In order to gather information more efficiently in terms of energy consumption, wireless sensor networks (WSNs) are partitioned into clusters. In clustered WSNs, each sensor node sends its collected data to the head of the cluster that it belongs to. The cluster-heads are responsible for aggregating the collected data and forwarding it to the base station through other cluster-heads in the network. This leads to a situation known as the hot spots problem where cluster-heads that are closer to the base station tend to die earlier because of the heavy traffic they relay. In order to solve this problem, unequal clustering algorithms generate clusters of different sizes. In WSNs that are clustered with unequal clustering, the clusters close to the base station have smaller sizes than clusters far from the base station. In this paper, a fuzzy energy-aware unequal clustering algorithm (EAUCF), that addresses the hot spots problem, is introduced. EAUCF aims to decrease the intra-cluster work of the cluster-heads that are either close to the base station or have low remaining battery power. A fuzzy logic approach is adopted in order to handle uncertainties in cluster-head radius estimation. The proposed algorithm is compared with some popular clustering algorithms in the literature, namely Low Energy Adaptive Clustering Hierarchy, Cluster-Head Election Mechanism using Fuzzy Logic and Energy-Efficient Unequal Clustering. The experiment results show that EAUCF performs better than the other algorithms in terms of first node dies, half of the nodes alive and energy-efficiency metrics in all scenarios. Therefore, EAUCF is a stable and energy-efficient clustering algorithm to be utilized in any WSN application.