The Goodman-Nguyen relation in uncertainty measurement. Adv. Intell. Syst. Comput. 190, 33–37 (2013)

    Google Scholar 

  23. Pelessoni, R., Vicig, P.: The Goodman-Nguyen relation within imprecise probability theory, Int. J. Approximate Reasoning, in press (2014)

    Google Scholar 

  24. Bamber, D., Goodman, I.R., Nguyen, H.T.: Robust reasoning with rules that have exceptions. Ann. Math. Art. Intell. 45, 83–171 (2005)

    Article  MathSciNet  Google Scholar 

  25. Draeseke, R., Giles, D.E.A.: A fuzzy logic approach to modelling the New Zeland underground economy. Math. Comp. Simul. 59, 115–123 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  26. Ene, C.M., Hurduc, N.: A fuzzy model to estimate Romanian underground economy. Intern. Auditing Risk Manage. 2(18), 1–10 (2010)

    Google Scholar 

  27. Pearl, J.: Causal inference in statistics: an overview. Statist. Surveys 3, 96–146 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  28. Holland, P.W.: Statistics and causal inference. J. Amer. Statist. Assoc. 81(396), 945–960 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  29. Greenland, S.: An overview of methods for causal inference from observational studies. In: Gelman, A., Meng, X.L. (eds.) Applied Bayesian Modeling and Causal Inference from Incomplete Data Perspectives, pp. 3–13. Wiley, New York (2004)

    Google Scholar 

  30. Gierz, G. et al.: A Compemdium of Continuous Lattices, Springer, Berlin (1980)

    Google Scholar 

  31. Waszkiewicz, P.: How to do domains model topologies? Electron. Notes Theoretical Comput. Sci. 83, 1–18 (2004)

    Google Scholar 

  32. Copi, R., Gil, M., Kiers, H.: The fuzzy approach to statistical analysis. Comput. Stat. Data Anal. 51, 1–14 (2006)

    Article  Google Scholar 

  33. Nguyen, H.T., Tran, H.: On a continuous lattice approach to modeling of coarse data in systems analysis. J. Uncertain Syst. 1(1), 62–73 (2007)

    Google Scholar 

  34. Nguyen, H.T., Wang, Y., Wei, G.: On Choquet theorem for upper semicontinuous functions. Int. J. Approximate Reasoning 46, 3–16 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  35. Nguyen, H.T., Kreinovich, V.: How ro fully represent expert information about imprecise properties in a computer system: random sets, fuzzy sets, and beyond. Int. J. Gen. Syst. 43, 586–609 (2014)

    Article  MATH  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

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Nguyen, H.T., Sriboonchitta, S. (2015). On Fuzzy Theory for Econometrics. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19683-1_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19682-4

  • Online ISBN: 978-3-319-19683-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics