Volume 6 , Issue 1 , PP: 21–33, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Agnes Osagie 1 * , Mohammad Abobala 2
Doi: https://doi.org/10.54216/NIF.060103
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.
Neutrosophic sets , Information fusion , Aggregation operators , Dempster-Shafer theory , MCDM , Uncertainty quantification , Survey , Research directions
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