Robust fuzzy filterings for a class of nonlinear stochastic systems with infinite Markov jump are explored based on T-S fuzzy model approach in this paper.First of all,the exponentially mean square stable filter with a prescribed H∞ performance is designed via linear matrix inequalities (LMIs).Secondly,H2/H∞ fuzzy filtering is solved in terms of LMIs by minimizing the estimation error energy under the worst case fuzzy disturbance.The corresponding fuzzy filter parameters can be received by convex optimization algorithms.And lastly,two illustrative examples are performed to manifest the validity of the proposed methods.