Skip to main content
Log in

A Regression Model for Fuzzy Initial Data

  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A fuzzy combined linear regression model for fuzzy initial data, which are tolerant (L-R)-numbers with constraints on the functions L and R, is designed. The model is called combined since it is a combination of two regression models—a fuzzy model and a classical model. Its coefficients are determined as unimodal (L-R)-numbers. The solution method consists in determining weighted intervals for the tolerant (L-R)-numbers and then applying of the least-squares method.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Chang, Y.-H. and Ayyub, B.M., Fuzzy Regression Methods—A Comparative Assessment, Fuzzy Sets Syst., 2001, no. 119, pp. 187-203.

    Google Scholar 

  2. Tanaka, H., Uejima, S., and Asai, Linear Regression Analysis with Fuzzy Model, IEEE. Syst. Trans. Syst. Man Cybernet., SMC-2, 1982, pp. 903-907.

  3. Chang, P.-T. and Lee, E.S., Fuzzy Linear Regression with Spreads Unrestricted in Sign, Comput. Math. Appl., 1994, no. 28, pp. 61-71.

    Google Scholar 

  4. Tanaka, H. and Ishibuchi, H., Identification of Possibilistic Linear Models, Fuzzy Sets Syst., 1991, no. 41, pp. 145-160.

    Google Scholar 

  5. Tanaka, H., Ishibuchi, H., and Yoshikawa, S., Exponential Possibility Regression Analysis, Fuzzy Sets Syst., 1995, no. 69, pp. 305-318.

    Google Scholar 

  6. Celmins, A., Least-Squares Model Fitting to Fuzzy Vector Data, Fuzzy Sets Syst., 1987, no. 22, pp. 245-269.

    Google Scholar 

  7. Celmins, A., Multidimensional Least-Squares Model Fitting of Fuzzy Models, Math. Modeling, 1987, no. 9, pp. 669-690.

    Google Scholar 

  8. Chang, Y.-H. and Ayyub, B.M., Reliability Analysis in Fuzzy Regression, Proc. Annual. Conf. North Am. Fuzzy Inf. Soc. (NAFIPS 93 ), Allentown, 1993, pp. 93-97.

  9. Chang, Y.-H., Johnson, P., Tokar, S., and Ayyub, B.M., Least-Squares in Fuzzy Regression, Proc. Annual. Conf. North Am. Fuzzy Inf. Soc. (NAFIPS 93 ), Allentown, 1993, pp. 98-102.

  10. Savic, D. and Pedrycz, W., Evaluation of Fuzzy Regression Models, Fuzzy Sets Syst., 1991, no. 39, pp. 51-63.

    Google Scholar 

  11. Chang, Y.-H., Hybrid Fuzzy Least-Squares Regression Analysis and Its Reliability Measures, Fuzzy Sets Syst., 2001, no. 119, pp. 225-246.

    Google Scholar 

  12. Tarantsev, A.A., Design Principles for RegressionModels for Initial Data with Fuzzy Description, Avtom. Telemekh., 1997, no. 11, pp. 27-32.

    Google Scholar 

  13. Poleshchuk, O.M., A Least-Squares Fuzzy Method in Regression Analysis of T-type Data, Obozrenie Prikl. Prom. Mat., 2002, vol. 9, no.2, pp. 434-435.

    Google Scholar 

  14. Domrachev, V.G. and Poleshchuk, O.M., Estimation of Regression Relation with Initial T-type Fuzzy Data, Vest. Samarsk. Gos. Aerokosm. Univ., 2002, no. 8, pp. 4-11.

    Google Scholar 

  15. Averkin, A.N., Batyrshin, I.Z., Blishun, A.F., et al., Nechetkie mnozhestva v modelyakh upravleniya i iskusstvennogo intellekta (Fuzzy Sets in Control and Artificial Intelligence Models), Moscow: Nauka, 1986.

    Google Scholar 

  16. Coleman, T.F. and Li, Y., A Reective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables, SIAM J. Optimiz., 1996, vol. 6, no.4, pp. 1040-1058.

    Google Scholar 

  17. Poleshchuk, O.M., Certain Approaches to Modeling Control Systems of Educational Processes, Telekom. Inf. Obrazovaniya, 2002, no. 3, pp. 54-72.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Domrachev, V.G., Poleshuk, O.M. A Regression Model for Fuzzy Initial Data. Automation and Remote Control 64, 1715–1723 (2003). https://doi.org/10.1023/A:1027322111898

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1027322111898

Keywords

Navigation