One of the most important goals of data-center management is to reduce cost through efficient use of resources. Virtualization techniques provide the opportunity of carving individual physical servers into multiple virtual containers that can be run and managed separately. A key challenge that comes with virtualization is the simultaneous on-demand provisioning of shared resources to virtual containers and the management of their capacities to meet service quality targets at the least cost. This paper proposes a two-level resource management system with local controllers at the virtual-container level and a global controller at the resource-pool level. Autonomic resource allocation is realized through the interaction of the local and global controllers. A novelty of the controller designs is their use of fuzzy logic to efficiently and robustly deal with the complexity of the virtualized data center and the uncertainties of the dynamically changing workloads. Experimental results obtained through a prototype implementation demonstrate that, for the scenarios under consideration, the proposed resource management system can significantly reduce resource consumption while still achieving application performance targets.