International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1635–1644 | Cite as

Logistic Regression for Fuzzy Covariates: Modeling, Inference, and Applications

  • Fatemeh Salmani
  • S. Mahmoud Taheri
  • Jin Hee Yoon
  • Alireza Abadi
  • Hamid Alavi Majd
  • Abbas Abbaszadeh


Logistic regression is an important tool to evaluate the functional relationship between a binary response variable and a set of predictors. However, in clinical studies, often there is insufficient precision or indefiniteness of state. Therefore, we need to explore some soft methods for inference when the variables are reported as imprecise quantities. In this regard, we propose a fuzzy regression model with fuzzy covariates for imprecise binary-based response. We apply a least-squares method to estimate the model parameters and a bootstrap method for both computing confidence intervals and testing the hypotheses for the model parameters. The proposed model is then applied for verification to a numerical example based on a real clinical study of the effect of beloved person’s voice on reducing patient pain during the chest tube removal after an open heart surgery. Finally, the proposed model is evaluated by a well-known goodness-of-fit index.


Fuzzy logistic regression Fuzzy covariate Least-squares method Bootstrap Pain 


  1. 1.
    Namdari, M., Yoon, J.H., Abadi, A., Taheri, S.M., Choi, S.H.: Fuzzy logistic regression with least absolute deviations estimators. Soft. Comput. 19(4), 909–917 (2015)CrossRefGoogle Scholar
  2. 2.
    Kao, C., Chyu, C.-L.: Least-squares estimates in fuzzy regression analysis. Eur. J. Oper. Res. 148(2), 426–435 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Chachi, J., Taheri, S.M., Arghami, N.R.: A hybrid fuzzy regression model and its application in hydrology engineering. Appl. Soft Comput. 25, 149–158 (2014)CrossRefGoogle Scholar
  4. 4.
    Arefi, M., Taheri, S.M.: Least-squares regression based on Atanassov’s intuitionistic fuzzy inputs–outputs and Atanassov’s intuitionistic fuzzy parameters. IEEE Trans. on Fuzzy Syst. on 23(4), 1142–1154 (2015)CrossRefGoogle Scholar
  5. 5.
    Kim, I.K., Lee, W.-J., Yoon, J.H., Choi, S.H.: Fuzzy regression model using trapezoidal fuzzy numbers for re-auction data. Int. J Fuzzy Log. Intell. Syst. 16(1), 72–80 (2016)CrossRefGoogle Scholar
  6. 6.
    Mendel, J.M.: On a novel way of processing data that uses fuzzy sets for later use in rule-based regression and pattern classification. Int. J. Fuzzy Log. Intell. Syst. 14(1), 1–7 (2014)CrossRefGoogle Scholar
  7. 7.
    Yu, J.R., Tseng, F.-M.: Fuzzy piecewise logistic growth model for innovation diffusion: a case study of the TV industry. Int. J. Fuzzy Syst. 18(3), 1–12 (2014)Google Scholar
  8. 8.
    Takemura, K.: Fuzzy logistic regression analysis for fuzzy input–output data. In: Proceedings of the Joint 2nd International Conference on Soft Computing and Intelligent Systems and the 5th International Symposium on Advanced Intelligent Systems, Japan 2004, pp. 1–6Google Scholar
  9. 9.
    Choi, S.H., Buckley, J.J.: Fuzzy regression using least absolute deviation estimators. Soft. Comput. 12(3), 257–263 (2008)CrossRefGoogle Scholar
  10. 10.
    Nagar, P., Srivastava, S.: Adaptive fuzzy regression model for the prediction of dichotomous response variables using cancer data: a case study. J. Appl Math Stat Infom (JAMSI) 4, 183–191 (2008)Google Scholar
  11. 11.
    Pourahmad, S., Ayatollahi, S., Taheri, S.: Fuzzy logistic regression: a new possibilistic model and its application in clinical vague status. Iran. J. Fuzzy Syst 8(1), 1–17 (2011)MathSciNetMATHGoogle Scholar
  12. 12.
    Namdari, M., Taheri, S.M., Abadi, A., Rezaei, M., Kalantari, N.: Possibilistic logistic regression for fuzzy categorical response data. In: 2013 IEEE International Conference on Fuzzy Systems 8(1), pp. 1–6. (2013)Google Scholar
  13. 13.
    Diamond, P.: Least squares fitting of several fuzzy variables. In: 2nd International Fuzzy Systems Association IFSA World Congress, pp. 329–331. (1987)Google Scholar
  14. 14.
    Agresti, A.: An introduction to categorical data analysis. Wiley, New York (1996)MATHGoogle Scholar
  15. 15.
    Hung, G.C.L., Cheng, C.T., Jhong, J.R., Tsai, S.Y., Chen, C.C., Kuo, C.J.: Risk and protective factors for suicide mortality among patients with alcohol dependence. J. Clin. Psychiatry 76(12), 1478–1693 (2015)Google Scholar
  16. 16.
    Kwak, J.Y., Kim, K.M., Yang, H.J., Yu, K.J., Lee, J.G., Jeong, Y.O., Shim, S.G.: Prevalence of colorectal adenomas in asymptomatic young adults: a window to early intervention? Scand. J. Gastroenterol. 51(6), 1–8 (2016)CrossRefGoogle Scholar
  17. 17.
    Sanchalika, A., Teresa, J.: Risk of gestational diabetes among South Asian immigrants living in New Jersey—a retrospective data review. J. Racial Ethn. Health Dispar. 2(4), 510–516 (2015)CrossRefGoogle Scholar
  18. 18.
    Zimmermann, H.: Fuzzy set theory and its applications. Springer, Massachusetts (2001)CrossRefGoogle Scholar
  19. 19.
    Pourahmad, S., Ayatollahi, S.M.T., Taheri, S.M., Agahi, Z.H.: Fuzzy logistic regression based on the least squares approach with application clinical studies. Comput. Math. Appl. 62(9), 3353–3365 (2011)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Kauffman, A., Gupta, M.M.: Introduction to fuzzy arithmetic: theory and application. Van Nostrand Reinhold, New York (1991)Google Scholar
  21. 21.
    Heilpern, S.: Representation and application of fuzzy numbers. Fuzzy Sets Syst. 91(2), 259–268 (1997)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Xu, R., Li, C.: Multidimensional least-squares fitting with a fuzzy model. Fuzzy Sets Syst. 119(2), 215–223 (2001)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Efron, B., Tibshirani, R.J.: An introduction to the bootstrap. CRC Press, Boca Raton (1994)MATHGoogle Scholar
  24. 24.
    Akbari, M.G., Rezaei, A.: Bootstrap statistical inference for the variance based on fuzzy data. Austrian J. Stat. 38(2), 121–130 (2009)CrossRefGoogle Scholar
  25. 25.
    Lee, W.-J., Jung, H.Y., Yoon, J.H., Choi, S.H.: The statistical inferences of fuzzy regression based on bootstrap techniques. Soft. Comput. 19(4), 883–890 (2015)CrossRefMATHGoogle Scholar
  26. 26.
    Taheri, S.M., Kelkinnama, M.: Fuzzy linear regression based on least absolute deviations. Iran. J. Fuzzy Syst. 9(1), 121–140 (2012)MathSciNetMATHGoogle Scholar
  27. 27.
    Babajani, S., Babatabar, H., Ebadi, A., Mahmoudi, H., Nasiri, E.: The effect of foot reflexology massage on the level of pain during chest tube removal after open heart surgery. J. Crit. Care Nurs. 7(1), 15–22 (2014)Google Scholar
  28. 28.
    Bruce, E.A., Howard, R.F., Franck, L.S.: Chest drain removal pain and its management: a literature review. J. Clin. Nurs. 15(2), 145–154 (2006)CrossRefGoogle Scholar
  29. 29.
    Sheikh Asadi, H.: Effects of distraction on pain relief with a loved one’s voice while pulling a chest tube after open heart surgery: (Master’s Thesis) Shahid Beheshti University of Medical Sciences (2013)Google Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Fatemeh Salmani
    • 1
  • S. Mahmoud Taheri
    • 2
  • Jin Hee Yoon
    • 3
  • Alireza Abadi
    • 4
  • Hamid Alavi Majd
    • 1
  • Abbas Abbaszadeh
    • 5
  1. 1.Department of Biostatistics, Faculty of Paramedical SciencesShahid Beheshti University of Medical SciencesTehranIran
  2. 2.Faculty of Engineering Science, College of EngineeringUniversity of TehranTehranIran
  3. 3.School of Mathematics and StatisticsSejong UniversitySeoulSouth Korea
  4. 4.Department of Community Medicine, Faculty of Medicine, Social Determinants of Health Research CenterShahid Beheshti University of Medical SciencesTehranIran
  5. 5.Department of Nursing, Nursing and Midwifery SchoolShahid Beheshti University of Medical SciencesTehranIran

Personalised recommendations