Selection of Suitable Aggregation Function for Estimation of Aggregate Pollution Index for River Ganges in India

Abstract

The present study aims to select the most appropriate aggregation function for estimation of the Ganga River pollution index (GRPI). Following the Delphi technique based on expert opinion, 16 water pollutant variables are selected; the weights of each pollutant variable based on their relative significance are determined, and the average subindex curves for each variable are drawn. Using the weights, average parameter’s value and the corresponding subindex value, 18 different aggregation functions are tested and analyzed. Literature reveals that most aggregation methods suffer from ambiguity and eclipsing problems due to faulty selection of aggregation function. From the results of the present analysis, 12 aggregation functions are screened out on the basis of ambiguity and eclipsing, constant functional behavior, and nonaccountability of weights in functions criteria. Finally, the remaining 6 aggregation functions are subjected to sensitivity analysis. From the results of sensitivity analysis, it is concluded that the weighted arithmetic mean function, being a true linear, least ambiguous and eclipsing free function, is the most representative aggregation function for estimation of GRPI for River Ganges.