Neutrosophic and Information Fusion

Assessment records in digital mathematics platforms contain a form of uncertainty that is not sufficiently expressed by binary correctness labels. A wrong answer may indicate a stable misconception, a temporary slip, or an unobserved knowledge boundary; similarly, a correct answer may reflect mastery or procedural guessing. This paper proposes a neutrosophic-oriented diagnostic model for higher-education mathematics assessment logs. Each topic and subtopic is represented as a single-valued neutrosophic object whose truth component denotes observed mastery, falsity denotes misconception pressure, and indeterminacy denotes the conflict between local evidence and global answer tendency. A lattice ordering is then defined over these objects to identify misconception boundaries rather than only low-performing concepts. The model is evaluated on the 2024 MathE assessment dataset, which contains 9,546 student-question responses from 372 students answering 833 questions across eight countries. Results show that the proposed indeterminacy-aware calculus separates difficult mathematical regions more clearly than accuracy-only and association-rule baselines. Partial Differentiation, Derivatives, Complex Numbers, and algebraic expressions form the highest falsityindeterminacy region, while level alone has very weak association with answer polarity. The findings support neutrosophic diagnosis as a principled alternative to crisp pass/fail analytics in educational decision-support systems.

Assessing drinking water safety requires integrating evidence from nine independent physicochemical measurements—pH, hardness, total dissolved solids, chloramines, sulfate, conductivity, organic carbon, trihalomethanes, and turbidity—each of which independently provides only weak discriminative power, so that conflicting evidence and high indetermi-nacy are structural features of the problem rather than anomalies. This paper develops a Neutrosophic Dempster-Shafer Evidence Theory (N-DSET) framework in which each measurement is treated as an independent evidence source mod-elled by a Neutrosophic Basic Probability Assignment (NBPA) constructed from class-conditional kernel densities. Evidence is fused through a modified Dempster combination rule that redirects inter-source conflict mass into the neutrosophic indeterminacy component rather than discarding it via normalisation—preserving epistemic information about measurement disagreement throughout the reasoning chain. Source reliability weights are derived from Deng entropy, and the final binary decision uses the pignistic probability transformation. Experiments on the Kaggle Water Quality Dataset (𝑛 = 3,276, Kaggle 2021) yield an AUC of 0.618 under ten-fold cross-validation, exceeding all five supervised baselines including Logistic Regression, Gradient Boosting Trees, and AdaBoost, whose AUC values lie in [0.521, 0.552] on this inherently ambiguous dataset. A sequential waterfall analysis demonstrates monotonically increasing AUC as each evidence source is successively fused, confirming the incremental value of each measure-ment. The belief-plausibility interval [𝐵𝑒𝑙(𝑃), 𝑃𝑙(𝑃)] provides a rigorous geometric characterisation of the three-way decision regions (Positive, Negative, Boundary), and its width—approximately 0.83—quantifies the structural indeter-minacy inherent in the potability classification task. Mathematical properties of the N-DSET operator—commutativity, associativity, convergence of conflict mass under growing evidence sets, and the equivalence of the combined pignistic probability to Bayesian posterior when no conflict is present—are formally established.

Real-time Internet of Things intrusion attribution is often formulated as direct multi-class classification, although packet traces contain incomplete, conflicting, and imbalanced evidence. This paper develops a mathematical neutrosophic signature calculus in which each flow is represented by truth, indeterminacy, and falsity memberships over class-specific attack signatures. The proposed model constructs entropy-contrast behavioral channels, maps each flow to class prototypes through a contradiction-aware single-valued neutrosophic transformation, and derives a closed-form attribution rule by coupling prototype truth, opposite-region falsity pressure, and explicit indeterminacy penalization. The study uses RT-IoT2022, a public UCI benchmark donated in 2024 with 123,117 flows, 83 features, and 12 normal/attack labels. The results show that the proposed calculus provides interpretable class attribution and stable macro-level behavior under severe class imbalance. The work supports neutrosophic signature modeling as a transparent route for IoT security decision support under inconsistent network evidence.

Post-treatment follow-up in differentiated thyroid cancer requires a decision model that is not limited to binary recurrence prediction. Patients may present with partially reassuring anatomical findings, incomplete biochemical response, hetero-geneous pathological subtype, or contradictory clinical history. These situations are better described as a triadic state composed of support for recurrence, support against recurrence, and unresolved indeterminacy. This paper proposes a recurrence shadow mapping model based on single-valued neutrosophic clinical evidence. The model transforms clinico-pathologic descriptors into truth, indeterminacy, and falsity memberships; aggregates evidence through entropy-contrast weighting; and produces a recurrence-shadow index that separates stable, observation, alert, and high-alert follow-up states. The proposed method is designed for healthcare decision support rather than automatic replacement of clinical judgment. Its mathematical contribution is a bounded neutrosophic score that penalizes inconsistent evidence without suppressing clinically meaningful warning signals. Experimental evaluation demonstrates that recurrence-oriented evidence sources can be expressed in a transparent mathematical form, and that indeterminacy itself becomes an interpretable clinical quantity. The findings support the use of neutrosophic information fusion for medical cases where uncertainty is structural rather than merely statistical.