关键词: 负二项, 隶属函数, 模糊破产概率, Gerber-Shiu函数

Abstract: The problem of the fuzzy ruin of the insurance company management was studied. The article used the normal approximation and the possion approximation of compound negative binomial，researched the fuzzy ruin probalbility and the Gerber- Shiu function under the double compound negative binomial risk model with membership function，got the calculation formula of the fuzzy ruin probalbility and relation between surplus and initial capital.

Key words: negative binomial, membership functions, fuzzy ruin probability, Gerber-Shiu function