Fog Computing is an approach involving smart devices. These devices carry out data processing to provide collaborative services to reach a common goal, usually, in the cloud. In the fog computing paradigm, uncertainty and vagueness are inherent to the data processing due to the limitations of computational and communication capabilities of the smart devices. Fuzzy logic and protoforms represent a powerful tool to model and compute imprecise data presented within the fog-computing paradigm. In this paper, we present a fuzzy cloud-fog approach based on fuzzy temporal windows and fuzzy aggregation. The innovations of this paper are: i) to model the uncertainty involved in fog nodes linguistically, ii) to compute and distribute relevant linguistic information (protoforms), and iii) to publish the computed protoforms in the cloud to generate complex protoforms, which reach the common goal. This new fuzzy cloud-fog approach is applied to the problem of activity recognition in smart homes. In this context, the smart devices in a smart home are represented by fog nodes, which cooperate for activity recognition using a fuzzy cloud-fog computing approach to provide solutions in ambient-assisted living. Finally, to demonstrate the effectiveness of the proposal in handling situations/environments where multiple and heterogeneous devices are involved (such as UWB beacons, smart objects and smart wearable devices), a case study of the proposed fuzzy cloud-fog approach is implemented in the smart lab of the University of Jaén. So, the results obtained with the proposed approach in the case study are compared to the results obtained with a non-fuzzy approach with the aim of showing the advantages of the fuzzy methodology.
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