A comparison of membership function shapes in a fuzzy-based fugacity model for disinfection byproducts in indoor swimming pools

Aleatory and epistemic uncertainty in human health risk assessment is virtually unavoidable. While probabilistic methods may adequately address exposure and risk model parameters with variability (body weight, exposure duration, exposure frequency), other methods are more helpful for handling uncertainty that arises from an incomplete understanding of the processes being modeled (mass transport). Due to the potential for cancer and other health risks, it is essential to understand of the concentrations of disinfection byproducts in swimming pool facilities and the related exposures. This study builds on previous probabilistic and fuzzy based fugacity models which estimate exposure to disinfection byproducts in swimming pools (Dyck, Water Res 45:5084–5098, 2011; Annual meeting of the North American Fuzzy Information Processing Society (NAFIPS), 2012). Those models estimated environmental concentrations based on mass transfer processes for which there are many possible formulas. The influence of membership function shape on the final estimated concentration required further investigation. In this study, three different trapezoidal membership functions are derived for the gas-side mass transfer coefficient k G . One triangular and one trapezoidal membership function are derived for the liquid-side mass transfer coefficient, k L . According to graphical output and percent difference between the actual concentration and the defuzzified output of the fuzzy based model, the best combination of shapes to use is the trapezoidal k G membership function which uses seven calculated values (to define the shape of the trapezoid) with either the triangular or trapezoidal k L membership function. Further study is recommended to combine the fuzzy based methods for poorly understood model processes with probabilistic methods for model parameters with aleatory uncertainty.