Investigating evidential reasoning for the interpretation of microbial water quality in a distribution network

Total coliforms are used as indicators for evaluating microbial water quality in distribution networks. However, total coliform provides only a weak "evidence" of possible fecal contamination because pathogens are subset of total coliform and therefore their presence in drinking water is not necessarily associated with fecal contamination. Heterotrophic plate counts are also commonly used to evaluate microbial water quality in the distribution networks, but they cover even a wider range of organisms. As a result, both of these indicators can provide incomplete and highly uncertain bodies of evidence when used individually. In this paper, it is shown that combing these two sources of information by an appropriate data fusion technique can provide improved insight into microbial water quality within distribution networks. Approximate reasoning methods like fuzzy logic and probabilistic reasoning are commonly used for data fusion where knowledge is uncertain (i.e., ambiguous, incomplete, and/or vague). Traditional probabilistic frameworks like Bayesian analysis, reasons through conditioning based on prior probabilities (which are hardly ever available). The Dempster-Shafer (DS) theory generalizes the Bayesian analysis without requiring prior probabilities. The DS theory can efficiently deal with the difficulties related to the interpretation of overall water quality where the redundancy of information is routinely observed and the credibility of available data continuously changes. In this paper, the DS rule of combination and its modifications including Yager's modified rule, Dubois-Prade disjunctive rule and Dezert-Smarandache rule are described using an example of microbial water quality in a distribution network.