In this research paper we construct the membership and non-membership functions with intuitionistic fuzzy model with single server queueing system. Also we construct the triangular and trapezoidal fuzzy numbers for N-policy IFM/IFM/1queueing system with server vacation start-up and time-out with the help of IFs α-cut method. Where the arrival rate, service rate and vacation time are intuitionistic fuzzy numbers. IFS queues are reduced to a family of intuitionistic Crisp queues based on IFS α-cut approach. The main objective of the paper is to analyze the expected system length of the queue in L. Finally to illustrated numerical example of this model.