Neutrosophic Measure-Integral Model for Advanced Cybersecurity Solutions Using Artificial Intelligence and Soft Computing Techniques

Cybersecurity analytics must decide under uncertainty: incomplete fields, delayed enrichment, and conflicting AI detectors are common. This work presents a mathematically rigorous neutrosophic measure-integral framework that retains three facets of evidence throughout modeling and evaluation: support 𝑡, indeterminacy 𝑖, and conflict 𝑓. On a measurable space (Ω, Σ), a neutrosophic measure is a triple 𝜈(𝐴) = (𝑡(𝐴),𝑖(𝐴),𝑓(𝐴)) ∈ ℝ3 which generalizes classical measure to settings with indeterminacy and enables a corresponding neutrosophic integral ∫ 𝑔 d𝜈 for Al and soft computing scores 𝑔[1,2]. The study derives neutrosophic precision and recall together with risk bounds that separate deterministic error from the explicit price of 𝑖 and 𝑓. A case study on enterprise email security (1,000 alerts) provides end-to-end computation: the proposed penalized neutrosophic precision improves from 0.6224 to 0.6952 after a feasible 20% reduction in indeterminacy on predicted positives; the risk upper bound tightens from 0.2369 to 0.2309. The approach plugs naturally into Advanced Cybersecurity Solutions Using Artificial Intelligence and Soft Computing Techniques by mapping neural scores, fuzzy memberships, and ensemble disagreement into ( 𝑡, 𝑖, 𝑓 ) while preserving interpretability and providing provable guarantees.