Neutrosophic and Information Fusion

Estimating whether ambient air quality exceeds regulatory thresholds requires combining evidence from multiple co-measured pollutants whose concentrations are simultaneously uncertain, interdependent, and subject to instrument noise. This paper introduces a Neutrosophic Cubic Correlation Fusion (NC-CF) model that represents each pollutant observation as a neutrosophic cubic value—a structure that simultaneously encodes an interval-valued membership [𝑇𝐿 , 𝑇𝑈] capturing measurement uncertainty and a crisp neutrosophic triple (𝑡, 𝑖, 𝑓 ) capturing the nominal risk assessment—and then quantifies closeness to ideal pollution profiles through a novel neutrosophic cubic correlation coefficient (NCC). Feature weights are derived from Jensen–Shannon (JS) divergence between class-conditional NCC distributions, providing an information-theoretically justified allocation of influence across pollutants without requiring labelled calibration. Experiments on a balanced 1500-instance subset of the Global Air Quality Dataset (Kaggle, 2023), comprising PM2.5, CO, Ozone, and NO2 measurements from world cities, demonstrate classification accuracy of 99.0% and AUC of 0.9996 under ten-fold cross-validation, matching or exceeding Logistic Regression, Decision Tree, Random Forest, and Gradient Boosting Trees. A systematic sensitivity analysis over the interval-to-crisp interpolation parameter 𝜆 ∈ [0, 1] reveals stable performance across the full range, confirming that the NCC’s interval component does not introduce instability. The mathematical properties of the neutrosophic cubic correlation coefficient—its reduction to standard cosine similarity for crisp inputs, its behaviour under ideal profile extremes, and the convergence of JS weights under increasing class separability—are formally established.

Healthcare-utilization prediction from survey data is mathematically difficult because the observable variables are categorical, self-reported, and partially discordant. A respondent may report poor physical health but no sleep disruption, or regular sleep-medication use with favorable mental-health ratings. Such cases are not well represented by classifiers that collapse all evidence into a single likelihood vector. This paper proposes a rough neutrosophic evidence-lattice model for stratifying older adults according to the number of doctors visited in a year. The model maps categorical sleep and wellness indicators into single-valued neutrosophic triples, estimates entropy-based evidence weights, introduces a rough boundary term from local equivalence classes, and ranks each respondent using an indeterminacy-penalized decision functional. The method is evaluated using the 2023 UCI National Poll on Healthy Aging schema and a reproducible computational implementation. The results show that the proposed lattice-based formulation improves macro-F1 over conventional categorical baselines while preserving interpretable truth, falsity, and indeterminacy degrees for each utilization class.

Accurate stratification of diabetes risk requires integrating clinically heterogeneous indicators under conditions of measurement ambiguity, borderline readings, and inconsistent self-reported data. This paper introduces a Neutrosophic Cosinesimilarity with CRITIC-weighted ideal-profile matching (NCRS-CRITIC) framework that maps each patient record to an ideal disease profile and an ideal healthy profile simultaneously, using neutrosophic truth, indeterminacy, and falsity membership functions. The degree of closeness to each profile is measured through a weighted neutrosophic cosine similarity, where feature weights are derived via the CRITIC (CRIteria Importance Through Intercriteria Correlation) method— capturing both the discriminative variability and the inter-feature correlation structure objectively. A relative closeness coefficient (RC) aggregates dual-profile similarity into a scalar risk score that respects both the evidence for and against disease simultaneously. Experiments on a balanced 2000-instance subset of the CDC Behavioral Risk Factor Surveillance System (BRFSS) 2021 Diabetes Health Indicators Dataset achieve an area under the ROC curve (AUC) of 0.869 and accuracy of 79.5% under ten-fold cross-validation, competitive with fully supervised classifiers including Gradient Boosting Trees, Logistic Regression, and Gaussian Naive Bayes. The framework’s mathematical properties—symmetry of the cosine measure, triangle inequality satisfaction, and weight convergence under vanishing intra-feature variance—are formally proved. A comprehensive discussion examines the clinical implications of the dual-profile architecture, the role of CRITIC weighting in capturing correlated health indicators, and directions for extending the framework to interval neutrosophic representations and ensemble neutrosophic fusion.

Multi-source decision systems require a representation in which supportive evidence, contradictory evidence, and weak evidence are not collapsed into the same numerical channel. This paper develops a dynamic reliability-kernel model for single-valued neutrosophic evidence fusion. Given a matrix of source signals, each source is transformed into a single-valued neutrosophic triplet whose truth, indeterminacy, and falsity memberships are governed by signed evidence strength. A time-varying reliability kernel then assigns larger mass to sources with lower recent instability, and a dispersion-augmented fusion operator produces a global neutrosophic state. The final decision rule is formulated as a penalized neutrosophic score and as a regularized probabilistic classifier over the fused triplet. The model is evaluated on a public weekly stock dataset containing six technology-market sources. The results show that the proposed representation achieves competitive chronological classification performance while providing explicit mathematical control over indeterminacy, disagreement, and reliability. Ablation and penalty-sensitivity analyses demonstrate that indeterminacy is a functional component of the decision model rather than a cosmetic label. The paper offers a reproducible mathematical framework for neutrosophic information fusion in uncertain intelligent decision-support systems.

Reliable early detection of cardiovascular disease requires integrating multiple clinical indicators under conditions of uncertainty, partial measurement, and inconsistent expert knowledge. This paper introduces a Single-Valued Neutrosophic Weighted Aggregation (SVNS-WA) framework that systematically models three independent dimensions of clinical information—truth-membership (T ), indeterminacy-membership (I), and falsity membership (F)—to produce an interpretable composite risk score for binary heart disease classification. Feature weights are derived from an entropy measure defined over neutrosophic components, ensuring that more discriminative attributes receive proportionally greater influence during aggregation. A score function S(x) = (2 + Tagg − Iagg −Fagg)/3 maps each aggregated neutro-sophic value to the unit interval, and an optimal decision threshold is identified via Youden’s J statistic. Experiments on the publicly available UCI Cleveland Heart Disease Dataset (n = 303) yield an area under the ROC curve (AUC) of 0.765 and a sensitivity of 83.45%, demonstrating the framework’s ability to capture indeterminate, disease-relevant information without supervised parameter optimisation. A detailed mathematical analysis establishes the convergence and monotonicity properties of the proposed aggregation operator, and a comparative study against Logistic Regres-sion, Decision Tree, Random Forest, and SVM classifiers contextualises the trade-off between predictive accuracy and interpretable uncertainty quantification. The discussion section examines implications for clinical decision support and identifies directions for extending the framework with interval neutrosophic operators and deep-feature integration.