Abstract
Uncertainty and imprecision in hydrologic reliability analysis procedures should be explicitly taken into account in both water quantity and water quality problems. A mix probabilistic/fuzzy logic based approach is presented, using the respective examples of flood protection reliability and control of pollutant loading reliability. In the flood protection example, the fuzzy risk-cost is calculated within the framework of a decision model with two states of nature S1 and S2, such that S1: X ≥ X0 and S2: X<X0, X being the flood stage and X0, the protection level. The probability of exceedance is calculated as a fuzzy number (FN) to account for model and sample uncertainty, as well as imprecision in the resistance X0. The protection costs C and the flood losses K are also taken as FN’s. The expected losses corresponding to each action can then be calculated by fuzzy arithmetic, also yielding FN’s. The action that results in the smallest FN is selected. Techniques for ranking FN are briefly discussed, and the fuzzy mean is used as a ranking criterion.
The water quality example considers the probability of non-exceedance of total pollutant load M into a water body, such as an aquifer or a stream. This mass M is calculated as a linear combination of random loadings with fuzzy (number) coefficients. It is assumed, without loss of generality, that M is a normal variate, whose mean and standard deviation are FN’s because the coefficients are FN’s. The probability of non-exceedance is thus calculated by the extension principle, yielding the safety or reliability of control as a fuzzy number. As it was done in the case of flood protection, the comparison of actions may be made by means of ranking the fuzzy numbers corresponding to each action. Overall, a mixed fuzzy-probabilistic approach to risk and reliability analysis appears to provide another useful viewpoint for analyzing the effect of uncertainties in both water quantity and quality problems.
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© 1991 Springer-Verlag Berlin Heidelberg
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Duckstein, L., Bogardi, I. (1991). Reliability with Fuzzy Elements in Water Quantity and Quality Problems. In: Ganoulis, J. (eds) Water Resources Engineering Risk Assessment. NATO ASI Series, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76971-9_14
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DOI: https://doi.org/10.1007/978-3-642-76971-9_14
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