Volume 27 • Issue 1 • PP: 246-259 • 2026
Extending One-Way ANOVA to Neutrosophic Sets: A Method for Uncertainty-Based Decision Making
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Classical statistical methods assume that data are precise and free from uncertainty, which may not hold in many real-world applications. Neutrosophic statistics provides a flexible framework for handling indeterminacy, vagueness, and inconsistency in data. In this paper, we propose a new formulation of one-way analysis of variance (ANOVA) within the neutrosophic framework. The method treats membership, indeterminacy, and non-membership components separately, with explicit F -tests for each, and employs a maximum-based decision rule to determine significance. We also compare the proposed method with the classical one-way ANOVA. The results demonstrate that the neutrosophic ANOVA is more sensitive in detecting group differences, particularly in cases where the classical approach yields smaller F -values and may fail to reject the null hypothesis. These findings highlight the potential of neutrosophic ANOVA as a more robust alternative to classical ANOVA for analyzing data with inherent uncertainty and indeterminacy.
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