Order-preserving structural mapping for message prioritization in intuitionistic fuzzy soft sets

In modern cybersecurity settings, prioritizing massive streams of incoming network traffic is challenging due to uncertainty and inherent hierarchical dependencies among features and threat indicators. Although intuitionistic fuzzy soft sets (IFSS) offer a powerful framework for handling uncertainty, existing approaches lack effective mechanisms for comparing structured domains while preserving order relations, which may lead to reduced consistency and interpretability of prioritization outcomes. To address this gap, this work presents an order-preserving structural frame work for message prioritization in the IFSS paradigm. The study incorporates three key components: (i) a similarity mapping mechanism for comparing ordered IFSS structures with same-level and compatible-level structural comparisons, (ii) the notion of order-isomorphism to capture structural equivalence between domains, and (iii) a topological sorting–based approach to identify the optimal feature–threat correspondences while maintaining hierarchical dependencies. An integrated prioritization pipeline is designed and experimentally validated on the NSL-KDD dataset. Experimental results demonstrate that the proposed approach achieves competitive and balanced performance, attaining the highest test accuracy (0.8365) and F1-score (0.8383), along with improved recall (0.7444), which is important for reducing undetected attacks. The main empirical advantage is reflected in the improved detection of attack instances and the reduced number of false negatives, while statistical significance testing, sensitivity analysis, and perturbation analysis further support the robustness and reliability of the proposed prioritization mechanism. These findings highlight that the integration of order-preserving similarity, structural equivalence, and topological reasoning within IFSS leads to more reliable, consistent, and interpretable prioritization, thereby supporting its relevance in practical applications and decision-making scenarios.