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Fuzzy queuing frameworks shed data on openness and fluctuation in each and every domain. In this detailed study, we present a model for assessing system characteristics in a tri-cum biserial bulk queuing systems with a server that exists commonly in an ambiguous environment. The estimates of two distinct ranking prototypes of a given queuing model are compared in this research. For the model's validity, we acquired numerical illustrations in the tabular form, showing that a fuzzy queue can be more realistic than a crisp queue.