A New Fuzzy Preference Relation (FPR) Approach to Prioritizing Drinking Water Hazards: Ranking, Mapping, and Operational Guidance

Abstract

This paper presents a practical and auditable methodology for prioritizing drinking water hazards based on fuzzy preference relations (FPR). The method is based on additive pairwise comparisons of tap water quality parameters, which are aggregated (median) into a complete preference matrix. For each parameter, a Fuzzy Priority Index (FPI) was determined as the average “advantage” over the others. The FPI values were mapped to five fuzzy priority levels (very low–very high) using triangular/trapezoidal membership functions, followed by a defuzzification process using the centroid of singletons (COGS) method. The final step is to map the categories to operational actions, ensuring a clear transition from assessment to decision (from routine monitoring to immediate intervention). The method was demonstrated on nine parameters that are relevant for regulatory (WHO/DWD) and operational purposes: As, Pb, THM, NO3, Hg, Cr, Mn, Cu, Fe. Thirty-six pairwise assessments were determined, which, after aggregation, formed fuzzy relations. The resulting ranking (FPI) is: As (0.76) > Pb (0.70) > THM (0.64) > NO3 (0.56) > Hg (0.50) > Cr (0.43) > Mn (0.36) > Cu (0.30) > Fe (0.25). Fuzzy categorization assigned As, Pb, THM to the High level, NO3, Hg, Cr to Medium, and Mn, Cu, Fe to Low, with the Score reflecting the “proximity” of higher levels. The approach is transparent, replicable, and supports sensitivity analysis. The combination of FPI with fuzzy categorization and a decision map transforms expert knowledge and uncertainty into prioritized, actionable steps for water safety management.

This paper presents a practical and auditable methodology for prioritizing drinking water hazards based on fuzzy preference relations (FPR). The method is based on additive pairwise comparisons of tap water quality parameters, which are aggregated (median) into a complete preference matrix. For each parameter, a Fuzzy Priority Index (FPI) was determined as the average “advantage” over the others. The FPI values were mapped to five fuzzy priority levels (very low–very high) using triangular/trapezoidal membership functions, followed by a defuzzification process using the centroid of singletons (COGS) method. The final step is to map the categories to operational actions, ensuring a clear transition from assessment to decision (from routine monitoring to immediate intervention). The method was demonstrated on nine parameters that are relevant for regulatory (WHO/DWD) and operational purposes: As, Pb, THM, NO3, Hg, Cr, Mn, Cu, Fe. Thirty-six pairwise assessments were determined, which, after aggregation, formed fuzzy relations. The resulting ranking (FPI) is: As (0.76) > Pb (0.70) > THM (0.64) > NO3 (0.56) > Hg (0.50) > Cr (0.43) > Mn (0.36) > Cu (0.30) > Fe (0.25). Fuzzy categorization assigned As, Pb, THM to the High level, NO3, Hg, Cr to Medium, and Mn, Cu, Fe to Low, with the Score reflecting the “proximity” of higher levels. The approach is transparent, replicable, and supports sensitivity analysis. The combination of FPI with fuzzy categorization and a decision map transforms expert knowledge and uncertainty into prioritized, actionable steps for water safety management.