We present an application of evolutionary-fuzzy prediction in inter-domain routing of broadband network connections with Quality of Services requirements in the case of an integrated ATM and S D H networking architecture. The higher-layer nature of inter-domain routing requires to review the whole routing process in order to maximize performance at low decision making cost, a clear case for fuzzy-set logic based algorithms. In order t o probabilistically avoid shortage of resources, besides effectively computing the feasible paths for an incoming connection request, under uncertainty, these paths should be compared in terms of the negative impact in resource supply which may be caused by other connections. To do this, besides enriching the protocol with vectors of per-class shadow cost metrics, quantized using fuzzy-set theory, we used a subset-interactive autoregressive time-series predictor which is based on fuzzy measures to evaluate path costs under supply metrics that change over time. Moreover, as the connections we are dealing with are semi-permanent, we must take into account the connections lifetime. The complete system is part of the MISA Management of Integrated SDH and ATM network architecture and will be implemented and evaluated in the global broadband connection service of the pan-European test-bed.