Extending One-Way ANOVA to Neutrosophic Sets: A Method for
Uncertainty-Based Decision Making
Sasiwimon Iwsakul1,∗, Ronnason Chinram1
1Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla
90110, Thailand
Emails: sasiwimon.i@psu.ac.th; ronnason.c@psu.ac.th
Abstract
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 indetermi-
nacy, 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 differ-
ences, 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.
Keywords: Neutrosophic sets; One-way analysis of variance; Group means; Decision-making