fuzzy logistic regression: a new possibilistic model and its application in clinical vague status

logistic regression models are frequently used in clinicalresearch and particularly for modeling disease status and patientsurvival. in practice, clinical studies have several limitationsfor instance, in the study of rare diseases or due ethical considerations, we can only have small sample sizes. in addition, the lack of suitable andadvanced measuring instruments lead to non-precise observations and disagreements among scientists in defining diseasecriteria have led to vague diagnosis. also,specialists oftenreport 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 formodeling and analyzing the problem. in this study, a model called the  `` fuzzy logistic model '' isproposed for the case when the explanatory variables arecrisp and the value of the binary response variable is reportedas a number between zero and one (indicating the possibility ofhaving the property). in this regard, the concept of `` possibilistic odds '' is alsointroduced. then, the methodology and formulationof 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.