Bounds of fuzzy reliability in the case of fuzzy strength and fuzzy stress

In the case of fuzzy strength and fuzzy stress, it is difficult to obtain the accuracy fuzzy reliability since the membership function of fuzzy safety event is not known. A method for calculating the bounds of fuzzy reliability is proposed to determine this problem. Firstly, fuzzy strength and fuzzy stress are remodeled into random sets. Then, the limit state function of a structure with fuzzy strength and fuzzy stress is mapped into a random set by using the extension principle of random set. Finally, two limit cumulative distribution functions of fuzzy safety event are calculated and are used as the upper and lower bounds of fuzzy reliability. An example is given and it shows that the proposed method is effective when the theory of fuzzy probability proposed by Zadeh can not be directly used to calculate the fuzzy reliability with fuzzy strength and fuzzy stress.