The application of fuzzy risk in researching flood disasters

To perform a fuzzy risk assessment the simplest way is to calculate the fuzzy expected value and convert fuzzy risk into non-fuzzy risk, i.e., a crisp value. In doing so, there is a transition from a fuzzy set to a crisp set. Therefore, the first step is to define an α level value, followed by selecting the elements x with a subordinate degree A(x) ≥ α. The fuzzy expected values, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$ \underline{E}_{\alpha } (x) $$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$ \overline{E}_{\alpha } (x) $$</EquationSource> </InlineEquation>, of a possibility–probability distribution represent the fuzzy risk values being calculated. Therefore, we can obtain a conservative risk value, a venture risk value and a maximum probability risk value. Under such an α level, three risk values can be calculated. As α adopts all values between the set [0, 1], it is possible to obtain a series of risk values. Therefore, the fuzzy risk may either be a multi-valued risk or a set-valued risk. Calculation of the fuzzy expected value of a flood risk in the Jinhua River basin has been performed based on the interior–outer-set model. The selection of an α value is dependent on the confidence in different groups of people, while the selection of a conservative risk value or a venture risk value is dependent on the risk preference of these people. Copyright Springer Science+Business Media B.V. 2010