Skip to main content
SpringerLink
Log in

An integrated shrinkage strategy for improving efficiency in fuzzy regression modeling

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The fuzzy linear regression (FLR) modeling was first proposed making use of linear programming and then followed by many improvements in a variety of ways. In almost all approaches, researchers put many efforts to change the meters, objective functions, or restrictions to improve the fuzzy goodness of fit (GOF) measures. However, conditions and restrictions in the methods of estimating parameters can reduce efficiency. In this paper, from a different viewpoint, we develop shrinkage strategy, frequently used in classical regression modeling, in the existing FLR to improve GOF measures. In fact, by adding an extra factor to the estimated parameters, without altering the estimation method, the performance of the resulting model is tuned and the GOF measures are improved. However, this method cannot be directly applied since it may give negative spreads for the estimates. Hence, to combat this disadvantage of the shrinkage method, we make refinement and propose an integrated fuzzy shrinkage (IFS) approach. For this approach, an optimal boundary for the shrinkage parameter selection is obtained for which the IFS performs better, comparatively. Further, a fuzzy hypothesis testing procedure is developed to significantly select important coefficients in the FLR model using the p value. Using a simulation study and some illustrative examples, we demonstrate the superiority of the proposed estimation method. In this respect, we show the IFS improves GOF measures dramatically compared to the existing methods.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Arabpour A, Moradi F (2010) Usage of bootstrap method in fuzzy least squares. Andishe Amari 15(1):56–68

    Google Scholar 

  • Celmiņš A (1987) Least squares model fitting to fuzzy vector data. Fuzzy Sets Syst 22(3):245–269

    Article  MathSciNet  Google Scholar 

  • Chachi J, Taheri SM, Fattahi S, Hosseini RSA (2016) Two robust fuzzy regression models and their applications in predicting imperfections of cotton yarn. J Text Polym 4(2):60–68

    Google Scholar 

  • Chen SP, Dang JF (2008) A variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy. Inf Sci 178(20):3973 – 3988 (special Issue on Industrial Applications of Neural Networks)

  • Choi SH, Buckley JJ (2008) Fuzzy regression using least absolute deviation estimators. Soft Comput 12(3):257–263

    Article  Google Scholar 

  • Deng W, Liu H, Xu J, Zhao H, Song Y (2020) An improved quantum-inspired differential evolution algorithm for deep belief network. IEEE Trans Instrum Meas, pp 1-1

  • Deng W, Xu J, Zhao H (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292

    Article  Google Scholar 

  • Diamond P (1988) Fuzzy least squares. Inf Sci 46(3):141–157

    Article  MathSciNet  Google Scholar 

  • Dubois D (1980) Fuzzy sets and systems: theory and applications. Mathematics in science and engineering, Elsevier, Amsterdam

    MATH  Google Scholar 

  • Efron B, Tibshirani R (1994) An introduction to the bootstrap. Chapman & Hall, London

    Book  Google Scholar 

  • Gildeh BS, Gien D (2002) A goodness of fit index to reliability analysis in fuzzy model. 3rd WSEAS international conference on fuzzy sets and fuzzy systems. Iterlaken, Switzerland, pp 11–14

    Google Scholar 

  • Hassanpour H, Maleki HR, Yaghoobi M (2009) A goal programming approach to fuzzy linear regression with non-fuzzy input and fuzzy output data. Asia-Pacific J Oper Res 26(05):587–604

    Article  MathSciNet  Google Scholar 

  • Hesamian G, Akbari MG (2019) Fuzzy lasso regression model with exact explanatory variables and fuzzy responses. Int J Approx Reason 115:290–300

    Article  MathSciNet  Google Scholar 

  • Hong DH, Do HY (1997) Fuzzy system reliability analysis by the use of t\(\omega \) (the weakest t-norm) on fuzzy number arithmetic operations. Fuzzy Sets Syst 90(3):307–316

    Article  MathSciNet  Google Scholar 

  • James W, Stein C (1961) Estimation with quadratic loss. University of California Press, Berkeley, pp 361–379

    MATH  Google Scholar 

  • Jiang L, Liao H (2020) Mixed fuzzy least absolute regression analysis with quantitative and probabilistic linguistic information. Fuzzy Sets Syst 387:35–48

    Article  MathSciNet  Google Scholar 

  • Kao C, Chyu CL (2002) A fuzzy linear regression model with better explanatory power. Fuzzy Sets Syst 126(3):401–409

    Article  MathSciNet  Google Scholar 

  • Kelkinnama M, Taheri S (2012) Fuzzy least-absolutes regression using shape preserving operations. Inf Sci 214:105–120

    Article  MathSciNet  Google Scholar 

  • Kim B, Bishu RR (1998) Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst 100(1):343–352

    Article  Google Scholar 

  • Lee WJ, Jung HY, Yoon JH, Choi SH (2015) The statistical inferences of fuzzy regression based on bootstrap techniques. Soft Comput 19(4):883–890

    Article  Google Scholar 

  • Modarres M, Nasrabadi E, Nasrabadi M (2005) Fuzzy linear regression models with least square errors. Appl Math Comput 163(2):977–989

    MathSciNet  MATH  Google Scholar 

  • Moradi F, Arabpour A, Shadrokh A (2016) A bootstrap-based method of statistical inference in fuzzy logistic regression. Eng Appl Sci 11(9):2105–2112

    Google Scholar 

  • Nasrabadi MM, Nasrabadi E (2004) A mathematical-programming approach to fuzzy linear regression analysis. Appl Math Comput 155(3):873–881

    MathSciNet  MATH  Google Scholar 

  • Rabiei MR, Arashi M, Farrokhi M (2019) Fuzzy ridge regression with fuzzy input and output. Soft Comput 23(23):12189–12198

    Article  Google Scholar 

  • Redden DT, Woodall WH (1996) Further examination of fuzzy linear regression. Fuzzy Sets Syst 79(2):203–211

    Article  MathSciNet  Google Scholar 

  • Sakawa M, Yano H (1992) Multiobjective fuzzy linear regression analysis for fuzzy input-output data. Fuzzy Sets Syst 47(2):173–181

    Article  Google Scholar 

  • Saleh A (2006) Theory of preliminary test and stein-type estimation with applications. Wiley, New Jersey

    Book  Google Scholar 

  • Saleh A, Arashi M, Kibria B (2019) Theory of ridge regression estimation with applications. Wiley Series in Probability and Statistics, Wiley, USA

    Book  Google Scholar 

  • Savic DA, Pedrycz W (1991) Evaluation of fuzzy linear regression models. Fuzzy Sets Syst 39(1):51–63

    Article  MathSciNet  Google Scholar 

  • Shakouri G, Nadimi R (2009) A novel fuzzy linear regression model based on a non-equality possibility index and optimum uncertainty. Appl Soft Comput 9(2):590–598

    Article  Google Scholar 

  • Sohn SY, Kim DH, Yoon JH (2016) Technology credit scoring model with fuzzy logistic regression. Appl Soft Comput 43:150–158

    Article  Google Scholar 

  • Stein CM (1981) Estimation of the mean of a multivariate normal distribution. Ann Stat 9(6):1135–1151

    Article  MathSciNet  Google Scholar 

  • Tanaka H, Uejima S, Asai K (1982) Linear regression analysis with fuzzy model. IEEE Trans Syst Manag Cybern 12(6):903–907

    Article  Google Scholar 

  • Yang MS, Ko CH (1996) On a class of fuzzy c-numbers clustering procedures for fuzzy data. Fuzzy Sets Syst 84(1):49–60

    Article  MathSciNet  Google Scholar 

  • Zeng W, Feng Q, Li J (2017) Fuzzy least absolute linear regression. Appl Soft Comput 52:1009–1019

    Article  Google Scholar 

  • Zhao H, Zheng J, Deng W, Song Y (2020) Semi-supervised broad learning system based on manifold regularization and broad network. IEEE Trans Circuits Syst I Regul Papers 67(3):983–994

    Article  MathSciNet  Google Scholar 

  • Zhou J, Zhang H, Gu Y, Pantelous AA (2018) Affordable levels of house prices using fuzzy linear regression analysis: the case of shanghai. Soft Comput 22(16):5407–5418

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the two anonymous reviewers for their insightful comments which substantially improved the paper.

Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

    Mojtaba Kashani, Mohammad Reza Rabiei & Mohammad Arashi

Authors
  1. Mojtaba Kashani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Reza Rabiei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Arashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Reza Rabiei.

Ethics declarations

Conflict of interest

On behalf of all authors of the above titled manuscript, I (as the corresponding author) certify that we have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Informed consent

There was no need for obtaining permission since the work has not conducted a healthcare intervention on a person, or for disclosing personal information.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kashani, M., Rabiei, M.R. & Arashi, M. An integrated shrinkage strategy for improving efficiency in fuzzy regression modeling. Soft Comput 25, 8095–8107 (2021). https://doi.org/10.1007/s00500-021-05690-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-05690-9

Keywords

Search

Navigation