**1. Introduction**

Home-based e-health programs are being increasingly used due to the proliferation of wearable devices and portable medical sensors which are seamlessly integrated into the daily lives of users to monitor vital signs and physical activity [1]. In this way, wearable devices, together with connectivity and ubiquitous computing in mobile applications [2], have provided a solution for monitoring a greater number of patients under prevention and rehabilitation programs in a personalized manner [3].

Moreover, wearable devices have been demonstrated to favor strategies for changes to healthy habits and the promotion of healthy physical activity [4]. To achieve this, a key aspect is to adapt high-quality clinical guidelines and protocols from health centers to home-based solutions [5] in order to provide real-time activity monitoring by means of wearable devices [6].

Motivated by these recent advances, in this work a cardiac rehabilitation program is embedded in a wrist-worn device with a heart rate sensor, which provides real-time monitoring of physical activity during sessions in a safe and effective way. For this, a linguistic approach based on fuzzy logic [7] is proposed in order to model the cardiac rehabilitation protocol and the expert knowledge from the cardiac rehabilitation team. Fuzzy logic has provided successful results in developing intelligent systems from sensor data streams [8–12], and more specifically, it has been described as an effective modeling tool in cardiac rehabilitation [13].

The remainder of the paper is structured as follows: in Section 1.1, the principles and motivation of cardiac rehabilitation together with previous related works are presented; in Section 2, we detail a standardized protocol for cardiac rehabilitation, and based on it, a fuzzy model is proposed for real-time monitoring the heart rate of patients. In Section 3, the developed architecture based on wrist-worn wearable and mobile applications for patients and a cloud web application for the cardiac rehabilitation team is presented; in Section 4, an evaluation of fuzzy modifiers and temporal windows from heart rate sessions is provided by the cardiac rehabilitation team in order to adjust the real-time monitoring of the fuzzy model in practice; and finally, in Section 5, conclusions and suggestions for future works are presented.
