## 2 Related Work  
[PERSON] published theorems related to fuzzy algorithms [10]. These theorems emphasize the significance of fuzzy problems instead of those involving uncertain data, including information processing, artificial intelligence, or decision-making processes. These conceptsare called fuzzy algorithms, where fuzzification is the foundational method for converting conventional (non-fuzzy) data into fuzzy statements that encompass fuzzy sets. Following this, fuzzification is continually refined and examined due to its ability to transform a precise quantity into a fuzzy representation [11], with the fuzzification process most accurately described by a membership function that indicates the degree of truth within fuzzy logic [12]. Graphical representations, such as membership functions, serve to illustrate fuzzy sets. An extensive literature review of fuzzy logic modeling identifies five principal types of membership functions frequently employed in industrial applications: triangular, trapezoidal, Gaussian, bell-shaped, and polynomial [4]. Evaluating and selecting an appropriate MF is critical to the modeling phase of an inference system. Numerous contributions have emerged within this framework to recommend MFs tailored to specific challenges in fuzzy logic controllers. [PERSON] et al. [7] present a study grounded in simulations regarding the fuzzy control of antenna azimuth positioning, where three membership functions--triangular, trapezoidal, and Gaussian--were assessed. The input and output variables of the Universe of Discourse (UoD) included the error (in degrees), the change in the error (in degrees), and the control action (in volts). This research effectively illustrated the impact of MFs on the problem at hand, revealing that the triangular MF exhibited superior performance concerning steady-state behavior. Conversely, the Gaussian MF performed inadequately, demonstrating that it is more suitable for systems dealing with probabilities and statistics. Similarly, it is feasible to examine other studies that have assessed MFs, including an evaluation of MFs in the context of induction motor drives, where five MFs were analyzed, one of which was the sigmoidal function. The findings indicate that the triangular MF yielded the most favorable performance. Nonetheless, the trapezoidal approach also demonstrated commendable results, facilitating the implementation of this category of control systems [3]. The portfolio optimization problem is characterized as a selection process whereby the investor determines the appropriate proportion of securities and other assets. Four MFs were scrutinized, and the numerical simulation indicated that the triangular MF adequately addressed the problem. However, uncertain measures exhibit greater resilience to alterations in shape, underscoring the need for thorough analysis of the number of triangles involved [13]. Furthermore, [PERSON] and [PERSON] [14] conducted a comparative evaluation of the MFs used to analyze the output performance of a solar photovoltaic array panel. The Mean Square of the Errors (MSE) was employed to correct the trends and assess the effectiveness of each method. The findings indicated that the triangular MF yielded the most favorable results, closely followed by the trapezoidal MF, while the Gaussian MF produced the least favorable outcomes. A similar comparison was conducted concerning the construction of a fuzzy logic controller to optimize the Maximum Power Point Tracking (MPPT) of solar photovoltaics. The results of various MFs were evaluated to facilitate a comparison and select the optimal one. The triangular, trapezoidal, Gaussian, and GBell functions were considered using analogous data. According to the results, applying trapezoidal and GBell functions surpassed the triangular and Gaussian methods. Although these two methods exhibited identical results at lower frequencies (5 and 10 kHz), when the frequency of change was increased to 20 kHz, the GBell method demonstrated superior outcomes compared to the trapezoidal method [15].