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At a post-Chernobyl conference on Probabilistic Safety Assessment and Risk management (PSA '87) held in September 1987, the inadequacies of the current Probabilistic Risk Assessment (PSA) came into sharp focus. Highlighting the importance of improvements in the current PSA, Professor Rasmussen - a pioneer in the PSA methodology - made a strong plea for reduction of rather large uncertainties in the results of current PSA. Obviously, amongst the ways to achieve this, one of the approaches would be to encourage collection and use of accurate failure data. However as the state of affairs is, a better alternative would be to develop a methodology which could handle imprecision of data and uncertainties of models which are existence in the current PSA. Fuzzy Set Theory (FST) provides a natural framework to achieve the above goal and therefore the present paper is intended to emphasize and explore the possibility of the use of such a theory to develop a methodology which is computationally simple and easy to use in the quantitative assessment of failure probability of catastrophic events in PSA, particularly, in level-I studies. Some illustrative examples are provided to demonstrate the feasibility and effectiveness of such an approach. It is demonstrated that a general purpose computer code can be developed without much difficulty to recast the PRA studies to incorporate fuzzy probabilities.