Bandwidth and power hungry applications are proliferating in mobile networks at a rapid pace. However, mobile devices have been suffering from a lack of sufficient battery capacity for the intensive/continuous use of these applications. In addition, the mobile ecosystem is currently heterogeneous and comprises a plethora of networks with different technologies such as LTE, Wi-Fi, and WiMaX. Hence, an issue must be addressed to ensure that quality of experience (QoE) is provided for the users in this scenario: an energy-efficient strategy that is designed to extend the battery lifetime of mobile devices. This paper proposes an architecture which provides an intelligent decision-making support system based on Fuzzy Logic for saving the energy of mobile devices within an integrated LTE and Wi-Fi network. The simulated experiments show the benefits of the solution this architecture can provide by using QoE metrics.