Fuzzy Multiple Linear Regression

Part of the SpringerBriefs in Water Science and Technology book series (BRIEFSWATER)


This chapter discusses the construction of the fuzzy multiple linear regression by embedding the spreading value and the crisp in the formulation. We begin by discussing the standard multiple linear regression. Then a method to calculate the spreading value is discussed in details. We propose a new method to calculate the spreading value. We establish the fuzzy multiple linear regression formulation by using fuzzy triangular number with symmetric property. This to ensure that, the calculation be made faster compared with asymmetric fuzzy triangular number.


Symmetric Spreading value Triangular fuzzy number Least square Fuzzy coefficient 


  1. 1.
    Abdullah L, Zakaria N (2012) Matrix driven multivariate fuzzy linear regression model in car sales. J Appl Sci (Faisalabad) 12(1):56–63CrossRefGoogle Scholar
  2. 2.
    Anand MCJ, Bharatraj J (2017) Theory of triangular fuzzy number. Proc NCATM 2017:80Google Scholar
  3. 13.
    Asai HTSUK, Tanaka S, Uegima K (1982) Linear regression analysis with fuzzy model. IEEE Trans. Systems Man Cybern 12:903–907CrossRefGoogle Scholar
  4. 4.
    Bhavyashree S, Mishra M, Girisha GC (2017) Fuzzy regression and multiple linear regression models for predicting mulberry leaf yield: a comparative study. Int J Agric Stat Sci 13(1):149–152Google Scholar
  5. 3.
    Buckley JJ, Eslami E (2002) An introduction to fuzzy logic and fuzzy sets, vol 13. Springer Science & Business Media, New YorkGoogle Scholar
  6. 5.
    Chang PT, Lee ES (1996) A generalized fuzzy weighted least-squares regression. Fuzzy Sets Syst 82(3):289–298CrossRefGoogle Scholar
  7. 6.
    Chang YHO, Ayyub BM (1997) Hybrid fuzzy regression analysis and its applications. In: Uncertainty modeling and analysis in civil engineering, pp 33–41Google Scholar
  8. 7.
    D’Urso P, Gastaldi T (2001) Linear fuzzy regression analysis with asymmetric spreads. In: Advances in classification and data analysis. Springer, Berlin, Heidelberg, pp 257–264Google Scholar
  9. 10.
    Hidayah Mohamed Isa N, Othman M, Karim SAA (2018) Multivariate matrix for fuzzy linear regression model to analyse the taxation in Malaysia. Int J Eng Technol 7(4.33):78–82Google Scholar
  10. 9.
    Lowen R (1976) Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 56(3):621–633CrossRefGoogle Scholar
  11. 8.
    Lowen R (1996) Fuzzy real numbers. In: Fuzzy set theory. Springer, Dordrecht, pp 143–168Google Scholar
  12. 11.
    Pan NF, Lin TC, Pan NH (2009) Estimating bridge performance based on a matrix-driven fuzzy linear regression model. Autom Constr 18(5):578–586CrossRefGoogle Scholar
  13. 12.
    Rommelfanger H, Słowiński R (1998) Fuzzy linear programming with single or multiple objective functions. In: Fuzzy sets in decision analysis, operations research and statistics. Springer, Boston, MA, pp 179–213 Google Scholar
  14. 14.
    Sakawa M, Yano H (1992) Multiobjective fuzzy linear regression analysis for fuzzy input-output data. Fuzzy Sets Syst 47(2):173–181CrossRefGoogle Scholar
  15. 15.
    Tranmer M, Elliot M (2008) Multiple linear regression. Cathie Marsh Cent Census Surv Res (CCSR) 5:30–35Google Scholar
  16. 16.
    Ubale A, Sananse S (2016) A comparative study of fuzzy multiple regression model and least square method. Int J Appl Res 2(7):11–15Google Scholar
  17. 18.
    Voskoglou M (2015) Use of the triangular fuzzy numbers for student assessment. arXiv preprint arXiv:1507.03257
  18. 17.
    Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Fundamental and Applied Sciences Department and Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous SystemUniversiti Teknologi PETRONASSeri IskandarMalaysia
  2. 2.Fundamental and Applied Sciences DepartmentUniversiti Teknologi PETRONASSeri IskandarMalaysia

Personalised recommendations