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Fuzzy logistic regression based on the least squares approach with application in clinical studies. (English) Zbl 1236.62083

Summary: To model fuzzy binary observations, a new model named “Fuzzy Logistic Regression” is proposed and discussed in this study. In fact, due to the vague nature of binary observations, no probability distribution can be considered for these data. Therefore, the ordinary logistic regression may not be appropriate. This study attempts to construct a fuzzy model based on the possibility of success. These possibilities are defined by some linguistic terms such as \(\dots,\) low, medium, high \(\dots \). Then, by use of the extension principle, the logarithmic transformation of “possibilistic odds” is modeled based on a set of crisp explanatory variables observations. Also, to estimate the parameters in the proposed model, the least squares method in fuzzy linear regression is used. For evaluating the model, a criterion named the “capability index” is calculated. Finall, because of the widespread applications of logistic regression in clinical studies and also, of the abundance of vague observations in clinical diagnoses, suspected cases of Systematic Lupus Erythematosus (SLE) disease is modeled based on some significant risk factors to detect the applications of the model. The results showed that the proposed model could be a rational substituted model of an ordinary one in modeling a clinical vague status.

MSC:

62J86 Fuzziness, and linear inference and regression
62J12 Generalized linear models (logistic models)
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
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