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 alpha level value, followed by selecting the elements x with a subordinate degree A(x) >= alpha. The fuzzy expected values, (E) under bar (alpha)(x) and (E) over bar (alpha)(x), 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 alpha level, three risk values can be calculated. As alpha 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 alpha 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.