A NEW APPROACH FOR PARAMETER ESTIMATION IN FUZZY LOGISTIC REGRESSION

Document Type: Research Paper

Authors

1 Department of Statistics, Anadolu University, Eskisehir, Turkey and Department of Statistics, Amasya University, Amasya,Turkey

2 Department of Statistics, Anadolu University, Eskisehir, Turkey

Abstract

Logistic regression analysis is used to model categorical dependent variable. It is usually used in social sciences and clinical research. Human thoughts and disease diagnosis in clinical research contain vagueness. This situation leads researchers to combine fuzzy set and statistical theories. Fuzzy logistic regression analysis is one of the outcomes of this combination and it is used in situations where the classical logistic regression assumptions' are not satisfied. Also it can be used if the observations or their relations are vague.  In this study, a model called “Fuzzy Logistic Regression Based on Revised Tanaka's Fuzzy Linear Regression Model” is proposed. In this regard, the methodology and formulation of the proposed model is explained in detail and the revised Tanaka's regression model is used to estimate the parameters. The Revised Tanaka's Regression model is an extension of Tanaka's Regression Model in which the objection function is developed.  An application is performed on birth weight data set. Also, an application of diabetes data set used in Pourahmad et al.'s study was conducted via our proposed data set. The validity of the model is shown by the help of goodness – of –fit criteria called Mean Degree Memberships (MDM).

Keywords


[1] G. Atalik, A New Approach for Parameter Estimation in Fuzzy Logistic Regression and
an Application, Master of Science Thesis, Anadolu University, Graduate School of Sciences,
Eskisehir (2014).
[2] H. Bircan, Lojistik Regresyon Analizi: Tp Verileri zerine Bir Uygulama, Kocaeli niversitesi
Sosyal Bilimler Enstits Dergisi, 8(1) (2004), 185-208.
[3] R. M. Dom, S. A. Kareem, A. Razak and B. Abidin, A learning system prediction method
using fuzzy regression, In Proceedings of the International MultiConference of Engineers and
Computer Scientists, Hong Kong, China, (2008), 19-21.

[4] Y. Q. He, L. K. Chan and M. L. Wu, Balancing productivity and consumer satisfaction
for profi tability: statistical and fuzzy regression analysis, European Journal of Operational
Resarch, 176(1) (2007), 252-263.
[5] S. S. Hirve and B. R. Ganatra, Determinants of low birth weight: a commun,ty based prospec-
tive cohort study, Indian Pediatrics, 31(10) (1994), 1221-1225.
[6] D. W. Hosmer and S. Lemeshow, Applied Logistic Regression, John Wiley and Sons, New
York, 2000.
[7] D. G. Kleinbaum and M. Klein, Logistic Regression, A Self-Learning Text (Second Edition
ed.), Springer - Verlag , New York, 2002.
[8] E. Kirimi and S. Pence, The affects of smoking during pregnancy to fetus and plasental
development, Van Medical Journal, 6(1) (1999), 28-30.
[9] D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis,
John Wiley and Sons, New York, 2001.
[10] P. Nagar and S. Srivastava, Adaptive fuzzy regression model for the prediction of dichotomous
response variables using cancer data: a case study, Journal of Applied Mathematics, Statistics
and Informatics, 4(2) (2008), 183-191.
[11] M. Namdari, A. Abadi, S. M. Taheri, M. Rezaei, M. Kalantari and N. Omidvar, Effect of
folic acid on appetite in children: Ordinal logistic and fuzzy logistic regressions, Nutrition,
30(3) (2014), 274-278.
[12] M. Namdari, J. H. Yoon, A. Abadi, S. M. Taheri and S. H. Choi, Fuzzy Logistic Regression
with Least Absolute Deviations Estimators, Soft Computing, 19(4) (2015), 909-917.
[13] S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri, Fuzzy logistic regression: a new possi-
bilistic model and its application in clinical vague status, Iranian Journal of Fuzzy Systems,
8(1) (2011), 1-17.
[14] S. Pourahmad, S. M. Ayatollahi and S. M. Taheri, Fuzzy logistic regression based on the
least squares approach with application in clinical studies, Computers and Mathematics with
Applications, 62(9) (2011), 3353-3365.
[15] H. Tanaka, S. Uejima and K. Asai, Lineer regression analysis with fuzzy model, IEEE Transactions
On Systems, Man, and Cybernetics, 12(6) (1982), 903-907.
[16] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
[17] L. A. Zadeh, Discussion: probability theory and fuzzy logic are complementary rather than
competitive, Technometrics, 37(3) (1995), 271-276.