Abstract: In fuzzy reliability analysis of generalized structural strength, fuzzy safety state can be defined by state variation, fuzzy allowable interval, generalized fuzzy strength. This paper studied the third case. Thus, The concepts of maximizing set and minimizing set are developed to decide the ordering value of each fuzzy number, and these values can be used to determine the order of the fuzzy numbers. On the basis of the works mentioned above, the membership function defining the fuzzy safety event can be calculated, and then the fuzzy reliability in the case of random stress and fuzzy strength is deduced. An example is given to illustrate the method.

Key words: Fuzzy reliability, Generalized fuzzy strength, Maximizing set, Minimizing set, Total utility value