This paper deals with the problem of bipartite consensus for Takagi-Sugeno fuzzy multiagent systems on multilayer cooperation-competition networks and its application to image communication. Fuzzy control laws are proposed by using relative output measurements between neighboring agents, where additive couplings are considered to show the different layered-interactions. Sufficient conditions for bipartite consensus of the multilayer networks with signed graphs are obtained by using the signed graph theory, Lyapunov stability theory and Takagi-Sugeno fuzzy systems theory. Then, coupled chaotic Lorenz systems over multilayer signed-networks are illustrated to show the effectiveness of the obtained results. Finally, a new multiagent image communication system is constructed based on the bipartite consensus of the fuzzy multilayer coopetition multiagent network, in which two agents in different layers for point-to-point communication use the output measurements from their own and neighboring agents as the synchronous encryption/decryption keystreams. The experimental results show that the proposed multiagent image communication system has excellent performance against some classical attacks.