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Computer network security (CNS) evaluation is a comprehensive analysis and assessment of a network system's security to identify potential vulnerabilities and threats, ensuring the system complies with relevant security standards. The evaluation includes the effectiveness of technical measures such as firewalls, intrusion detection, access control, and encryption, to ensure the confidentiality, integrity, and availability of data, ultimately enhancing overall security defenses. The evaluation of CNS is a multi-attribute group decision-making (MAGDM) problem. Recently, both the CoCoSo method and the information entropy approach have been applied to solve MAGDM challenges. Type-2 Neutrosophic Sets (T2NSs) are utilized to represent uncertain data during the network security evaluation process. In this study, the CoCoSo method is adapted for MAGDM with T2NSs. Furthermore, the type-2 Neutrosophic Number with CoCoSo (T2NN-CoCoSo) approach based on T2NN is developed for MAGDM. Finally, a numerical example is provided to demonstrate the application of the T2NN-CoCoSo approach in CNS evaluation. The key contributions of this study include: (1) the development of a MAGDM method using the T2NN-CoCoSo approach with T2NSs, and (2) the proposal of a novel MAGDM approach for CNS evaluation using the T2NN-CoCoSo method. [ABSTRACT FROM AUTHOR]