Optimizing Fuzzy Membership Functions for Tuberculosis Diagnosis: A Comparative Study of Gaussian and Triangular Functions with PSO

In fuzzy logic‑based diagnostic systems, the shape of membership functions (MFs) significantly influences model performance. This study investigates the impact of Gaussian versus triangular MFs on tuberculosis (TB) diagnosis within a neuro‑fuzzy framework optimized by particle swarm optimization (PSO). Using a dataset of 1200 subjects (850 TB cases, 350 controls) from the Centers for Disease Control and Prevention, we compared two model variants: one with Gaussian MFs and one with triangular MFs, both optimized concurrently with neural network weights via PSO. A baseline neuro‑fuzzy model (without PSO) served as a reference. The Gaussian‑based PSO‑optimized model achieved 86% sensitivity, 79% specificity, and 85% accuracy, outperforming the triangular‑based variant (79% sensitivity, 72% specificity, 77% accuracy). Convergence analysis showed that the Gaussian model reached stable optimum within 100 iterations, whereas the triangular model required 150 iterations. Sensitivity analysis of PSO parameters revealed that a linearly decreasing inertia weight (0.9→0.4) and balanced acceleration coefficients (c₁ = c₂ = 2.0) yielded best results for both MF types. The Gaussian MFs produced smoother decision boundaries and better handled overlapping clinical categories, as reflected in higher performance. This study provides empirical evidence that Gaussian membership functions, when optimized concurrently with network weights using PSO, lead to superior diagnostic accuracy, and offers practical guidance for designing high‑performance neuro‑fuzzy medical diagnosis systems.