In this paper the architecture and learning algorithms of a hybrid computing intelligent network based on the Group Method of Data Handling (GMDH) and the fuzzy bagging approach are suggested and investigated. The system consists of a sequence stacks. Stacks are formed by different fuzzy models connected in parallel and designed to solve the same problem. Odd stacks are ensembles, and even stacks are metamodels that are designed for fuzzy bagging and calculate the levels of fuzzy membership of each member of the ensemble to the optimal result. The process of increasing the number of stacks is based on the principles of GMDH and continues until the desired accuracy of the final result is achieved. Thus, the number of stacks is determined automatically in the learning process. The proposed system provides online work and does not require large volumes of training samples.