Sensors_**2011**, _11_, 3381-3400; doi:10.3390/s110303381  
_Sensors_  
**ISSN 1424-8220**  
www.mdpi.com/journal/sensors  
_Article_  
**A Reliable Energy-Efficient Multi-Level Routing Algorithm for Wireless Sensor Networks Using Fuzzy Petri Nets**  
**[PERSON] \({}^{1,\star}\), [PERSON] \({}^{1}\), [PERSON] \({}^{2}\) and [PERSON] \({}^{3}\)**  
\({}^{1}\) School of Telecommunication Engineering, Air Force Engineering University, Xi'an 710077, China; E-Mail: [EMAIL_ADDRESS]  
\({}^{2}\) School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China; E-Mail: [EMAIL_ADDRESS]  
\({}^{3}\) Cyber-Physical Networking Laboratory, Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA; E-Mail: [EMAIL_ADDRESS]  
\({}^{\star}\) Author to whom correspondence should be addressed; E-Mail: [PERSON]ADDRESS]63.com. _Received: 25 January 2011; in revised form: 16 February 2011 / Accepted: 4 March 2011 / Published: 22 March 2011_  
A reliable energy-efficient multi-level routing algorithm in wireless sensor networks is proposed. The proposed algorithm considers the residual energy, number of the neighbors and centrality of each node for cluster formation, which is critical for well-balanced energy dissipation of the network. In the algorithm, a knowledge-based inference approach using fuzzy Petri nets is employed to select cluster heads, and then the fuzzy reasoning mechanism is used to compute the degree of reliability in the route sprouting tree from cluster heads to the base station. Finally, the most reliable route among the cluster heads can be constructed. The algorithm not only balances the energy load of each node but also provides global reliability for the whole network. Simulation results demonstrate that the proposed algorithm effectively prolongs the network lifetime and reduces the energy consumption. **Keywords:** wireless sensor networks; routing algorithm; clustering; fuzzy Petri netsIntroduction  
Wireless sensor networks (WSNs) have become a vibrant and exciting research and development area in recent years and can be used in many different applications, including battlefield surveillance, home security, smart spaces, environmental monitoring, and target tracking [1,2]. A wireless sensor network consists of a large number of tiny, low-powered, energy-constrained sensor nodes with sensing, data processing and wireless communication components. Sensor nodes in WSNs are small battery powered devices with limited energy resources, and their batteries cannot be recharged once the sensor nodes are deployed. Therefore, minimizing energy consumption is an important issue in the design of WSNs protocols. The energy is also the major consideration in designing the routing protocol. Cluster routing is an effective solution in reducing energy consumption, prolonging the lifetime of the networks and providing network scalability [3]. In the cluster routing, sensor nodes are divided into groups and form clusters. Each cluster has a leader, often referred to as the cluster head [4]. A cluster head can collect data from nodes within the cluster, and aggregate the data and forward it to the base station. Through data aggregation of the sensors' data at the cluster heads, the total amount of data sent to the base station can be significantly decreased. Therefore the overhead can be significantly reduced, and energy and bandwidth resources can be saved. In recent years clustering routing technique has been widely investigated in the context of WSNs [4]. Although the existing cluster-based routing protocols have been proposed, most of them focus on the node energy and the number of hops in a cluster instead of the network topology and reliability of routes [5]. The route with the minimum number of hops may not always be the optimal and reliable route. Since WSNs suffer from different kinds of uncertainty, randomness, and fuzziness [6], a reliable routing protocol with adapting capabilities to high variability and uncertainty is needed.