An Explainable Fuzzy Clustering Framework for Modeling Learning Trajectories in Outcome-Based Education

Although various studies have applied clustering and categorization techniques in educational assessment, most rely on deterministic thresholds or heuristic-based partitions that fail to uncover latent conceptual structures. Existing fuzzy clustering applications in education also seldom incorporate rigorous validity-index-driven model selection or explainability-focused interpretation, leaving a gap in modeling the gradual and overlapping nature of learning progression. Outcome-Based Education (OBE) emphasizes measurable learning outcomes as the cornerstone of curriculum design and assessment. However, traditional methods for classifying student performance—typically based on fixed score thresholds—fail to reflect the inherent complexity of conceptual learning. This study proposes an Explainable Fuzzy Clustering Framework to model student learning trajectories in an OBE environment. Using final scores derived from multiple Course Learning Outcomes (CLOs), the Fuzzy C-Means (FCM) algorithm is applied to cluster students into conceptual performance levels with soft membership assignments. The optimal number of clusters is determined using the Tang–Sun–Sun (TSS) and Xie–Beni (XB) validity indices. The resulting fuzzy clusters are then compared with three conventional manual classification schemes—fixed thresholding, quantile partitioning, and mean–standard deviation banding—using cross-tabulation, heatmaps, and quantitative agreement metrics such as Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI). Visualization techniques including stacked membership plots and cluster-size bar charts are employed to enhance interpretability. Results show that fuzzy clustering moderately aligns with manual schemes while revealing latent transitions and overlapping boundaries that rigid methods overlook. Quantitatively, the fuzzy clusters formed a natural distribution of 17.9% Low, 36.9% Moderate, and 45.2% High performers, with agreement scores of ARI = 0.405–0.462 and NMI = 0.550–0.629. These findings confirm the robustness and interpretability of the proposed model. The framework provides a principled, explainable, and adaptive approach to formative assessment, contributing to the advancement of interpretable learning analytics in higher education.