A Linear Regression Model for Nonlinear Fuzzy Data

  • Juan Carlos Figueroa-García
  • Jesus Rodriguez-Lopez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6840)

Abstract

Fuzzy linear regression is an interesting tool for handling uncertain data samples as an alternative to a probabilistic approach. This paper sets forth uses a linear regression model for fuzzy variables; the model is optimized through convex methods. A fuzzy linear programming model has been designed to solve the problem with nonlinear fuzzy data by combining the fuzzy arithmetic theory with convex optimization methods.

Two examples are solved through different approaches followed by a goodness of fit statistical analysis based on the measurement of the residuals of the model.

Keywords

Fuzzy Number Linear Regression Model Fuzzy Variable Linear Programming Model Fuzzy Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bargiela, A., et al.: Multiple regression with fuzzy data. Fuzzy Sets and Systems 158(4), 2169–2188 (2007)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Gladysz, B., Kuchta, D.: Least squares method for L-R fuzzy variable. In: 8th International Workshop on Fuzzy logic and Applications, vol. 8, pp. 36–43. IEEE, Los Alamitos (2009)CrossRefGoogle Scholar
  3. 3.
    Kao, C., Chyu, C.: Least-Squares estimates in fuzzy regression analysis. European Journal of Operational Research 148(2), 426–435 (2003)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs (1992)MATHGoogle Scholar
  5. 5.
    Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Englewood Cliffs (1995)MATHGoogle Scholar
  6. 6.
    Melgarejo, M.A.: Implementing Interval Type-2 Fuzzy processors. IEEE Computational Intelligence Magazine 2(1), 63–71 (2007)CrossRefGoogle Scholar
  7. 7.
    Mendel, J.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice Hall, Englewood Cliffs (1994)MATHGoogle Scholar
  8. 8.
    Tanaka, H., et al.: Linear Regression analysis with Fuzzy Model. IEEE Transactions on Systems, Man and Cybernetics 12(4), 903–907 (1982)MATHGoogle Scholar
  9. 9.
    Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) an outline. Information Sciences 172(1), 1–40 (2005)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Juan Carlos Figueroa-García
    • 1
  • Jesus Rodriguez-Lopez
    • 1
  1. 1.Universidad Distrital Francisco José de CaldasBogotáColombia

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