This paper delves into some significant performance measures (PMs) of a bulk arrival queueing system with constant batch size b, according to arrival rates and service rates being fuzzy parameters. The bulk arrival queuing system deals with observation arrival into the queuing system as a constant group size before allowing individual customers entering to the service. This leads to obtaining a new tool with the aid of generating function methods. The corresponding traditional bulk queueing system model is more convenient under an uncertain environment. The $\alpha$-cut approach is applied with the conventional Zadeh's extension principle (ZEP) to transform the triangular membership functions (Mem. Fs) fuzzy queues into a family of conventional bulk
queues. This new model focus on mixed-integer non-linear programming (MINLP) tenders a mathematical computational approach is known as (0 -1) variables. To measures the efficiency of the method, the efficient solution strategy plays a crucial role in the adequate application of these techniques. Furthermore, different stages of the $\alpha$-cut intervals were analyzed and the final part of the article gives a numerical solution of the proposed model to achieve practical issues.