Neutrosophic and Fuzzy Statistical Methods
Summary
Neutrosophic and fuzzy statistical methods extend classical probability by accommodating vagueness, indeterminacy and partial truth. Fuzzy statistics introduces membership functions to represent degrees of belonging, enabling the modelling of imprecise observations in areas such as risk assessment and quality control. Neutrosophic statistics further generalises this by assigning to each element three independent degrees—truth, indeterminacy and falsity—thus capturing incomplete, conflicting or ambiguous information. Together these frameworks underpin advanced hypothesis tests, regression models and estimators that yield interval-valued or set-valued results rather than single-point estimates. Practical applications range from geotechnical engineering, where joint roughness coefficients are expressed as neutrosophic intervals to retain geological uncertainty, to biomedical diagnostics, where fuzzy classifiers and neutrosophic decision tables improve robustness in the presence of unclear or missing data. By integrating these approaches, researchers can quantify and propagate uncertainty through statistical analyses, enhancing decision-making in complex real-world contexts.
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Neutrosophic and Fuzzy Statistical Methods publication trend
The graph below shows the total number of articles in neutrosophic and fuzzy statistical methods across all publications each year (not limited to Nature Index journals).
Technical terms
Fuzzy set: A collection characterised by a membership function assigning each element a degree between zero and one, reflecting partial belonging.
Membership function: A mapping that quantifies the degree to which an element belongs to a fuzzy set.
Neutrosophic logic: A logical framework in which each proposition is associated with independent truth, indeterminacy and falsity values.
Neutrosophic number: An interval-valued quantity defined by lower and upper bounds subject to a degree of indeterminacy.
Indeterminacy: The component of neutrosophic logic representing uncertainty or lack of information about a proposition.
References
- Cochran’s Q test for analyzing categorical data under uncertainty. Journal of Big Data (2023).
- Incorporating the neutrosophic framework into kernel regression for predictive mean estimation. Heliyon (2024).
- Expressions of Rock Joint Roughness Coefficient Using Neutrosophic Interval Statistical Numbers. Symmetry (2017).
- Neutrosophic ratio-type estimators for estimating the population mean. Complex & Intelligent Systems (2021).
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