This paper focuses on a new model called fuzzy exchange economy (FXE), which integrates fuzzy consumption, fuzzy initial endowment and the agent's fuzzy preference (vague attitude) in the fuzzy consumption set. Also, the existence of the fuzzy competitive equilibrium for the FXE is verified through a related pure exchange economy. We define a core-like concept (called weak fuzzy core) of the FXE and prove that any fuzzy competitive allocation belongs to the weak fuzzy core. The fuzzy replica economy, which is the r-fold repetition of the FXE, is considered. Finally, we show that the weak fuzzy core of the r-fold fuzzy replica economy, i. e., the set of all fuzzy allocations which cannot be blocked by any coalition of agents, converges to the set of fuzzy competitive allocations of the FXE as r becomes large.