Abstract: In this study membership function of the steady state system performance measures of priority queues with two classes of customers is constructed using mixed integer non linear programming approach. Here, type 1 are considered to have priority over the type 2 customers. In this system with non preemptive priority, a low priority customer in service is not interrupted upon arrival of a higher priority customer at a queuing system and they are served with different service rates. Here, the arrival rate and service rate are considered to be fuzzy. The basic idea of this study is to use Zadeh’s extension principle, α-cut approach and mixed integer non linear programming problem to construct the lower and the upper bound of the system performance measures. Using α-cut approach the fuzzy queues are transformed into crisp queues. For different values of α the membership function is constructed. The defuzzification of the performance measures is provided by Yager’s ranking index. A numerical example is solved to demonstrate the validity of given model.