Enhancing cyber defense strategies with discrete multi-dimensional Z-numbers: a multi-attribute decision-making approach

With the rapid advancement of intelligent technologies and network environments, the efficient and accurate handling of uncertain decision-making information has become an urgent challenge. Traditional methods often struggle to process complex and incomplete information, especially in cyber defense. To address this, we introduce discrete multi-dimensional Z-numbers (MZs) as a mathematical tool for modeling uncertainty and reliability in network defense decisions. This paper proposes a synthesis method for MZs, enabling the integration of multi-source information while considering both uncertainty and reliability. By leveraging a hidden probability model, we extend MZs into multi-dimensional Z+-numbers, enhancing their expressiveness in handling uncertainty. Furthermore, we define utility functions based on MZs and develop a multi-attribute group decision-making framework tailored for network defense. This approach offers a novel perspective for designing strategies against highly adaptive and covert cyberattacks. The proposed method is validated through a case study on the network security assessment of an intelligent logistics company. Results demonstrate significant improvements in the accuracy and efficiency of decision-making, highlighting the method’s advantages and broad potential in cyber defense. Beyond logistics, this integrated MZ-based decision framework provides an adaptable and intelligent tool for strengthening network security defenses.