Home emergencies affect greatly the health of inhabitants (mostly children, elderly and dependent persons). Nowadays, the deployment of smart home doesn't require purchasing expensive devices due to advances in communication and computing technologies. However, implementing a customized home emergencies management system is not an easy task. Indeed, it involves two disciplines: (i) Medicine and (ii) Information and Communication Technologies as mentioned by the World Health Organization. In this paper, we propose an approach that hybridizes the two concepts: FSM theory and set theory. The aim is being to facilitate (i) the design of the system behavior for the health professionals, (ii) the translation of the human readable format (emergency management rules) to a machine readable format for the computer specialist, and (iii) mainly the verification of the FSM properties for reducing human errors for both of them. The paper gives the formal description of the set-based FSM, properties that have to be taken into account and the representation of process algebra expressions. Finally, we describe a case study to illustrate the benefits of the proposed FSM.