## 2 Related Work  
The cluster routing technique involves sensor nodes in multi-hop communication within a cluster, and then the cluster head aggregates the data to decrease the number of transmitted messages to the base station. Low-energy adaptive clustering hierarchy (LEACH) [7] is the first cluster-based routing protocols in wireless sensor networks. LEACH selects cluster heads with some probability, and the cluster heads fuse and aggregate data arriving from nodes that belong to the respective cluster. Cluster heads are periodically rotated among the nodes to balance energy consumption, and enhances the network lifetime. However, some cluster heads may be very close to each other and cannot be uniformly deployed in the networks by probability mechanism, and cluster heads number is not always equal to the preestablished number. To uniformly deploy cluster heads, a centralized version of LEACH, LEACH-C [3], and a centralized energy-efficient routing protocol-BCDCP [8] are proposed. However, these centralized algorithms bring worse scalability and robustness to large networks than distributed algorithms. To overcome the limitations of LEACH, a fuzzy logic approach to cluster head election [9] is proposed which uses three fuzzy variables (concentration, energy and centrality). However, this algorithm is a centralized election mechanism, and the base station has to collect the energy and distance information from all sensor nodes. In [10], cluster head election mechanism using fuzzy logic (CHEF) is proposed, which is a localized cluster head election mechanism. CHEF uses energy and local distance as fuzzy variables in the fuzzy if-then rules. Simulation results show that the cluster heads in CHEF are more evenly distributed over the network than those in LEACH, and then CHEF further prolongs the network lifetime. But CHEF does not construct multi-hop routes in cluster heads. A generalized fuzzy logic based energy-aware routing [11] is presented which is a soft, tuneable parameter based algorithm. But this algorithm assumes that a cluster head is much powerful as compared to the other sensor nodes and has no energy limitation. A fuzzy self-clustering algorithm (FSCA) [12] considers the node residual energy and local density to improve the lifetime of WSNs. To uniformly distribute clusters over the networks, FSCA employs migration fuzzy module to recluster and merge existed clusters. However, reclustering the whole network adds more control overhead and needs more time. In [13], an energy and mobility-aware geographical multipath routing (EM-GMR) algorithm is presented, which is based on fuzzy logic system considering the remaining battery capacity, mobility, and distance to the destination node. Power-efficient gathering in sensor information systems (PEGASIS) [14] organizes sensor nodes into a chain using a greedy algorithm, so each node only communicates with its neighbors. Nevertheless, PEGASIS requires the global knowledge of the network topology and the farther nodes will result in a bigger data delay. A hybrid energy-efficient distributed clustering approach (HEED) [15] uses a hybrid metric consisting of residual energy and communication cost as attributes for cluster head election. The primary parameter is residual energy and the secondary parameter is the average minimum reachability power. HEED ensures a uniform distribution of cluster heads across the network and adjusts the probability of cluster head election to ensure intracluster connectivity. However, HEED relies on the assumption that cluster heads can communicate with each other and form a connected graph; it is difficult to realize HEED in practical WSNs. In a distributed energy-efficient clustering algorithm (DEEC) [16], cluster heads are elected by a probability based on the ratio between the residual energy of each node and the average energy of the total networks. However, DEEC is required to estimate the total energy of the networks according to the network topology and broadcasts it to all nodes.