A Stochastic Computational Approach for the Analysis of Fuzzy Systems

Fault tree analysis (FTA) has been widely utilized as a reliability evaluation technique for complex systems, such as nuclear power plants and aerospace systems. However, it is hard to obtain the crisp failure probabilities of basic events, owning to the insufficient information about some complex engineering systems. Hence, fuzzy set theory and fuzzy arithmetic operation (FAO) have been used as effective methods to analyze system reliability. However, it is cumbersome to evaluate complex systems based on FAO. To improve the evaluation efficiency, stochastic computational models are proposed in this paper to perform reliability analysis of a fuzzy system. Due to the features of Gaussian distribution in stochastic computation, a basic event's failure possibility given by a fuzzy number is transformed into the expected value of it. The standard deviation of stochastic computational results gives the spread of the fuzzy number. A fuzzy system is then converted into a deterministic system. The analysis of an illustrating example shows that the proposed stochastic approach can efficiently evaluate the failure probability of a system.