Fuzzy Entropy-Based Prioritization of Critical Water Quality Parameters for Sustainable Drinking Water Management

Abstract

Safe drinking water remains inaccessible to approximately 2.2 billion people globally, partly because existing assessment frameworks do not adequately capture the uncertainty embedded in water quality data and expert judgment. This study proposes a compounded fuzzy entropy framework that integrates Triangular Fuzzy Number (TFN) representation, alpha-cut interval reduction at a confidence level of 0.8, defuzzification through an optimism index of 0.5, and Shannon entropy-based objective weighting. The framework ranks six drinking water parameters Dissolved Oxygen (DO), Biochemical Oxygen Demand (BOD), pH, Turbidity, Temperature, and total Coliform against four decision criteria: Environmental Impact, Human Health Risk, Variability, and Treatment Complexity. Working through the full numerical chain from expert ratings to weighted composite scores, Coliform emerges as the most critical parameter (S = 0.2153), followed by BOD (0.2056), DO (0.1721), pH and Turbidity (0.1555 each), and Temperature (0.0961). Health Risk carries the heaviest criterion weight (W = 0.3671), a result that follows directly from the entropy calculation: health-related ratings vary more across parameters than any other criterion, producing maximum discriminatory power. The approach avoids the consistency constraints of conventional fuzzy AHP and does not require full pairwise comparison matrices. Sensitivity tests across alpha in [0.6, 1.0] and lambda in [0.3, 0.7] confirm that Coliform and Temperature rankings are structurally stable, while intermediate ranks show modest sensitivity to the optimism index. The results support a tiered monitoring strategy prioritising microbiological surveillance and organic load reduction ahead of physical parameters.