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The paper focuses on the distributed filtering problem over wireless sensor networks (WSNs) for a class of discrete-time T-S fuzzy systems with immeasurable premise variables and Sigma-Delta quantiser. Two defectives are considered including packet losses and multiplicative noises, which can be represented by some mutual independent random variables, respectively. Unlike conventional logarithmic quantiser, by utilising the Sigma-Delta dynamic quantiser, the quantised measurement outputs are broadcasted to the distributed filters over WSNs, only requiring a finite number of quantisation levels, and the static errors can be eliminated simultaneously. Using non-PDC scheme, an estimated premise variable-dependent distributed filter is designed over WSNs. Then treating the premise variables as uncertainties, a robust distributed filtering problem is considered for such an uncertain filtering error system. Based on the fuzzy Lyapunov function, the less conservative mean-square stable conditions with a prescribed performance index for the uncertain filtering error dynamical systems are presented. The filter parameters are determined by solving a set of linear matrix inequalities (LMIs). Finally, a tunnel diode circuit model and a numerical example are presented to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]