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One of the main features of future networks will be heterogeneity in the wireless access environment, and consequently, network selection mechanisms play an important role in ensuring QoS for users in this environment. In this paper, we propose a novel network selection mechanism, the goal of which is to guide users to select the Always-most-Suitable-Connection (ASC) access network, realizing a well tradeoff between the performance optimization of single application and efficient utilization of network resources. Besides, we give a comprehensive decision criteria set including QoS requirements of applications, providers' prices and user preference. Furthermore, we combine the Analytical Hierarchy Process (AHP) method to decide the factor weights, as well as the modified Grey Relational Analysis (MGRA) to select the ASC network. Simulation results demonstrate the effectiveness of the proposed network selection mechanism in integrated UMTS/WLAN networks.