Abstract: In order to consider the influence of the correlation between multi-dimensional seismic demands in the seismic fragility analysis of reticulated shell structures, the Copula function is introduced to establish the joint distribution function of the structural multi-dimensional seismic demand. At the same time, in order to consider the fuzzy uncertainty of the limit state of the structural performance, a seismic fragility analysis method for multi-dimensional joints of the structure is constructed upon the fuzzy failure criterion. The structural probabilistic seismic demand models with different performance indexes are established from the perspective of displacement and energy, and the membership function is used to describe the fuzziness of the limit state. Furthermore, the structural seismic fragility function considering the fuzziness of failure criteria is presented, based on the fuzzy probability integral theory. Then the joint probabilistic seismic fragility curve considering the correlation of multi-dimensional seismic demand is obtained by selecting the optimal Copula function and combining the failure probability of single performance index. The analysis results show that: compared with the seismic fragility using single-parameter performance index, the multi-dimensional joint seismic fragility considering the fuzzy failure criterion can predict the failure probability of the structure under different damage levels more accurately. To a certain extent, the seismic risk value of the structure is improved and it is beneficial to improve the safety of the structure.