Analysis on fuzzy risk of landfall typhoon in Zhejiang province of China

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 a fuzzy set to crisp set. Therefore, the first step is to define an α level value, and then select the elements x with a subordinate degree A(x) ≥ α. The higher the value of α, the lower the degree of uncertainty—the probability is closer to its true value. The lower the value of α, the higher the degree of uncertainty—this results in a lower probability serviceability. The possibility level α   is dependent on technical conditions and knowledge. A fuzzy expected value of the possibility–probability distribution is a set with E_α(x) and E¯α(x) as its boundaries. The fuzzy expected values E_α(x) and E¯α(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 α level, three risk values can be calculated. As α 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 landfall typhoon risk in Zhejiang province has been performed based on the interior–outer set model. Selection of an α 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.