‎Fuzzy Logistic Regression Analysis Using the Least Squares Method

Subject Areas : Transactions on Fuzzy Sets and Systems

Zahra Behdani ¹ , Majid Darehmiraki ²

1 - .گروه آمار- دانشکده علوم پایه- دانشگاه صنعتی خاتم الانبیاء
2 - Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Khouzestan, Iran.

Received: 2024-05-16 Accepted : 2024-08-21 Published : 2024-11-05

Keywords: Least square‎, ‎Distance measure‎, ‎Logistic regression‎.,

Abstract :

One of the most efficient statistical tools for modeling the relationship between a dependent variable and several independent variables is regression‎. ‎In practice‎, ‎observations relating to one or more variables‎, ‎or the relationship between variables‎, ‎may be vague or non-specific‎. ‎In such cases‎, ‎classic regression methods will not have enough capability to model data‎, ‎and one of the alternative methods is regression in a fuzzy environment‎. ‎The fuzzy logistic regression model provides a framework in the fuzzy environment to investigate the relationship between a binary response variable and a set of covariates‎. ‎The purpose of this paper is to attempt to develop a fuzzy model that is based on the idea of the possibility of success‎. ‎These possibilities are characterized {by several} linguistic phrases‎, ‎including low‎, ‎medium‎, ‎and high‎, ‎among others‎. ‎Next‎, ‎we {use a set of precise explanatory variable observations to model the logarithm transformation of‎ "‎possibilistic odds.‎" ‎We assume that the model's parameters are triangular fuzzy numbers.} We use the least squares method in fuzzy linear regression to estimate the parameters of the provided model‎. ‎We compute three types of goodness-of-fit criteria to evaluate the model‎. ‎Ultimately‎, ‎we model suspected cases of Systemic Lupus Erythematosus (SLE) disease based on significant risk factors to identify the model's application‎. ‎We do this due to the widespread use of logistic regression in clinical studies and the prevalence of ambiguous observations in clinical diagnosis‎. ‎Furthermore‎, ‎to assess the prevalence of diabetes in the community‎, ‎we will collect a sample of plasma glucose levels‎, ‎measured two hours after a meal‎, ‎from each participant in a clinical survey‎. ‎The proposed model has the potential to rationally replace an ordinary model in modeling the clinically ambiguous condition‎, ‎according to the findings‎.

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