Skip to main content
SpringerLink
Log in

A Statistical Basis for Fuzzy Engineering Economics

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper introduces a systematic way to analyze fuzzy data in both engineering fields and economics, with emphasis on fuzzy engineering economics. The approach is statistical in nature, in which fuzzy information and data are treated as bona fide random elements within probability theory. This provides not only a coexistence for randomness and fuzziness in the complex task of handling all kinds of uncertainty in real-world problems, but also a statistical theory supporting empirical analyses in applications. This can also viewed as a complement to two usual approaches in the literature, namely, either using only fuzzy methods, or using some forms of fuzzifying statistics. We will give illustrating and motivating important examples, in the area of regression (for prediction purposes) with seemingly unobservable variables, in which, fuzzy rule-based technology provides nonlinear models for estimating unobservables (from determinants/causal variables), followed by statistics with fuzzy data in linear regression models. The main contribution of this paper is the rigorous formulation of statistics with fuzzy data using continuous lattice structure of upper semicontinuous membership functions (random fuzzy closed sets) which can be used in a variety of useful applied situations where fuzziness and randomness coexist.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baaquie, B.E.: Quantum Finance. Cambridge University Press, Cambridge (2007)

    MATH  Google Scholar 

  2. Sullivan, W., Wicks, E., Koelling, C.: Engineering Economy, 15th edn. Prentice-Hall, Upper Saddle River (2010)

    Google Scholar 

  3. Nguyen, H.T., Sugeno, M.: Fuzzy Systems: Modeling and Control. Kluwer Academic, Boston (1998)

    Book  MATH  Google Scholar 

  4. Nguyen, H.T., Prasad, N.R., Walker, C., Walker, A.: A first Course in Fuzzy and Neural Control. Chapman and Hall/CRC, Boca Raton (2003)

    MATH  Google Scholar 

  5. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)

    Book  MATH  Google Scholar 

  6. Viertl, R.: Statistical Methods for Fuzzy Data. Wiley, Chichester (2011)

    Book  MATH  Google Scholar 

  7. Kahraman, C.: Fuzzy Engineering Economics with Applications. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  8. Yoon, K.P.: A probabilistic approach to fuzzy engineering economic analysis. In: Kahraman, C. (ed.) Fuzzy Engineering Economics with Applications, pp. 217–230. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Nguyen, H.T., Wu, B.: Random sets and fuzzy sets in coarse data analysis. Comput. Stat. Data Anal. 51, 70–85 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic, 3rd edn. Chapman and Hall/CRC, London (2006)

    Google Scholar 

  13. Aubin, J.P.: Cooperative fuzzy games. Math. Oper. Res. 6(1), 1–13 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  14. Aubin, J.P.: Optima and Equilibria. Springer, Berlin, New York (1993)

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Chapter  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. 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 

  21. Nguyen, H.T., Kreinovich, V.: How to fully represent expert information about imprecise properties in a computer system: random sets, fuzzy sets, and beyond: an overview. Int. J. Gen. Syst. 43(6), 586–609 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  22. Kutner, M.H., Nachtsheim, C.J., Neter, J.: Applied Linear Regression Models. McGraw-Hill, New York (2004)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  24. Ene, C.M., Hurduc, N.: A fuzzy model to estimate Romanian underground economy. Intern. Audit. Risk Manag. 2(18), 29–38 (2010)

    Google Scholar 

  25. Pearl, J.: Causal inference in statistics: an overview. Stat. Surv 3, 96–146 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. Holland, P.W.: Statistics and causal inference. J. Am. Stat. Assoc. 81(396), 945–960 (1986)

    Article  MATH  Google Scholar 

  27. 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, Hoboken (2004)

    Google Scholar 

  28. Aumann, R.J., Shapley, L.S.: Values of Non-atomic Games. Princeton University Press, Princeton (1974)

    MATH  Google Scholar 

  29. B. Das and S.I. Resnick, QQ Plots, random sets and data from a heavy tailed distribution, Stochastic Models, 103-132, 2008

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

    MATH  Google Scholar 

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

    Article  Google Scholar 

  32. Verdier, G.: Application of copulas to multivariate control charts. J. Stat. Plan. Inference 143, 2151–2159 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  33. Montgomery, D.C.: Statistical Quality Control: A Modern Introduction, 6th edn. Wiley, New York (2009)

    Google Scholar 

  34. Hartigan, J.A.: Estimation of a convex density contour in two dimensions. J. Am. Stat. Assoc. 82, 267–270 (1975)

    Article  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

  36. van der Klaauw, W.: Regression-discontinuity analysis: a survey of recent developments in economics. J. Compil. 22(2), 219–245 (2008)

    Google Scholar 

  37. Gierz, G.: Continuous Lattices and Domains. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  38. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA

    Hung T. Nguyen

  2. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

  3. Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan

    Berlin Wu

Authors
  1. Hung T. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Songsak Sriboonchitta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Berlin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hung T. Nguyen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nguyen, H.T., Sriboonchitta, S. & Wu, B. A Statistical Basis for Fuzzy Engineering Economics. Int. J. Fuzzy Syst. 17, 1–11 (2015). https://doi.org/10.1007/s40815-015-0010-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-015-0010-y

Keywords

Search

Navigation