FUZZY LOGISTIC REGRESSION BASED ON LEAST SQUARE APPROACH AND TRAPEZOIDAL MEMBERSHIP FUNCTION

Document Type : Research Paper

Authors

Department of Mathematics and Statistics, Pir Mehr Ali Shah Arid Agriculture University, Rawalpindi, Pakistan

Abstract

Logistic regression is a non-linear modification of the linear
regression. The purpose of the logistic regression analysis is to
measure the effects of multiple explanatory variables which can be
continuous and response variable is categorical. In real life there are
situations which we deal with information that is vague in
nature and there are cases that are not explained
precisely. In this regard, we have used the concept of possiblistic
odds and fuzzy approach. Fuzzy logic deals with linguistic
uncertainties and extracting valuable information from linguistic
terms. In our study, we have developed fuzzy possiblistic logistic
model with trapezoidal membership function and fuzzy possiblistic
logistic model is a tool that help us to deal with imprecise
observations. Comparison fuzzy logistic regression model with classical
logistic regression has been done by goodness of fit criteria on real life as an example.

Keywords

References

[1] A. R. Arabpour and M. Tata, Estimating the parameters of a fuzzy linear regression model,
Iranian Journal of Fuzzy Systems, 5(2) (2008), 1-19.
[2] S. C. Bagleu, H. White and B. A. Golomb, Logistic regression in the medical literature:
standards for use and reporting with particular attention to one medical domain, Journal of
Clinical Epidemiology, 54 (2001), 979-985.
[3] A. Celmins, Least squares model tting to fuzzy vector data, J. Fuzzy sets and systems, 22
(1987), 245-269.
[4] P. T. Chang, E. S. Lee and S. A. Konz, Applying fuzzy linear regression to VDT legibility,
Fuzzy Sets and Systems, 80 (1996), 197-204.
[5] P. Diamond, Least squares fi tting of several fuzzy variablesin: Proc. of the Second IFSA
Congress, Tokyo, Japan, 1 (1987), 329{331.
[6] E. N. King and Ryan. T. P. A preliminary investigation of maximum likelihood logistic
regression versus exact logistic regression, J. of the American Stats, 56 (2002), 163-170.
[7] R. Korner and W. Nather, Linear regression with random fuzzy variables: extended classical
estimates, best linear estimates, least squares estimates, Information Sciences, 109 (1998),
95{118.
[8] W. I. Lee, A comparative study on the forecast of fresh food sales using logistic regression,
moving average and bpnn methods, J. of marine Sci. and Tech., 20 (2012), 142{152.
[9] M. Modarres, E. Nasrabadi and M. M. Nasrabadi, Fuzzy linear regression models with least
square errors, J. Appl. Math. and Comp., 20 (2005), 977{989.
[10] M. Namdari, A. Abadi, S. M. Taheri, M. Rezaei, N. Kalantari and N. Omidvar, Effect of folic
acid on appetite in children: Ordinal logistic and fuzzy logistic regressions, Nutrition, 30(3)
(2014), 274-278.
[11] 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 (2015), 909-917.
[12] S. Pourahmad, S. M. Ayatollahi, S. M. Taheri and Z. H. Agahi, Fuzzy logistic regression based
on the least squares approach with application in clinical studies, J. Camwa., 62 (2011), 3353-
3365.
[13] S. Pourahmad, S. M. Ayatollahi, S. M. Taheri, Fuzzy Logistic Regression: A New Possibilistic
Model And Its Application In Clinical Vague Status, Iranian Journal of Fuzzy Systems, 8(1)
(2011), 1-17.
Iranian Journal of Fuzzy Systems
Volume 15, Issue 6
November and December 2018
Pages 97-106

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