Water quality evaluation of Haihe River with fuzzy similarity measure methods

Fuzzy similarity measures, which are used to judge the closeness of two fuzzy sets, are presented to evaluate the water quality of the Haihe River. Based on the membership functions and coefficient of variation as the weights, four fuzzy similarity measures (including Lattice similarity measure, Hamming similarity measure, Euclidean similarity measure and the max-min similarity measure) are used to classify the 299 samples into the proper water quality standard ranks. The results are compared with the traditional distance discriminant methods. The calculation of two traditional distance discriminant methods (both Euclidean distance and absolute value distance) is also based on the use of coefficients of variation as the weights. Without the Lattice similarity measure, for this method loses some information, the correct assignment of samples classified into the same water quality ranks is 75.92% with the other three similarity measures and two distance discriminant methods. This result shows the reliability of the five methods. Only considering the three similarity measures, there were only 1.01% of the samples that did not classify to the same ranks, while the corresponding ratio of the two distance discriminant methods was 5.69%. The results of leave-one-out cross validation show that more than 88% of the samples are classified to the proper ranks, which demonstrates that the similarity measures are suitable to evaluate the water quality of the Haihe River.