Discrete event simulation requires modeling input parameters using probability distributions. However, in some cases it may not be possible to obtain a probability distribution for an input parameter because of lack of data. Fuzzy set theory may be used in these cases to model the input parameters using fuzzy sets. The event list will contain events with fuzzy time sets that usually overlap and the problem becomes how to rank these fuzzy sets and advance the simulation clock. In this paper the authors present a ranking algorithm that can generate all possible system evolutions. The algorithm was applied to a single server model where the inter-arrival time and the service time were modeled as triangular fuzzy numbers. Results obtained were compared with results obtained from a comparable triangular distribution and a normal distribution used as benchmarks. Performance parameter used is the utilization percentage of the facility. Results show similar utilization rates and convergence.