Dual-Indeterminacy Neutrosophic Fusion for Calibrated and Selective Multi-Source Classification under Source Conflict

Erina Kovachiskaya

doi:https://doi.org/10.54216/NIF.060104

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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Vol. Volume 5 / Iss. Issue 1

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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

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2026

Indeterminacy-Balanced Evidence Granulation for Ecotoxicological Prioritization under Single-Valued Neutrosophic Assessments

Decision environments that combine laboratory indicators, expert warnings, chemical descriptors, and regulatory traces rarely produce a single consistent description of risk. Classical aggregation rules usually collapse incomplete, contradictory, and partially reliable evidence into one scalar before the contradiction itself has been modelled. This paper develops an indeterminacy-balanced neutrosophic granulation method for prioritization problems in which truth, falsity, and hesitation must remain simultaneously visible during fusion. Each alternative is represented by a single-valued neutrosophic profile, criterion weights are obtained from a contrast-sensitive entropy functional, and the final ranking is produced by an indeterminacy-penalized evidence score. The mathematical contribution is a bounded fusion operator that separates positive support, negative pressure, and contradiction-induced hesitation. A numerical study reports detailed intermediate matrices, criterion weights, fused memberships, ranking stability, sensitivity to the indeterminacy penalty, ablation results, and computational complexity. The findings show that retaining indeterminacy during fusion changes the ordering of borderline alternatives and makes the decision trace easier to audit than scalar aggregation alone.

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Arwa Hajjari mail

link https://doi.org/10.54216/NIF.060102

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Vol. Volume 6 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2026

Neutrosophic Information Fusion: Foundations, Frameworks, Algorithms, and Research Frontiers

Neutrosophic set theory, which explicitly models truth (T ), indeterminacy (I), and falsity (F) as independent membership components, has emerged as one of the most active mathematical frameworks for uncertain information fusion over the 2020–2025 period. This comprehensive survey reviews, synthesises, and critically analyses more than 200 research contributions spanning single-valued neutrosophic sets (SVNS), interval neutrosophic sets (INS), neutrosophic cubic sets (NCS), neutrosophic Z-numbers, linguistic neutrosophic sets, and their integration with Dempster-Shafer evidence theory. We organise the literature across four interlocking axes— mathematical foundations, aggregation operators, information measures, and decision-support methods—and map these onto seven application domains including medical diagnosis, supply chain management, environmental assessment, and engineering fault diagnosis. Three representative algorithms are formally presented with pseudocode, complexity analysis, and mathematical justifications: (i) the SVNWA entropy weighted aggregation framework, (ii) the Neutrosophic Dempster-Shafer Evidence Theory (N-DSET) fusion pipeline with conflict r edistribution, a nd (iii) the Neutrosophic TOPSIS multi-criteria d ecision-making a lgorithm. A comparative performance analysis shows that neutrosophic methods achieve mean AUC improvements of +4.2% to +7.1% over intuitionistic fuzzy set baselines across reported experimental studies. Six precisely formulated open problems are identified, and a five-horizon research roadmap from 2025 to 2030 is proposed, covering mathematical completeness, computational scalability, hybrid deep-learning architectures, domain expansion to quantum and large language model settings, and the long-term vision of a unified neutrosophic information quality standard.

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Agnes Osagie mail -

Mohammad Abobala mail

link https://doi.org/10.54216/NIF.060103

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Vol. Volume 6 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2026

Dual-Indeterminacy Neutrosophic Fusion for Calibrated and Selective Multi-Source Classification under Source Conflict

Reliable multi-source AI requires a distinction between two non-equivalent failure modes: within-source ambiguity and between-source contradiction. This paper formulates dual-indeterminacy neutrosophic fusion (DINF), in which calibrated posteriors ps ∈ ΔK−1 are transformed into class-wise triples Nk = ⟨Tk, Ik,Fk⟩. Source weights combine chance-corrected validation reliability, normalized entropy, and a robust Jensen–Shannon consensus discount. Intrinsic ambiguity U and class-specific contradiction Ck are retained separately and joined by Ik =U +Ck −UCk. The decision distribution qk ∝ Tk exp(−λIk) therefore penalizes conflict without collapsing neutrosophic evidence into a probability simplex. Boundedness, permutation invariance, consensus preservation, conflict monotonicity, log-odds sensitivity, and missing-source neutrality are established. Repeated experiments on three public benchmarks examine clean data, 30% source dropout, 30% confident contradiction, and 40% mixed failure. Under contradiction, DINF achieves macro-F1 0.910, NLL 0.445, and selective accuracy 0.939 at approximately 90% coverage; the corresponding logarithmic-pool values are 0.896, 0.469, and 0.929. The results identify robust agreement discounting and explicit contradiction-sensitive indeterminacy as complementary mechanisms for calibrated failure-aware fusion.

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Erina Kovachiskaya mail

link https://doi.org/10.54216/NIF.060104

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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