Application of possibility-probability distribution in risk analysis of landfall hurricane—A case study along the east coast of the United States

The type of probability pattern that landfall hurricane variations along the east coast of the United States follow is still unknown, and the sample volume actually measured is relatively small, with the characteristics of fuzzy information. Because probability estimation based on such samples is not accurate, it is advisable to determine landfall hurricane risk in the future using the possibility-probability distribution. 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 can be a multi-valued risk or set-valued risk. Calculation of the fuzzy expected value of landfall hurricane risk along the east coast of the United States has been performed based on the interior-outer set model. From the fuzzy expected value of landfall hurricane risk along the east coast of the United States, we can get a conservative risk value (RC) of 26.88 in. for landfall hurricane risk along the east coast of the United States, a venture risk value (RV) of 27.32 in., and a maximum probability risk value (RM) of 27.19 in. for the α = 0.25 level cut set.