Truth–Indeterminacy–Falsity Fusion in Neutrosophic Intelligent Systems: A Mathematical Review, Algorithmic Taxonomy, and Research Agenda

Murat; Arash

doi:https://doi.org/10.54216/NIF.060101

Neutrosophic and Information Fusion | 2025

A Single-Valued Neutrosophic Weighted Aggregation Framework for Multi-Attribute Heart Disease Risk Assessment: An Information Fusion Perspective

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.

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Jeong Chan Park mail -

Sajid Khan mail

link https://doi.org/10.54216/NIF.050101

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Vol. Volume 5 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2025

Dynamic Reliability Kernels for Single-Valued Neutrosophic Evidence Fusion: A Mathematical Model for Multi-Source Market-State Classification

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.

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Samandarboy Sulaymanov mail -

Maha Ibrahim mail

link https://doi.org/10.54216/NIF.050102

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Vol. Volume 5 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2025

Neutrosophic Cosine Similarity Fusion with CRITIC-Weighted Ideal Profile Matching for Multi-Attribute Diabetes Risk Stratification: Evidence from the CDC BRFSS 2021 Dataset

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.

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Dae Yu Kim mail -

Jeong Chan Park mail

link https://doi.org/10.54216/NIF.050103

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Neutrosophic and Information Fusion | 2025

Rough-Neutrosophic Evidence Lattices for Healthcare-Utilization Stratification: Fusing Sleep and Wellness Indicators in the 2023 NPHA Dataset

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.

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Sajid Khan mail -

Arash Salehpour mail

link https://doi.org/10.54216/NIF.050104

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Neutrosophic and Information Fusion | 2025

Neutrosophic Cubic Correlation Fusion with Jensen–Shannon Divergence Weighting for Multi-Pollutant Urban Air Quality Index Estimation

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.

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Anvar Suleymanov mail -

Murod Khidoyatov mail

link https://doi.org/10.54216/NIF.050105

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Vol. Volume 5 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2025

Recurrence Shadow Mapping under Neutrosophic Clinical Evidence: An Uncertainty-Oriented Model for Post-Treatment Healthcare Decision Support

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.

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Murodbek Ahrorov mail -

Ahmed Aziz mail

link https://doi.org/10.54216/NIF.050201

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Vol. Volume 5 / Iss. Issue 2

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Neutrosophic and Information Fusion | 2025

From Packet Traces to Contradiction Scores: A Neutrosophic Signature Calculus for Real-Time IoT Intrusion Attribution

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.

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Rozina Ali mail

link https://doi.org/10.54216/NIF.050202

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Vol. Volume 5 / Iss. Issue 2

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Neutrosophic and Information Fusion | 2025

A Neutrosophic Dempster-Shafer Evidence Fusion Framework with Conflict-Redistribution and Pignistic Decision for Multi-Source Water Potability Classification

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.

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Abd-Alrida Basheer mail

link https://doi.org/10.54216/NIF.050203

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Vol. Volume 5 / Iss. Issue 2

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Neutrosophic and Information Fusion | 2025

Indeterminacy Lattices for Diagnosing Mathematical Misconception Boundaries in Higher-Education Assessment Logs

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.

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Agnes Osagie mail

link https://doi.org/10.54216/NIF.050204

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Vol. Volume 5 / Iss. Issue 2

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Neutrosophic and Information Fusion | 2026

Truth–Indeterminacy–Falsity Fusion in Neutrosophic Intelligent Systems: A Mathematical Review, Algorithmic Taxonomy, and Research Agenda

Neutrosophic information fusion has become a rigorous computational approach for modeling evidence that is simultaneously supportive, opposing, and unresolved. This review synthesizes recent studies published from 2020 to 2025 and organizes the field around the operational semantics of truth, indeterminacy, and falsity. Rather than presenting neutrosophic sets only as an extension of fuzzy sets, the paper analyzes neutrosophic fusion as a mathematical problem of evidence representation, operator design, source weighting, contradiction control, and decision reduction. The review covers single-valued neutrosophic similarity measures, EDAS and TOPSIS extensions, neutrosophic Z-number aggregation, Einstein and Aczel–Alsina operators, trigonometric credibility operators, dynamic aggregation, divergence measures, uncertainty-aware multi-source information fusion, and evidence theoretic comparisons. A relatedwork section of more than twenty verified 2020–2025 studies is added, followed by a selection protocol, formal definitions, propositions, algorithms, operator-property analysis, and research directions. The paper concludes with a research agenda for benchmark construction, data-driven membership learn-ing, explainable indeterminacy, scalable dynamic fusion, and trustworthy integration of neutrosophic logic with intelligent decision-support systems.

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Murat Ozcek mail -

Arash Salehpour mail

link https://doi.org/10.54216/NIF.060101

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Vol. Volume 6 / Iss. Issue 1

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