In this article, the extended dissipative performance of distributed parameter systems (DPSs) with stochastic disturbances and multiple time-varying delays is studied by using a new fuzzy aperiodic intermittent sampled-data control strategy. Different from the previous fuzzy sampled-data control results, the state sampling of the proposed sampled-data controller occurs only in space and is intermittent rather than continuous in the time domain. By introducing a novel multitime-delay-dependent switched Lyapunov functional to explore the dynamic characteristics of the controlled system, and by means of the famous Jensen’s inequality with reciprocally convex approach, Wirtinger’s inequality, the criterion of the system’s mean square stabilization is established based on the LMI technique, which quantitatively reveals the relationship between the control period, the control length, and the upper bound of the control sampling interval. Especially, the optimal control gain is given by designing an optimized algorithm in the article, which greatly reduces the cost. Finally, two numerical examples are presented to demonstrate the effectiveness and superiority of the proposed approach.