Clustering is one of the most energy-efficient techniques for extending the lifetime of wireless sensor networks (WSNs). In a clustered WSN, each sensor node transmits the data acquired from the sensing field to the leader node (cluster head). The cluster head (CH) is in charge of aggregating and routing the collected data to the Base station (BS) of the deployed network. Thereby, the selection of the optimum CH is still a crucial issue to reduce the consumed energy in each node and extend the network lifetime. To determine the optimal number of CHs, this paper proposes an Enhanced Fuzzy-based LEACH (E-FLEACH) protocol based on the Fuzzy Logic Controller (FLC). The FLC system relies on three inputs: the residual energy of each node, the distance of each node from the base station (sink node), as well as the node's centrality. The proposed protocol is implemented using the Castalia simulator in conjunction with OMNET++, and simulation results indicate that the proposed protocol outperforms the traditional LEACH protocol in terms of network lifetime, energy consumption, and stability.