Fuzzy approach to analyzing a three-factor experiment with binary levels - Thakur, Rahul; Malik, S.C.; Raj, Masum (Decision Making and Analysis, 2026)
A factorial experiment is a widely used statistical analysis technique in experimental studies in agricultural and engineering sciences. The classical factorial experiment design considers several factors at different crisp levels, which are quantitatively measurable. However, factor levels are often imprecise, vague, incomplete, or described linguistically. In such cases, fuzzy statistics are used instead of classical statistics when analyzing data with uncertain observations. In this paper, we propose an extension of the classical factorial design for analyzing experiments with fuzzy observations. The experimental data are represented using triangular fuzzy numbers and transformed using the α-cut interval approach, resulting in lower-level and upper-level factorial models. These models are analyzed separately to evaluate the effects of factors and their interactions under uncertainty. The results are also compared with classical ANOVA applied to defuzzified data to highlight the advantages of incorporating uncertainty through fuzzy representations. Furthermore, the robustness of the proposed approach is examined through sensitivity analysis across different α levels. The findings demonstrate that the proposed fuzzy factorial approach provides a more flexible framework for analyzing experimental data in the presence of imprecision and uncertainty.