In this chapter, we propose an adaptive fuzzy control design for the distributed competitive control problem of multiagent systems (MASs) with multiple unknown control directions. The bipartite synchronization control is investigated by using the fuzzy backstepping control framework and fuzzy logic systems. To broaden the application field for the distributed protocol design, we consider practical bipartite synchronization of a group of MASs consisting of followers subject to heterogeneous unknown control directions. To address these multiple unknown control directions, a novel Nussbaum-type function is developed. Moreover, to reduce the communication bandwidth, this chapter proposes an event-triggered control strategy to avoid any unnecessary sampling, further improving the efficiency and feasibility of the developed bipartite protocol design. The experimental results indicate that the proposed control method can effectively realize bipartite synchronization of MASs with multiple unknown control directions.