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The design of a fast and efficient media independent handover function (MIHF) for a 4G mobile supporting heterogeneous networks is the goal of this paper. This will be carried out for two classes of traffic with different quality of service requirements. Due to the imprecision and fast variability of the measured or estimated input parameters, the corresponding decision engines to be used in the MIHF, were based on fuzzy logic design. Three parameters are to be considered: the signal strength, the available bandwidth, and the connection cost. The two designed funtions showed a clear adaptability to the requirements of the two considered classes of traffic.