# Fuzzy-Logic Based Distributed Energy-Efficient Clustering Algorithm for Wireless Sensor Networks  
[PERSON]  
1 College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China; [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (D.H.); [EMAIL_ADDRESS] (R.Z.) [PERSON]  
2 Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2  
of CHs, which will be helpful for the lifetime extension of the networks. CHs are responsible for gathering the collected information from all the member nodes. After data fusion, the data in CHs will be forwarded to the base station (BS) by single hop to achieve the data upload [5]. In clustered network system, nodes are usually deployed as non-uniform distribution with different energy consumptions and different distances between each other. If we divide them into the same scale clusters, it will always lead to uneven energy consumption, especially for some CH nodes. Thus, for the sake of load balancing in the system, we usually choose unequal clustering algorithm for WSNs. Unlike the centralized optimization, the distributed clustering algorithm does not depend on the global topology of the networks, and the node can implement the information analysis only depending on the relative information of itself and its neighbor nodes, which greatly reduces the unnecessary overhead of communication with the base station compared with centralized algorithms. Thus, this type of scheme is more reasonable to be used in WSNs currently. In clustering routing algorithm, there is no doubt that CH nodes should consume much more energy than the member nodes. However, during the intra-cluster multi-hop communication, the nodes that are close to CH have to undertake more duties of data receiving and forwarding to the CH than the farther nodes, which may lead to more extra energy consumption. As a result, this extra consumption would reduce the lifetime of the corresponding relay nodes and have a serious influence on load balancing of the whole sensor network [6]. Especially for monitoring networks such as underwater wireless sensor networks, if the relay nodes within the cluster die prematurely due to insufficient residual energy during each round, the further associated nodes have to do routing discovery once more and reestablish the routing link, which will cause more extra energy consumption. It will destroy the stability of communication and weaken the performance of network systems. Thus, it can be seen that the residual energy of the neighbor nodes of the CHs also plays an important role in the data transmission process actually. When designing the distributed clustering algorithm for WSNs, many factors such as node energy, node degree, and the energy situation for the surrounding neighbor nodes may all need to be considered momentarily. Therefore, how to elect the appropriate CH under the multi-condition equilibrium makes a big influence on the stability of the whole clustered networks. However, a fuzzy logic system can just provide an appropriate solution for this kind of multi-factor evaluation problem like CHs election [7]. In other words, the fuzzy logic system can integrate various clustering factors for CHs election. To overcome some weakness such as the lack of accuracy when modeling some complex and high-dimensional systems, we now widely use scatter fuzzy partitions instead of the classical grid-based ones to do fuzzy analysis, in such a way that every single rule has its own meaning [8; 9]. The framework of the fuzzy logic system is shown in Figure 1. We convert crisp parameters such as the current residual energy in sensor nodes into the input of fuzzy linguistic variables through fuzzification interface, and the process in defuzzification interface is carried out on the contrary. The middle part in this system is mainly composed of inference system and knowledge base.