Generalized Bayesian (GB) is a Bayesian approach based on the learning rate parameter (LRP) ( $0<\eta <1$) as a fraction of the power of the likelihood function. In this paper, we consider the GB method to perform inference studies for a class of exponential distributions. Generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the considered distributions are obtained based on the censored type Ⅱ samples. In addition, generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP) are considered using a one-sample prediction scheme. Monte Carlo simulations and illustrative example are performed for one parameter models to compare the performance of the GBE and GEBE estimation results and the GBP and GEBP prediction results for different values of the LRP.