Razi University

   Regression models are frequently employed in clinical research. Although linear regression describes the relationship between the conditional mean of a response variable and one or more independent variables, it often performs poorly in data analysis. For instance, least squares estimators are sensitive to outliers and yield biased estimates in the presence of non-normal error distributions or heteroscedasticity. Hence, quantile regression can be utilized to address such issues. In practice, clinical studies face numerous limitations. For example, in the investigation of rare diseases or due to ethical considerations, only small sample sizes can be considered. Moreover, the lack of advanced and appropriate measurement tools leads to imprecise observations and disagreements among scientists regarding the diagnosis of disease criteria. Therefore, an alternative approach to uncertainty namely, possibility is considered instead of probability for modeling such observations. In this context, fuzzy regression models are often employed to model ambiguous binary observatio   fuzzy quantile regression is one such approach. In this regard, some medical researchers have found that vague observations should be reliable to a certain extent in order to facilitate more rational decision-making. Fuzzy sets cannot represent reliability; thus, this poses a challenge. Consequently, new methods for modeling and analyzing the problem are required. The present dissertation proposes a fuzzy quantile regression model based on Z-numbers, such that the explanatory variables are real-valued and the response variable is fuzzy-valued based on Z-numbers. The proposed methodology is discussed in detail, and a novel approach for estimating the model parameters is then developed. Given the extensive applications of quantile regression in clinical studies and the prevalence of ambiguous observations in clinical diagnoses, the risk of heart disease is modeled. Finally, it can be concluded that the proposed model is more applicable than the conventional fuzzy model in modeling ambiguous clinical status.