On the Analysis of Variance for Symmetrical Triangular and Normal Fuzzy Observations in a Randomized Complete Block Design
DOI:
https://doi.org/10.62933/1ydbft70Keywords:
ANOVA, Fuzzy set, Symetrical, Triangular, NormalAbstract
Fuzzy ANOVA has been successfully applied in one-way experimental designs, where fuzzy observations are modelled using symmetrical triangular fuzzy numbers (STFNs) and normal fuzzy numbers (NFNs). These approaches have proven helpful in various fields, such as environmental sciences, agriculture, and engineering, where data uncertainty is pervasive. However, previous work has focused mainly on Completely Randomized Designs (CRD), which assume homogeneity among experimental units. This assumption often oversimplifies real-world conditions where variability among experimental units cannot be ignored. Thus, this study proposed fuzzy Analysis of Variance (ANOVA) within a Randomised Complete Block Design (RCBD) framework using Symmetric Triangular Fuzzy Numbers (STFNs) and Normal Fuzzy Numbers (NFNs) to address measurement imprecision commonly encountered in experimental data. The methodology preserves the structural integrity of classical ANOVA while incorporating fuzziness to enhance data interpretation in the presence of uncertainty. Simulated datasets were analyzed to evaluate the performance of the proposed fuzzy ANOVA, and both treatment and block effects were found to be statistically significant, demonstrating the method’s effectiveness in detecting variability and treatment differences. STFNs provided a simple approach for modeling symmetric uncertainty, whereas NFNs offered smoother, more continuous representations, including visual tools such as triangular and Gaussian membership function plots, which further improved result interpretation and accessibility. The findings affirm that fuzzy ANOVA is a robust and interpretable extension of classical ANOVA, suitable for various areas where uncertain data is prevalent.
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Copyright (c) 2026 Muhammed Mujitaba Muhammed, Yahaya Zakari, Sani Ibrahim Doguwa, Ibrahim Abubakar Sadiq, Naziru Isah Muhammed, Jamilu Garba (Author)
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