## 1 Introduction  
Today, diverse methods exist for analyzing and publishing data among academic domains. Usually, values are categorized by classes (groups) or are transformed into intervals (discretized) to be understood by people (e.g., dogs are part of the animal class). However, some objects do not have precisely defined membership criteria in the real world (e.g., come home soon). To deal with these cases, [PERSON] addressed the uncertainty between objects and science in 1965 [1], when a new theory, called fuzzy logic and approximate reasoning, originated, which has been used to address uncertainty through mathematical functions. Approximate reasoning and fuzzy logic have been probed in multiple knowledge domains, such as chemical science, the healthcare industry, agriculture, political science, operations research, households, and, of course, environmental sciences [2]. They generate well-accepted, traceable, and robust solutions to complex problems using human logic with low computing costs. Fuzzy logic itself is not fuzzy. It is focused on dealing with the fuzziness in data. To achieve this, a fuzzy controller has three core tasks: the fuzzification methods, the inference mechanism (a base of rules), and the defuzzification methods. For the fuzzification task, it is known that a membership function characterizes fuzziness. Therefore, this leads to representing Membership Functions (MFs) as the degree of truth in fuzzy logic. MFs are used to convert the supplied crisp sets into the fuzzy inference system, allowing the MFs to describe the fuzziness in the data. Graphical forms can represent many MFs. In the context of the work of [3], who also evaluated MFs for their study field, it is possible to list the following forms of MFs: triangular, trapezoidal, Gaussian, two-sided Gaussian, bell-shaped, sigmoid-right, sigmoid-left, difference-sigmoid, polynomial-Z, polynomial-S, and polynomial-pi. However, according to a review of real-world applications by [4], the first four MFs are used in production environments. Concerning the inference mechanism, three main approaches are present in the literature: (a) [PERSON]'s fuzzy inference, developed using a set of linguistic variables, where the fuzzy rules in such a control system are obtained from experienced human operators; (b) the Takagi-Sugeno fuzzy method, where the antecedent of the rule is in fuzzy form, but the consequent of the rule is represented by a function \(z=f(x,y)\); if \(f()\) is constant, then the inference system is zero order, which is a particular case of the Mamdani fuzzy model, making this the best option for mathematical analysis; and (c) the Tsukamoto fuzzy inference, where a fuzzy set with a monotonic MF represents the rule. This system is not commonly used because it is less transparent than the Mamdani fuzzy model [5]. In a subsequent scenario, an output generated by the inference system is classified as a fuzzy set; consequently, it necessitates the conversion into a crisp value. The defuzzification process is implemented in this context, wherein a mathematical function facilitates this conversion. The established methods include the centroid, bisector, Largest Of Maximum (LOM), Smallest Of Maximum (SOM), and Middle Of Maximum (MOM) [6]. These three fundamental tasks enable the development of diverse fuzzy systems for prediction, optimization, estimation, control, selection, and monitoring [4]. Nevertheless, it is imperative to ascertain the appropriate method for each task to achieve a high-quality system, irrespective of its intended purpose, as required from a standard perspective. Empirical evaluations of MFs to identify the most effective estimator predicated on fuzzy logic and approximate reasoning have been conducted in various domains, including controlled induction motor drives [3], electronic controller performance [7], and power systems [8]. Nonetheless, a comprehensive assessment of the relationship between MFs and defuzzification methodologies is lacking.