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A distinctive analyzation of intuitionistic fuzzy queueing system using Erlang service model

This paper proposes a mathematical programming approach for membership and non-member functions of steady-state performance measures in infinite capacity queues in the Erlang service, where the arrival rate and service rate are intuitionistic fuzzy numbers. The rudimentary idea is based on an Atanassov’s extension principle and (α, β)- cut approach. Two pairs of mixed-integer nonlinear programs(MINLP) with binary variables are regulated to calculate the upper and lower bounds of the system performance measure of possibility level (α, β). The main objective of the paper is to investigate the expected and awaiting number of customers in the queue and their waiting time in service. Finally, a numerical example is illustrated to show the efficiency of the proposed method.