# FUZZY LOGISTIC REGRESSION: A NEW POSSIBILISTIC MODEL AND ITS APPLICATION IN CLINICAL VAGUE STATUS

Document Type : Research Paper

Authors

1 Department of Biostatistics, School of Medicine, Shiraz University of Medical Sciences, Shiraz, 71345-1874, Iran

2 Department of Biostatistics, School of Medicine, Shiraz University of Medical Sciences, Shiraz, 71345-1874, Iran

3 Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

Abstract

Logistic regression models are frequently used in clinical
research and particularly for modeling disease status and patient
survival. In practice, clinical studies have several limitations
For instance, in the study of rare diseases or due ethical considerations, we can only have small sample sizes. In addition, the lack of suitable and
advanced measuring instruments lead to non-precise observations and disagreements among scientists in defining disease
criteria have led to vague diagnosis. Also,
specialists often
report their opinion in linguistic terms rather than numerically. Usually, because of these  limitations, the assumptions of the statistical model do not hold and hence their use is questionable. We therefore need to develop new methods for
modeling and analyzing the problem.
In this study, a model called the  `` fuzzy logistic model '' is
proposed for the case when the explanatory variables are
crisp and the value of the binary response variable is reported
as a number between zero and one (indicating the possibility of
having the property). In this regard, the concept of `` possibilistic odds '' is also
introduced. Then, the methodology and formulation
of this model is explained in detail and a linear programming approach is use to estimate the model parameters. Some goodness-of-fit criteria are proposed and a numerical example is given as an example.

Keywords

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