This paper proposes a hybrid fuzzy-Particle Swarm Optimization (PSO) approach for power allocation in bidirectional Light Fidelity (LiFi)-enabled Internet of Things (IoT) communication systems. The approach integrates fuzzy logic and PSO to achieve efficient and robust power allocation, considering energy efficiency and Quality of Service (QoS) requirements. The hybrid approach leverages flexibility of fuzzy logic to handle uncertainties and variations in system parameters, such as channel conditions and QoS requirements. Fuzzy sets and membership functions are defined to represent linguistic variables, and fuzzy rules are formulated based on expert knowledge and system-specific considerations. This allows the approach to adaptively adjust power allocation based on varying channel conditions and QoS requirements, enhancing the robustness of the power allocation strategy. The PSO algorithm is employed for iterative optimization to explore for ideal power allocation solution. The particles in swarm signify possible power allocation configuration, and its position in the search space corresponds to a specific power allocation. The particles update their positions based on local best-known positions and globally best-known positions, allowing the swarm to converge toward the optimal solution. Through extensive simulations and analysis, the proposed hybrid fuzzy-PSO approach is evaluated with regard to energy efficiency and QoS satisfaction. The results demonstrate its effectiveness in achieving energy-efficient power allocation while meeting diverse QoS requirements. The proposed approach outperforms existing methods such as channel- and Orthogonal Multiple Access (OMA)-based power allocation schemes.