In this work, we propose SemBox - Semantic interoperability in a Box, to enable wireless on-the-go communication between heterogeneous wearable health monitoring devices. It can connect wirelessly to the health monitoring devices and receive their data packets. It uses a Mamdani-based fuzzy inference system with data pre-processing to classify the received data packet into one of the classes of the vital parameters. It enables semantic interoperability by labelling and annotating the data packets based on the extracted packet information. We implement SemBox using three different health monitoring wearables, with different keywords used for each vital parameter representation in the data packet. SemBox shows a maximum classification accuracy of 85.71%, with a maximum PDR of 1 at the SemBox with varying device parameters. Overall, SemBox is a potential plug-and-play solution to achieve semantic interoperability and collaboration between heterogeneous health monitoring wearable devices, irrespective of their commercial and proprietary specifications. It is customizable for applications that use multiple heterogeneous devices for collaborative monitoring and decision support. SemBox enables interoperability among health monitoring devices, introduces flexibility and ease the inter-device dynamics in the domain of biomedical research.