This paper presents two novel blind set-theoretic adaptive filtering algorithms for Multiple Access Interference (MAI) suppression in DS/CDMA systems. We naturally formulate the problem of MAI suppression as minimizing asymptotically a sequence of cost functions under some linear constraint defined by desired user's signature. The proposed algorithms embed the constraint in the direction of adaptation, and thus the adaptive filter moves toward the optimal filter without stepping away from the constraint set. In addition, using parallel processors, the proposed algorithms attain good performance behavior with low computational complexity. Geometric interpretation clarifies an advantage of the proposed methods over some conventional methods. Simulation results demonstrate that the proposed algorithms achieve much faster convergence than the conventional methods with a moderate number of concurrent processors.