The flood risk management practice deals with temporal or spatial variability of risk. However, there is a need to understand the dynamic characteristics of flood risk and its spatial variability in the same time. The new methodology, presented in this paper, is based on the use of fuzzy reliability theory. The two-dimensional (2-D) fuzzy set, with one dimension for the universe of discourse and the other dimension for its membership degree, is not sufficient to handle spatial and temporal variation of flood risk. This paper presents the development of a three dimensional (3-D) fuzzy set for the description of flood risk variability in space and time. The proposed methodology extends the partial flood damage concept to a 3-D representation. The flood risk is defined using three performance indices (i) a combined fuzzy reliability-vulnerability, (ii) fuzzy robustness and (iii) fuzzy resiliency. The fuzzy performance indices are computed for river flood risk analysis. The analysis is illustrated using the Red River flood of 1997 (Manitoba, Canada) as a case study. Dynamic maps present the fuzzy reliability indices and provide additional decision support for (a) land use planning, (b) selection of appropriate flood mitigation strategies, (c) planning emergency management measures, (d) selecting an appropriate construction technology for flood prone areas, and (e) flood insurance.
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