Fuzzy Synthetic Evaluation of Water Quality with Membership Functions Constructed by Linear Interpolation

Abstract

By analyzing traditional membership functions for fuzzy synthetic evaluation of water quality, some problems emerged: difficulties in determining parameters in traditional membership functions and insufficient samples for constructing proper membership functions. To solve these problems, more information was obtained by analyzing the shapes of traditional membership functions and the physical meaning of boundaries in water quality standard, and linear interpolation algorithm was applied to expand the sample size when considering the similar application for artificial neural network (ANN) evaluation of water quality. Finally, membership functions were constructed and a new method for evaluation water quality based on fuzzy synthetic evaluation was proposed. Comparisons between different evaluation methods show that the proposed method, grey relation analysis (GRA), and ANN are similar to each other, especially between GRA and the proposed method. These relations would be ascribed to fundamental assumptions of each method. For these similarities, the proposed method seems appropriate for evaluating water quality. The method may also provide some hints for other synthetic evaluation with similar problems concerning boundaries or inadequate sample size.