This study aims to address the critical challenges of spatial imbalance and low utilization efficiency in the siting of electric taxi charging facilities in large-scale urban environments. To this end， this paper proposes a multi-objective particle swarm optimization algorithm integrating epsilon-constraint handling and fuzzy mathematical programming， referred to as FMPPSO， with the objective of achieving a balanced and efficient charging facility layout that simultaneously considers economic cost， service efficiency， and battery health. The proposed method formulates the electric taxi charging station siting problem as a multi-objective optimization model incorporating construction and operation costs， taxi charging waiting time （reflecting passenger pickup rate）， and battery degradation cost. To overcome the limitations of traditional weighted-sum methods and conventional evolutionary algorithms， fuzzy membership functions are constructed to normalize heterogeneous objectives into a unified fuzzy decision space， enabling adaptive adjustment of objective preferences while preserving the original optimization structure. Furthermore， an epsilon-constraint mechanism is introduced to transform secondary objectives into dynamic constraints， which effectively balances solution convergence and Pareto front diversity， mitigates premature convergence， and enhances global search capability. The transformed problem is solved using an enhanced particle swarm optimization framework， where particles represent candidate charging station locations and evolve iteratively under fuzzy-evaluated fitness and epsilon-controlled feasibility conditions. Extensive simulation experiments are conducted based on realistic electric taxi operation scenarios， and the proposed FMPPSO algorithm is compared with several state-of-the-art multi-objective optimization algorithms. Experimental results demonstrate that FMPPSO achieves superior performance in terms of convergence speed， solution stability， and Pareto solution diversity. Quantitatively， the proposed method improves the final objective values by approximately 3.8% compared with benchmark algorithms， while also exhibiting faster convergence under the same computational budget.