A Note on q-Fractional Neutrosophic Sets and Graphs

Takaaki; Ajoy Kanti; Suman; Sankar Prasad

doi:https://doi.org/10.54216/GJMSA.130204

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.

groups

Arwa Hajjari mail

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

Volume & Issue

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

Volume & Issue

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.

groups

Erina Kovachiskaya mail

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

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2026

A Single-Valued Neutrosophic TOPSIS Model for Supplier Selection under Indeterminate Judgements: A Decision-Support Perspective on Information Fusion

Supplier selection is a recurrent multi-criteria decision-making (MCDM) problem in which expert judgements are rarely crisp: procurement managers routinely hesitate, disagree, and abstain. Classical fuzzy models capture membership and (at most) non-membership, but they cannot separately encode the indeterminacy that pervades real committee evaluations. This paper develops a supplier-selection model built on single-valued neutrosophic sets (SVNSs), where every judgement is represented by an independent triple of truth, indeterminacy and falsity degrees. Group opinions are aggregated by a single-valued neutrosophic weighted averaging operator, providing a transparent information-fusion step, after which an extended TOPSIS procedure ranks the alternatives by their relative closeness to neutrosophic ideal solutions. A worked case with five suppliers and six criteria illustrates the pipeline end to end, and a sensitivity study over the score function and criteria weights confirms that the top-ranked supplier is stable across 200 weight perturbations. Benchmarked against fuzzy-TOPSIS and intuitionistic-fuzzy TOPSIS baselines, the neutrosophic model separates genuinely ambiguous suppliers from clearly dominated ones more reliably, preserving a wider spread of closeness coefficients in the contested middle of the ranking.

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Indu Duhari mail -

Naglaa Fathi mail

link https://doi.org/10.54216/NIF.060105

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Neutrosophic and Information Fusion | 2026

Neutrosophic Information Fusion of Imaging and Clinical Evidence for Multimodal Disease Screening

Modern screening rarely relies on a single source of evidence: a clinician weighs an imaging finding against laboratory markers and patient history, and these sources routinely conflict. We propose a neutrosophic informationfusion framework that represents each evidence channel as a neutrosophic triple (t, i, f )—the degree to which the channel supports disease, the degree to which it is indeterminate (noisy, borderline, missing), and the degree to which it argues against disease. Channels are combined with a conflict-aware neutrosophic fusion rule that routes disagreement into the indeterminacy component instead of silently averaging it away. A decision is issued only when fused indeterminacy falls below a referral threshold; otherwise the case is escalated for expert review. On a synthetic two-modality screening cohort the framework attains 91.8% accuracy while flagging 12% of cases as indeterminate, and it degrades gracefully when one modality is corrupted—losing only 2.3 accuracy points against 6.1 for score-level averaging. A cost-sensitive analysis shows the referral gate lowers expected clinical cost when a missed positive is much more expensive than a review.

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Ali Refaat mail -

Anvor Sulymanov mail

link https://doi.org/10.54216/NIF.060201

Volume & Issue

Vol. Volume 6 / Iss. Issue 2

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Neutrosophic and Information Fusion | 2026

A Neutrosophic Control Chart for Monitoring Processes with Indeterminate Measurements: An Information-Fusion Approach to Statistical Quality Control

Classical Shewhart control charts assume each measurement is a single determinate number. In many real processes— automated gauges reporting tolerance bands, human inspectors giving ranges, or sensors whose readings are only trustworthy within an interval—each observation is better described by a lower and an upper value together with a degree of indeterminacy. We formulate process monitoring in the neutrosophic statistics framework, where a measurement is a neutrosophic number xN = xL+xUIN with indeterminacy interval IN ∈ [IL, IU], and we treat the reconciliation of the determinate and indeterminate parts as an information-fusion step. We derive neutrosophic control limits for the process mean, propose a three-state signalling rule (in-control / watch / out-of-control), and study the average run length (ARL) by simulation. The neutrosophic chart reduces to the Shewhart chart when indeterminacy vanishes, raises the in-control ARL modestly, and under moderate measurement indeterminacy detects a one-sigma mean shift with a smaller out-of-control ARL than a Shewhart chart applied to interval midpoints.

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Maha Ibrahim mail -

Sajid Khan mail

link https://doi.org/10.54216/NIF.060202

Volume & Issue

Vol. Volume 6 / Iss. Issue 2

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Neutrosophic and Information Fusion | 2026

Trust-Aware Cluster-Head Selection in IoT Wireless Sensor Networks via Interval-Neutrosophic Information Fusion

Cluster-based routing extends the lifetime of an Internet-of-Things wireless sensor network (WSN), but the quality of a cluster head (CH) depends on several mutually uncertain factors—residual energy, link quality, centrality and behavioural trust—each measured imperfectly and reported as a range rather than a point. We model each candidate node with an interval-neutrosophic set (INS), so every factor carries an interval of truth, indeterminacy and falsity, and we fuse the factors with an interval-neutrosophic weighted aggregation operator into a single suitability score. Cluster heads are then elected by a possibility-degree ranking of the fused interval scores, subject to a minimum-trust guard. Simulation of a 200-node network shows that interval-neutrosophic CH selection extends first-node-death time by 18–24% over a standard energy-and-distance heuristic and cuts the share of misbehaving nodes elected as heads from 14.7% to 1.3%. The method degrades gracefully as measurement indeterminacy grows and adds only modest per-round overhead.

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Durdona Uktamova mail -

Adnan Manzoor mail

link https://doi.org/10.54216/NIF.060203

Volume & Issue

Vol. Volume 6 / Iss. Issue 2

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Neutrosophic and Information Fusion | 2026

A Neutrosophic Information-Fusion Framework for Renewable-Energy Site Selection under Conflicting Sustainability Criteria

Siting a solar or wind farm forces planners to reconcile criteria that disagree by nature: irradiation or wind resource, land cost, grid proximity, ecological sensitivity and social acceptance. The evidence for each criterion is heterogeneous and uncertain—remote-sensing estimates, cadastral records, and public-consultation sentiment—and experts often cannot commit to a definite rating. This paper proposes a neutrosophic information-fusion framework that encodes each expert rating as a single-valued neutrosophic number, derives objective criterion weights by neutrosophic entropy, fuses the ratings with a single-valued neutrosophic weighted geometric operator (which, unlike the arithmetic operator, penalises a poor score on any single criterion), and ranks candidate sites by a deneutrosophied score. Applied to six candidate sites and seven criteria, the framework selects a site that balances a strong resource against low ecological conflict, and a full sensitivity analysis over the weight scheme and the risk attitude shows the choice is robust. A comparison against fuzzy-AHP and SVN-TOPSIS indicates the neutrosophic geometric model better exposes sites whose ranking rests on contested, high-indeterminacy criteria.

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Abudulkadir Shermatov mail -

Safina Tashabayeva mail

link https://doi.org/10.54216/NIF.060204

Volume & Issue

Vol. Volume 6 / Iss. Issue 2

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Galoitica: Journal of Mathematical Structures and Applications | 2026

On Edge-MetaGraphs

This paper studies graph-based higher-order structures related to metagraphs and edge-labeled hierarchical networks. After reviewing MetaGraphs and Iterated MetaGraphs, we introduce the notion of an Edge-MetaGraph, in which each edge is labeled by a two-ported internal graph, allowing edge-substitution expansion through port gluing. We then define Iterated Edge-MetaGraphs recursively, so that edges may carry nested Edge-MetaGraph structures. Concrete examples from biomedical systems, software pipelines, and logistics are presented to illustrate the expressive power of the proposed framework

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Takaaki Fujita mail -

Ajoy Kanti Das mail -

Suman Das mail -

Sankar Prasad Mondal mail -

Volkan Duran mail

link https://doi.org/10.54216/GJMSA.130203

Volume & Issue

Vol. Volume 13 / Iss. Issue 2

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Galoitica: Journal of Mathematical Structures and Applications | 2026