A search for methods to assess the fuzzy fracture probability of spherical tanks

Let the fracture event be a fuzzy event. It seems that between the fracture region and the safe region there is a fuzzy region. In the fuzzy region the structure will be either fractured or safe. Through the membership function, the fracture possibility of each point in the fuzzy region is determined. By using Monte-Carlo simulation, Edgeworth's series and the advanced first-order second-moment method, the fuzzy fracture probability of a spherical tank is determined in this paper.