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This paper revisits the problem of multisession multicast tree construction with bandwidth allocation in wireless sensor networks. Previous work has shown that when the goal is to find multicast routing tree, the problem becomes NP-complete. In this work, we present a heuristic Energy-Efficient Multisession Multicast protocol (EEMM) that uses fuzzy logic to evaluate nodes' and network conditions during the multicast tree construction process. Our proposed solution includes an online rate assignment algorithm that aims at maximizing the overall network throughput by accepting as many streams in the network as possible. The proposed solution allows receivers to request multiple sessions from, possibly, different sources with different data rates. We conduct extensive evaluations to study the performance of the proposed protocol compared to other existing approaches, namely shortest path and minimum transmission tree routing. Simulation results show that our protocol effectively improves the network throughput and utilization, while conserving and balancing out per node energy consumption ensure prolonged network lifetime.