A finite buffer queue subject to balking and startup under N-policy with fuzzy parameters is studied. This paper aims to put forward a technique for acquiring the function of membership for the N-policy queue. The function of membership for the performance characteristic of this queueing system wherein the rates of arrival, service, and startup are fuzzy numbers is built by making use of mathematical programming. The transformation from the fuzzy N-policy queue to a family of conventional crisp N-policy queues is done by employing the alpha cut technique and principle of Zadeh’s extension. A useful set of rules is constructed for determining the ideal solutions at or distinct possibility level α. Furthermore, the usefulness of the proposed model is demonstrated by giving appropriate real-life example. Numerical examples are solved successfully.