Energy-Efficient Fuzzy Logic Routing Protocol with Mathematical Optimization for Underwater Wireless Sensor Networks

Underwater Wireless Sensor Networks (UWSNs) are facing critical energy constraints be- cause of harsh aquatic environments and limited bat- tery replacement capabilities. This paper is present- ing an energy-efficient fuzzy logic routing protocol with comprehensive mathematical optimization and formal proofs for UWSNs. The proposed protocol is integrating four key network parameters which are residual energy, hop count, link quality, and node depth into a fuzzy inference system that dynamically selects optimal routing paths. We are providing rig- orous mathematical analysis including convergence proofs, energy consumption bounds, and network lifetime optimization theorems. Extensive simula- tions using NS-3 with the Aqua-Sim NG extension and validation against the SUNRISE real-world un- derwater dataset are demonstrating significant im- provements: 47% extended network lifetime, 31% reduction in energy consumption, 94.3% packet de- livery ratio, and balanced energy distribution across the network. The theoretical framework and empir- ical validation are establishing the protocol’s effec- tiveness for practical underwater IoT deployments in ocean monitoring, environmental sensing, and ma- rine exploration applications.