An index model for quality evaluation based on the formula of similarity membership functions in the fuzzy c-means (FCM) clustering algorithm is proposed. Summing up the weighted similarity degrees between an observation and designed specific quality-ordered levels develops an alternative overall index. Stretching the values of the controlling parameters in the formula of the similarity membership functions causes diverse patterns of overall index models. Applying this proposed fuzzy index model to the trophic evaluation of reservoir waters is studied to demonstrate the practical application of this index. Every measurement of the variables is standardized by the membership function of quality evaluation on the interval [0,1], referring to the trophic status clarified in the Carlson Trophic State Index. The sensitivity analyses are studied both in the proposed index system and the Carlson Trophic State Index. Besides, a case study of the trophic status evaluation of the Feitsui Reservoir from 1987 to 2003 is presented to demonstrate the feasibility of applying the proposed evaluation model.
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