In this paper we have considered an unreliable retrial queueing system with setup times and repair under the two types of uncertainty--fuzzy uncertainty and intuitionistic fuzzy uncertainty for the queueing model given by Tian et al. (2023). We have investigated the system by taking a numerical example both under the fuzzy environment and the intuitionistic fuzzy environment. Triangular fuzzy numbers and intuitionistic triangular fuzzy numbers have been used to obtain different system probabilities and performance measures. We have verified stability condition for the system using a ranking function for the triangular fuzzy numbers and using magnitude concept for the intuitionistic triangular fuzzy numbers. We have obtained various system probabilities and performance measures in fuzzy and intuitionistic fuzzy form. A comparative study of performance measures under both the fuzzy and the intuitionistic fuzzy domain has been made. Our paper exemplifies the successful use of fuzzy and intuitionistic fuzzy arithmetic to such a complex retrial queueing system that contains nine uncertain variables.

Unreliable retrial queueing system, Triangular fuzzy number, Intuitionistic triangular fuzzy number.