## 1 Introduction
This experiment opened avenues for FLC to address imprecise linguistic variables in real-world scenarios, including industrial processes, traffic control, and robotics. It demonstrated that FLC could outperform conventional methods in environments marked by high levels of uncertainty and complexity. [PERSON] et al. [15] enhanced the efficiency of a hybrid photovoltaic proton exchange membrane electrolyzer system by controlling the water temperature of the electrolyzer using FLC. [PERSON] et al. [16] implemented an FLC controller to maintain the stack temperature in a medium-sized 5 kW residential PEM fuel cell system during dynamic load profiles. Further advancements in FLC included the development of multivariable fuzzy controllers, which expanded the FLC approach to handle multiple-input and multiple-output (MIMO) systems, enhancing its control efficiency in highly complex environments. [PERSON] et al. [17] introduced a multivariable fuzzy controller based on [PERSON]'s implication, which provided a more robust handling of interactions between variables in systems with complex interdependencies. More recently, [PERSON] et al. [18] applied a MIMO FLC method for real-time temperature and humidity management in PEM fuel cells, demonstrating significantly improved performance compared to conventional PID control systems, particularly in maintaining system stability and efficiency under dynamic operating conditions. [PERSON] et al. [19] developed a liquid-cooled PEM fuel cell control model incorporating thermal, electrical, and airflow components, and they suggested an adaptive control strategy for managing thermal dynamics during system startup and load changing. [PERSON] et al. [20] proposed a nonlinear observer-based multivariable sliding mode control scheme for PEM fuel cell systems to maintain various parameters including the output voltage, compressor gas flow rate, fuel cell system temperature, and hydrogen production rate from the water electrolyzer. Most existing thermal control methods for electrolyzers involve adjusting the flow rate of chilled water to either the electrolysis stack or the heat exchanger for effective cooling. Typically, these methods separate system cooling into two parts: cooling the hydrogen and cooling the electrolysis stack. However, due to space and cost considerations, our experimental setup deviated from conventional designs by integrating both cooling components to share a single chiller. An electric three-way valve was installed at the junction of gas and electrolyte cooling to regulate the flow rate of chilled water on both sides. The electric three-way valve cannot adjust the flow rate in real-time due to the delay in angle switching, which hinders precise control. Unlike other studies where cooling was achieved by directly controlling the flow rate of the chilled water, in this experiment, the chiller itself cannot adjust the flow rate and relies on the electric three-way valve for adjustments, making it difficult to achieve the ideal flow rate instantaneously. The chilled water temperature in this study also differs from others, being 5 \({}^{\circ}\)C instead of room-temperature water, which makes the flow rate even harder to control. Hence, this study proposes a novel thermal control strategy combining FLC and a long short-term memory neural network (LSTMNN), specifically designed for this experimental setup, to enhance the system's precision and stability. FLC can handle system uncertainty and nonlinearity, while the LSTMNN can predict temperature change trends. The LSTMNN, a type of recurrent neural network (RNN), is widely used for time series prediction due to its ability to capture both short-term and long-term dependencies. Originally developed by [PERSON] and [PERSON], the LSTMNN addresses the vanishing gradient problem that often plagues conventional RNNs, making it particularly effective for tasks involving sequential data.