Assessing river water quality with fuzzy interpolation

Abstract: This work concerns the interpolation of environmental data using fuzzy splines in order as alternative to statistical analysis in order to monitor water quality in a river. A fuzzy interpolated model representing the river water quality is constructed and then queried in order to retrieve information useful for planning precautionary measures. The results are compared with statistical model to evaluate significance of the quality classification. Geographical data concerning environment pollution consist of a large set of temporal measurements (representing, e.g.monthly measurements for several years) at a few scattered spatial sites. In this case the temporal data at a given site must be summarized in some form in order to employ it as input to build a spatial model. Summarizing the temporal data (data reduction) will necessarily introduce some form of uncertainty which must be taken into account. Fuzzy numbers can represent this uncertainty in a conservative way without any statistical ”a priori ” hypothesis. This method has been employed for ocean floor geographical data by Patrikalakis (1995), in the interval case, and Anile et al. (2000), for fuzzy numbers, and to environmental pollution data by Anile et al.(2004) Fuzzy interpolation is carried out with splines to get a deterministic model for environmental pollution data. Then the model is interrogated by fuzzy queries to find the sites exceeding a quality threshold