In this article, we study the problems of bipartite and cooperative consensus with a strictly dissipative performance for fuzzy multiagent systems (MASs) in a unified framework. First, we prove that bipartite consensus over a structurally balanced signed graph is equivalent to cooperative consensus over the corresponding unsigned graph by leveraging the gauge transformation for a class of nonlinear MASs. Then, a polynomial fuzzy model is constructed to describe the nonlinear MAS formed by one leader and followers. For mitigating communication and computational load, a mode-dependent event-triggered transmission strategy is proposed. By establishing the switching topologies through Markovian process, a new sampled-data event-triggered consensus protocol is designed. With a mode-dependent Lyapunov–Krasovskii function, a novel relaxed dissipative criterion is obtained. The criterion guarantees that all agents can achieve both event-triggered cooperative consensus and event-triggered bipartite consensus with the same magnitude but opposite signs for MASs over structurally balanced signed directed graphs and Markovian switching topologies. Moreover, the event-triggered parameters and consensus control gains can be numerically solved via the sum-of-squares method. Simulation results are given to show the effectiveness of the proposed design method.