Environmental modeling with a satisfaction levels of the end user in relation to a defined parameter coupled with imprecision that stems from the field data is a key issue. In the context of this issue success of possibility theory based on fuzzy sets has high visibility in comparison with conventional probability theory. Environmental impact assessments of a high level waste- repository is focused using the new approach because the problems under consideration includes a number of qualitative uncertainties at different levels, apart from being quite complex; decision-maker's need to have a transparent assessment result that will enable him to understand underlying assumptions and to judge resulting doses. Fuzzy dlstributions have been tried to resolve the issues related to the safety of environment from the waste repository. Paper describes the details of fuzzy distribution, fuzzy logic and its possible application to deal the qualitative and quantitative uncertainty in connection with waste repository.