Statistical analysis of lifetime distributions under Type-II censoring scheme is based on precise lifetime data. However, in real situations all observations and measurements of Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. This paper deals with the estimation of exponential mean parameter under Type-II censoring scheme when the lifetime observations are fuzzy and are assumed to be related to underlying crisp realization of a random sample. We use Newton-Raphson algorithm as well as EM algorithm to determine the maximum likelihood estimate (MLE) of parameter. We also obtain the estimate, via moment method and Bayesian procedure, of the unknown parameter. In addition, a new numerical method for parameter estimation is provided. Monte Carlo simulations are performed to investigate performance of the different methods. Finally, an example is presented in order to illustrate the methods of inference discussed here.