Solution to membership function of multiple-server fuzzy queues

The definition of a-cut and Zadeh's extension principle are applied to transforming multiple-server fuzzy queues, of which the arrival rate and service rate are both fuzzy numbers, into conventional multiple-server queues. Then, the system eigenvalues are described separately by programming a set of parameters to solve upper and lower bounds of the relevant membership function. For instance, there is a 2-server fuzzy queues system of outpatients in a hospital, in which the average arrival rate and service rate are both regarded as trapezoidal fuzzy numbers. With a numerical computation of different α levels, the membership function of the average staying time for all the outpatients can thus be solved. This method can provide more abundant information for managerial decision-making in hospitals.