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This paper deals a mathematical model of intermediate queue before two semi parallel but heterogeneous servers under fuzzy environment. Queue discipline before the servers are considered on the basis of high priority while the service of intermediate queue is considered to be low priority. Steady state analysis of the model has been derived with the help of generating function technique, laws of calculus and statistical techniques. In some of these kinds of systems, it happens that the arrival and service parameters both are uncertain. Hence, we have considered the fuzzy arrival and fuzzy service rate which result in deriving the state probabilities and queue length of system in fuzzy expression. α- cut has been applied to shorten the length of the interval. A numerical illustration has also been given in order to clarify the concept. The model finds its application to public transportation problem.