Practical Study on the Fuzzy Risk of Flood Disasters

The simplest way to perform a fuzzy risk assessment 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 the fuzzy set to the crisp set. Therefore, the first step is to define an alpha level value, and then select the elements x with a subordinate degree A(x) >= alpha. The higher the value of alpha, the lower the degree of uncertainty-the probability is closer to its true value. The lower the value of alpha, the higher the degree of uncertainty-this results in a lower probability serviceability. The possibility level alpha is dependant on technical conditions and knowledge. A fuzzy expected value of the possibility-probability distribution is a set with (E) under bar (alpha)(x) and (E) over bar alpha(x) as its boundaries. 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 throughout the set [0, 1], it is possible to obtain a series of risk values. Therefore, the fuzzy risk may be a multi-valued risk or set-valued risk. Calculation of the fuzzy expected value of flood risk in the Jinhua River basin has been performed based on the interior-outer set model. Selection of an alpha value depends on the confidence in different groups of people, while selection of a conservative risk value or venture risk value depends on the risk preference of these people.