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Representation and decomposition of complex decision-making tasks are bottleneck problem of complex task decision. This paper uses multi-agent technology to construct an agent organization-based distributed intelligence decision support system (AOBDIDSS) structure model, applies generalized decision function (GDF) to the decomposition of decision task specifications, and determines decomposition criteria and properties of decision task specifications based on GDF. Because the task decomposition based on G DF is equivalent to the decomposition of Bayesian network, we present the representation and decomposition methods of decision tasks and properties based on Bayesian network. On these bases, the decision task decomposition problems can be entailed basically to construct a multi-sectioned Bayesian network and sub-Bayesian networks related to decision task specifications. The method is used to analyze the representation and decomposition of decision tasks in medical diagnosis. The results show that the model and method is not only feasible, but also effective and novel.