# Fuzzy-Based Control System for Solar-Powered Bulk Service Queueing Model with Vacation
## 6 Methodological and Technical Details  
The fuzzy inference method has widespread applications in renewable energy systems, particularly in solar power management, where it aids in optimizing solar panel performance, regulating battery storage, enhancing power distribution efficiency, and adjusting solar tracking angles for optimal energy absorption. A key advantage of this approach is its ability to simultaneously evaluate multiple influencing factors, ensuring more precise and adaptive decision-making in dynamic energy environments.  
In these situations, the intricate relationships between input and output variables, along with the interdependencies among input factors, make it challenging to develop precise mathematical models. This is where fuzzy inference systems excel, as their If-Then rule-based approach leverages practical experience to facilitate real-time decision-making without relying on exact mathematical equations. While attaining a perfectly optimal solution through traditional modeling can be difficult, fuzzy inference greatly simplifies computations and provides a practical, efficient framework for optimizing solar power performance.  
While the fuzzy inference system offers valuable advantages for solar energy management, it is essential to recognize a key challenge--its reliability is not absolute due to inherent uncertainties in its design. One of the most significant sources of uncertainty is the construction of membership functions (MFs) for the fuzzy sets used in If-Then rules. Even with well-defined rules and an efficient inference mechanism guided by expert knowledge, inadequately designed membership functions can distort the reasoning process, leading to an inaccurate mapping between inputs and outputs. This, in turn, may diminish the system's responsiveness to subtle changes in input values.  
For instance, in the solar power system, uncertainties emerge when defining input variables like solar irradiance and battery charge level, raising critical questions such as  
* What is the most suitable type of membership function?
* How many membership functions should be used to represent \"solar irradiance\"?
* Should the membership functions for the same input overlap?  
These considerations also apply to output variables like solar power efficiency. While individual membership functions for each variable may seem logical, the underlying input-output relationships often remain obscured within a black box. To enhance the transparency and controllability of the fuzzy inference system, especially when using the  
\begin{table}
\begin{tabular}{l l l l l} \hline \multirow{2}{*}{**Rule**} & **IF Arrival** & **AND Service** & **THEN Performance** & \multirow{2}{*}{**Firing Strength**} \\  & **Rate Is...** & & & Is... \\ \hline R1 & Medium & Low & Poor & min (1.0, 1.0) = 1.0 \\ R2 & High & Low & Poor & min (0.5, 1.0) = 0.5 \\ R3 & Medium & Medium & Moderate & min (1.0, 0.0) = 0.0 \\ \hline \end{tabular}
\end{table}
Table 8: The Fuzzy rules evaluation.  
Mamdani inference method, it is essential to examine how membership functions shape the input-output dynamics in solar power optimization.  
We acknowledge the lack of clarity in linking the methodology to the results and have thoroughly revised the manuscript to explicitly connect each methodological component to the outcome.