The theory of fuzzy set is applied to discuss the fuzzy fault tree analysis and its application based on triangular fuzzy number arithmetic operations.

We first define the fuzzy number intuitionistic fuzzy set and give its some operations. we also discuss the links of it and the interval valued intuitionistic fuzzy set, the intuitionistic fuzzy set.

In the paper, concepts, operations and laws of operations of multi-dimensional fuzzy error set are first studied on base of needs of objective practice.