This paper presents a novel approach to uncertainty quantification in logistic regression using random fuzzy sets and belief functions. The method, called evidential logistic regression, extends traditional Bayesian inference by incorporating epistemic uncertainty through the use of possibility distributions and belief functions. The approach is applied to both binomial and multinomial regression models. In the binomial case, the predictive belief function is computed by numerically integrating the possibility distribution of the posterior probability. In the multinomial case, the solution is obtained by combining constrained nonlinear optimization with Monte Carlo simulation. The method uses a normal approximation to the relative likelihood function to simplify computations. Numerical experiments show that decision rules based on predictive belief functions achieve lower error rates compared to those based on posterior probabilities. The approach is compared to other evidential methods, including Inferential Models, and is shown to be more effective in capturing both aleatory and epistemic uncertainty. The paper also discusses the use of prior information, regularization, and prediction in logistic regression, demonstrating the effectiveness of the evidential approach in handling uncertainty in classification tasks.This paper presents a novel approach to uncertainty quantification in logistic regression using random fuzzy sets and belief functions. The method, called evidential logistic regression, extends traditional Bayesian inference by incorporating epistemic uncertainty through the use of possibility distributions and belief functions. The approach is applied to both binomial and multinomial regression models. In the binomial case, the predictive belief function is computed by numerically integrating the possibility distribution of the posterior probability. In the multinomial case, the solution is obtained by combining constrained nonlinear optimization with Monte Carlo simulation. The method uses a normal approximation to the relative likelihood function to simplify computations. Numerical experiments show that decision rules based on predictive belief functions achieve lower error rates compared to those based on posterior probabilities. The approach is compared to other evidential methods, including Inferential Models, and is shown to be more effective in capturing both aleatory and epistemic uncertainty. The paper also discusses the use of prior information, regularization, and prediction in logistic regression, demonstrating the effectiveness of the evidential approach in handling uncertainty in classification tasks.