This paper introduces hesitant uncertain discrete linguistic Z-numbers (HUDLZNs) based on Z-numbers and linguistic models. HUDLZNs can serve as a effective tool to depict complex and uncertain decision-making information and reflect the hesitancy of DMs. Based on above, a multi-criteria group decision-making(MCGDM) approach using discrete T-norm fusion and positive ideal of alternative is proposed. Firstly, linguistic information is handled with the help of the linguistic scale function, after which the distance and $\lambda$-cut of HULZNs and $\lambda$-cut of C are defined. Then, information fusion of discrete T-norm based on HUDLZNs is proposed. Subsequently, combining the very best of information fusion of discrete T-norm and linguistic scale functions, a MCGDM approach based on HUDLZNs is developed. Finally, an illustrative example of ERP system selection is provided for demonstration, and the feasibility and effectiveness of the proposed method are further proved by sensitivity analysis and comparison with an existing method.