Mobile terminals in 4G heterogeneous wireless networks continuously undergo horizontal and vertical handovers. In order for a mobile terminal to be connected to a network in the best possible way in terms of QoS performance and energy consumption, access network selection as the main decision within the handover process is obviously crucial. This paper presents a novel method that takes into account user preferences, network conditions, QoS and energy consumption requirements in order to select the optimal network which achieves the best balance between performance and energy consumption. The proposed network selection method incorporates the use of parameterized utility functions in order to model diverse QoS elasticities of different applications, and adopts different energy consumption metrics for real-time and non-real-time applications. User preferences are easily configured for different application and situation contexts through the use of linguistic assessments and their representation as triangular fuzzy numbers. The aggregation of multiple criteria for the calculation of the overall rating of the networks is performed through the use of the Fuzzy Set Representation TOPSIS method that resolves the issue of inconsistency related to conflicting decision criteria and is modified through the use of the employed utility functions for the elimination of the ranking abnormality problem. Finally, simulations are conducted in order to demonstrate how the proposed method would work and confirm its suitability and effectiveness.