Truth–Indeterminacy–Falsity Fusion in Neutrosophic Intelligent
Systems: A Mathematical Review, Algorithmic Taxonomy, and Research
Agenda
Murat Ozcek1,*, Arash Salehpour2
1Gaziantep University, Department of Mathematics, Gaziantep, Turkey
2Department Cybersecurity, University, Istanbul, T¨urkiye
Emails: muratozcek.12@gmail.com; arashsalehpour@halic.edu.tr
Abstract
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, neutro-sophic 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.
Keywords: Neutrosophic set; Single-valued neutrosophic set; Information fusion; Indeterminacy; Contradiction; Aggregation
operator; Decision support; Mathematical review