<p>Battery energy storage systems (BESS) participating in day-ahead and real-time electricity market arbitrage face a critical trade-off between short-term economic revenue and long-term underlying electrochemical lifespan, particularly the non-linear damage induced by deep discharges. Traditional Model Predictive Control (MPC) and rule-based strategies typically rely on fixed penalty weights or rigid physical boundaries, struggling to achieve a dynamic balance between capturing price peaks and avoiding extreme State of Charge (SOC) conditions.To address this issue, this paper proposes a novel adaptive predictive control framework, termed Fuzzy Logic Controller-based Model Predictive Control (FLC-MPC). Specifically, a Fuzzy Logic Controller (FLC) serves as the upper-level decision module, dynamically adjusting the SOC deviation penalty weight in the underlying MPC cost function based on real-time electricity price fluctuations and current SOC conditions. Furthermore, to overcome the limitations of traditional linear throughput degradation models, a deep discharge implicit cost model based on a quadratic barrier function is formulated and integrated into the comprehensive health-economic benefit optimization system. Comprehensive ablation studies demonstrate that, compared with traditional aggressive MPC, conservative MPC, and industrial rule-based control, the proposed FLC-MPC algorithm achieves an effective Pareto trade-off. While maintaining an online solving efficiency of roughly 15&#xa0;ms, the strategy effectively prevents the system from operating in the critical low-SOC region, substantially mitigates the equivalent physical State of Health (SOH) fade, and optimizes the comprehensive final benefit from a life-cycle perspective. This study provides an industry-applicable adaptive scheduling solution for BESS that combines high economic returns, robust hardware protection, and transparent explainability.</p>