Due to the large number of elderly people with physical and cognitive issues, there is a strong need to provide indoor location systems that help caregivers monitor as many people as possible and with the best quality possible. In this paper, a fuzzy indoor location methodology is proposed in a smart environment based on mobile devices and Bluetooth Low Energy (BLE) beacons where a set of Received Signal Strength Indicators (RSSI) is received by mobile devices worn by the inhabitants. The use of fuzzy logic and a fuzzy linguistic approach is proposed to deal with the imprecise nature of the RSSI values, which are influenced by external factors such as radio waves, causing significant fluctuations. A case study carried out at the Smart Lab of the University of Jaén (UJAmI Smart Lab) is presented to demonstrate the effectiveness of the proposed methodology, where our proposal is compared with a non-fuzzy logic approach, obtaining an accuracy of 91.63%, approximately 10 points higher than the methodology without using fuzzy logic. Finally, our theoretical proposal is accompanied by a description of the UJAmI Location system, which applies the theory to the functionality of locating elderly people in indoor environments.