Skip to main content
SpringerLink
Log in

Monte Carlo methods in fuzzy linear regression

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

We apply our new fuzzy Monte Carlo method to a certain fuzzy linear regression problem to estimate the best solution. The best solution is a vector of triangular fuzzy numbers, for the fuzzy coefficients in the model, which minimizes one of two error measures. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. We consider an example problem and show this Monte Carlo method obtains the best solution for one error measure and is approximately best for the other error measure.

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

  • Choi SH, Buckley JJ (2007) Fuzzy regression using least absolute deviation estimators. Soft Comput (to appear)

  • Buckley JJ, Eslami E (2002) Introduction to fuzzy logic and fuzzy sets. Springer, Heidelberg

    MATH  Google Scholar 

  • Buckley JJ (2007) Monte Carlo studies with random fuzzy numbers. Springer, Heidelberg (to appear)

    Google Scholar 

  • Cheng C-B (2001) Fuzzy regression analysis by a fuzzy neural network and its application to dual response optimization. In: Proceedings joint 9th IFSA World congress and 20th NAFIPS international Conference, Vancouver, Canada, Vol 5, pp 2681–2686

  • D’Urso P (2003) Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data. Comput Stat Data Anal 42:47–72

    Article  MathSciNet  Google Scholar 

  • Feuring T, Golubski W, Gassmann M (2000) Fuzzy regression: a genetic programming approach. In: Fourth international Conference knowledge-based intelligent engineering systems and allied technologies, Aug 30–Sept 1, Brighton, UK

  • Henderson SG, Chiera BA, Cooke RM (2000) Generating “dependent” quasi-random numbers. In: Proceedings of the 2000 winter simulation conference, Orlando, FL, Dec 10–13, pp 527–536

  • Hogg RV, Tanis EA (2001) Probability and statistical inference, 6th edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Kim B, Bishu RR (1998) Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst 100:343–352

    Article  Google Scholar 

  • Lindgren BW (1976) Statistical theory, 3rd edn. MacMillan, New York

    MATH  Google Scholar 

  • Press WH, Flannery BP, Teukolsky SA, Vetterling WT (2002): Numerical recipes in C: the art of scientific computing, 6th edn. Cambridge University Press, Cambridge

  • Savic DA, Pedryzc W (1991) Evaluation of fuzzy linear regression models. Fuzzy Sets Syst 39:51–63

    Article  MATH  Google Scholar 

  • Tanaka H (1987) Fuzzy data analysis by possibilistic linear regression models. Fuzzy Sets Syst 24:363–375

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama, 35294, USA

    Areeg Abdalla & James J. Buckley

Authors
  1. Areeg Abdalla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James J. Buckley
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James J. Buckley.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abdalla, A., Buckley, J.J. Monte Carlo methods in fuzzy linear regression. Soft Comput 11, 991–996 (2007). https://doi.org/10.1007/s00500-006-0148-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-006-0148-5

Keywords

Search

Navigation