Enhancing Network Security Solutions Techniques with Redefined Normal Bipolar Complex Fuzzy Soft Set Using a Multi-Criteria Group Decision-Making Methodology

Abstract

Effective network security requires the integration of carefully designed protective mechanisms with continuous monitoring to safeguard computer networks against evolving cyber threats. Five essential security strategies are considered to strengthen network resilience against conventional and emerging vulnerabilities, providing a systematic foundation for addressing contemporary cybersecurity challenges. Within this context, the present research introduces novel theoretical constructs and methodological perspectives intended to improve the representation and interpretation of complex, uncertain, and ambiguous information encountered in practical decision-making environments. Specifically, the study develops a reformulated framework of normal bipolar complex fuzzy soft sets by integrating the mathematical foundations of bipolar complex fuzzy sets and soft sets into a unified structure. The principal objective is to establish the operational foundations of aggregation mechanisms and examine the proposed framework through weighted averaging and geometric aggregation operators, together with their associated mathematical properties. Building upon these formulations, an innovative multi-criteria group decision-making approach is developed to evaluate alternative solutions for mitigating network security threats using the proposed aggregation operators. The mathematical consistency of these operators is investigated through fundamental algebraic properties, including boundedness, commutativity, idempotency, and monotonicity. Furthermore, a structured decision-making algorithm is formulated to enhance computational accessibility, practical applicability, and procedural simplicity relative to existing approaches. The effectiveness, robustness, and reliability of the proposed theoretical framework are subsequently assessed through sensitivity analysis, validity testing, and comparative evaluation. To demonstrate its operational relevance, the study incorporates a systematic decision-making procedure supported by practical examples illustrating the applicability and utility of the proposed sets in real-world decision environments. Finally, a comparative examination of the newly developed formulations and established theoretical approaches is undertaken to clarify their distinguishing characteristics and demonstrate the contributions of the proposed framework.