The Dempster-Shafer (DS) belief theory is often used within data fusion, particularly in applications rife with uncertainty that causes problems for probabilistic models. However, when a large number of variables is involved, DS theory (DST) based techniques can quickly become intractable. In this paper, we present a method for complexity reduction of DST methods based on statistical sampling, a tool commonly used in probabilistic-based signal processing (e.g., particle filters). In particular, we use sampling-based approximations to reduce the number of propositions with non-zero support, upon which the computational complexity of many DST-based algorithms are directly dependent on, thereby significantly reducing the computational overhead. We present some preliminary results that demonstrate the validity and accuracy of the proposed method, along with some insights into further developments. We also compare the proposed method to previously presented approximation methods.