Skip to main content

Advertisement

SpringerLink
Log in

Fuzzy logistic regression with least absolute deviations estimators

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This study is an investigation of fuzzy logistic regression model for crisp input and fuzzy output data. The response variable is non-precise and is measured by linguistic terms. Especially this research develops least absolute deviations (LAD) method for modeling and compares the results with the least squares estimation (LSE) method. For these, two estimation methods, min–max method and fitting method, are provided in this research. This study presents new goodness-of-fit indices which are called measure of performance based on fuzzy distance \((M_p)\) and index of sensitivity \((I_S)\). The study gives two numerical examples in real clinical studies about systematic lupus erythematosus and the other one in the field of nutrition to explain the proposed methods. In addition, we investigate the sensitivity of two estimation methods in the case of outliers by a numerical example.

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

Fig. 1

Similar content being viewed by others

References

  • Agresti A (2002) Categorical data analysis. Wiley, New York

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Chachi J, Taheri SM (2013) A least-absolutes regression model for imprecise response based on the generalized Hausdorff-metric. J Uncertain Syst 7:265–276

    Google Scholar 

  • Chang PT, Lee CH (1994) Fuzzy least absolute deviations regression based on the ranking of fuzzy numbers. In: Proceedings of IEEE world congress on computational intelligence, pp 1365–1369

  • Choi SH, Buckley J (2008) Fuzzy regression using least absolute deviation estimators. Soft Comput 12:254–263

    Google Scholar 

  • Choi SH, Kim HK, Park KO (2000) Nonlinear regression quantiles estimation. J Korean Stat Soc 29:187–199

    MathSciNet  Google Scholar 

  • Dielman TE (1986) A comparison of forecasts form least absolute value and least squares regression. J Forecast 5:189–195

    Article  Google Scholar 

  • Diamond P (1987) Least squares fitting of several fuzzy variables. In: Proceedings of the second IFSA congress, Tokyo, pp 20–25

  • Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York

    Book  MATH  Google Scholar 

  • Fauci AS, Braunwald E, Kasper DL, Hauser SL, Longo DL, Jameson JL, Loscalzo J (2008) Harrison’s principals of internal medicine. Wiley, New York

    Google Scholar 

  • Hatamizadeh N, Eftekhar H, Shafaghi B, Mohammad K (2007) Effects of folic acid on preschool childrens appetite: randomized triple-blind clinical trial. Pediatr Int 49:558–563

    Article  Google Scholar 

  • Hong DH, Lee S, Do DY (2001a) Fuzzy linear regression analysis for fuzzy input-output data using shape preserving operations. Fuzzy Sets Syst 122:513–526

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  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 

  • Klir GJ (1987) Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like? Fuzzy Sets Syst 24:141–160

    Article  MATH  MathSciNet  Google Scholar 

  • Neter J, Wasserman W, Kutner MH, Nachtsheim C (1996) Applied linear statistical models. McGraw-Hill, Boston

    Google Scholar 

  • Pourahmad S, Ayatollahi SMT, Taheri SM (2011a) Fuzzy logistic regression, a new posssibilistic regression and its application in clinical vague status. Iran J Fuzzy Syst 8:1–17

    MATH  MathSciNet  Google Scholar 

  • Pourahmad S, Ayatollahi SMT, Taheri SM, Agahi ZH (2011b) Fuzzy logistic regression based on the least squares approachs with application in clinical studies. Comput Math Appl 62:3353–3365

    Article  MATH  MathSciNet  Google Scholar 

  • Ramli AA, Watada J, Pedrycz W (2011) Possibilistic regression analysis of influential factors for occupational health and safety management systems. Saf Sci 49:1110–1117

  • Taheri SM, Kelkinnama M (2012) Fuzzy linear regression based on least absolute deviations. Iran J Fuzzy Syst 9:121–140

    MATH  MathSciNet  Google Scholar 

  • Taheri SM, Mirzaei Yeganeh M (2009) Logistic regression with non- precise data. In: Proceedings of the 57th ISI (International Statistical Institute) Congress, South Africa, Durban, pp 1–9

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

    Article  MATH  Google Scholar 

  • Torabi H, Behboodian J (2007) Fuzzy least-absolute estimates in linear models. Commun Stat Theory Methods 36:1935–1944

    Article  MATH  MathSciNet  Google Scholar 

  • Tseng FM, Lin L (2005) A quadratic interval logit model for forecasting bankruptcy. Omega 33:85–91

    Article  Google Scholar 

  • Wolfram Research Inc (2007) Mathematica, Version 6.0, Champaign, IL

  • Zimmerman HJ (2001) Fuzzy set theory and its applications. Kluwer Nihoff, Boston

    Book  Google Scholar 

Download references

Acknowledgments

The child’s appetite data which was used in the second numerical example of this paper was a part of a project which was funded by National Nutrition and Food Technology Research Institute of Shahid Beheshti University of Medical Sciences. The authors acknowledge their gratitude to Dr. M. Rezaei, Dr. N. Kalantari and Dr. N. Omidvar for that project. The authors acknowledge the anonymous reviewers for their valuable comments and suggestions to improve the article.

Author information

Authors and Affiliations

  1. Department of Biostatistics, Faculty of Paramedical Sciences and Dental School, Shahid Beheshti University of Medical Sciences, Tehran, Iran

    Mahshid Namdari

  2. School of Mathematics and Statistics, Sejong University, Seoul, South Korea

    Jin Hee Yoon

  3. Department of Health and Community Medicine, School of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran

    Alireza Abadi

  4. Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

    S. Mahmoud Taheri

  5. School of Liberal Arts and Sciences, Korea Aerospace University, Koyang, South Korea

    Seung Hoe Choi

Authors
  1. Mahshid Namdari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jin Hee Yoon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alireza Abadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Mahmoud Taheri
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Seung Hoe Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seung Hoe Choi.

Additional information

Communicated by J.-W. Jung.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Namdari, M., Yoon, J.H., Abadi, A. et al. Fuzzy logistic regression with least absolute deviations estimators. Soft Comput 19, 909–917 (2015). https://doi.org/10.1007/s00500-014-1418-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-014-1418-2

Keywords

Search

Navigation