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.

Cyberbullying and hate speech increasingly appear in multi-modal social media posts, where images and text are combined in diverse and fast changing ways across platforms. These posts differ in style, vocabulary and layout, and labeled data are sparse and noisy, which makes it difficult to train detectors that are both reliable and deployable under tight computational budgets. Many high performing systems rely on large vision language backbones, full parameter fine tuning, online retrieval or model ensembles, which raises training and inference costs. We present a parameter efficient cross-platform multi-modal transfer learning framework for cyberbullying and hateful content detection. Our framework has three components. First, we perform domain adaptive pretraining of a compact ViLT backbone on in domain image-text corpora. Second, we apply parameter efficient fine tuning that updates only bias terms, a small subset of LayerNorm parameters and the classification head, leaving the inference computation graph unchanged. Third, we use noise aware knowledge distillation from a stronger teacher built from pretrained text and CLIP based image-text encoders, where only high confidence, temperature scaled predictions are used as soft labels during training, and teacher models and any retrieval components are used only offline. We evaluate primarily on Hateful Memes and use IMDB as an auxiliary text only benchmark to show that the deployment aware PEFT + offline-KD recipe can still be applied when other modalities are unavailable. On Hateful Memes, our student updates only 0.11% of parameters and retain about 96% of the AUROC of full fine-tuning.

With the rapid development of intelligent logistics and network environment, it has become an urgent problem to efficiently and accurately handle and analyse the huge amount of uncertain decision information. Traditional decision making methods often fail to make the best use of complex and incomplete information, especially in the field of cyber defence. To address these problems, this paper introduces a new mathematical tool, discrete multidimensional Z-numbers (MZs), for expressing and dealing with uncertainty and reliability in network defence decisions. In this paper, we first introduce the synthesis method of discrete multidimensional Z-numbers, which allows us to consider the uncertainty and reliability of multi-source information in network defence strategy. Then, the hidden probability of MZs is calculated by using the hidden probability model, and the multidimensional Z+−number is proposed, which improves the expressiveness of the model in dealing with information uncertainty. Based on MZs, we define a variety of utility functions and build a multi-attribute group decision framework for network defence around these functions. The MZs provides a novel perspective for analysing and designing response strategies, especially against highly adaptive and covert attacks. The method in this paper is verified by a case of network security assessment of an intelligent logistics company. The results show that this method can significantly improve the accuracy and efficiency of decision making, demonstrating its unique advantages and wide application potential in network defence. This integrated discrete multidimensional Z-number group decision method is not only suitable for intelligent logistics decision making, but also provides an efficient decision support tool for network defence, which helps to improve the intelligence and adaptability of network security defence.