**4. Overview of Interval Type-2 Fuzzy Logic Systems**

The first interval type-2 method was proposed by Zadeh in 1975. Then, many other authors started to implement the IT-2 FLC system in many applications. The IT-2 FLC method consists of five components: fuzzifier, rules, inference engine, type reducer, and defuzzifier. The structure of the IT-2 FLC method is given in Figure 3. The crisp inputs of the IT-2 FLC are obtained from the input sensors. The fuzzifier converts the physical input values into a normalized fuzzy subset. The inference engine of the IT-2 FLC system uses the same rules as those used in a T-1 FLC system. Then, the type reducer converts the IT-2 FLC to a T-1 FLC. Finally, defuzzification is usually called output processing [32]. The fuzzifier is the first stage in applying fuzzy logic control. The fuzzifier converts the physical input values into a normalized fuzzy subset. The physical input values of the sensors are mapped to a set of input fuzzy values [0, 1] by the membership functions. Finally, the fuzzifier converts the physical input values to a fuzzy input of the inference engine [33]. The general membership functions of the IT-2 FLC are given in Figure 4.

**Figure 3.** The general structure of the interval type-2 fuzzy logic control.

**Figure 4.** Proposed structure of the interval type 2 fuzzy logic control (IT-2 FLC) system.

The inference engine is the second stage in applying fuzzy logic control. The inference engine is regarded as a transformer, which from a given input maps an output by using linguistic variables. The inference engine generates functional mapping between the output and the input using fuzzy mapping rules. The inputs of the inference engine are implemented by a set of fuzzy mapping rules (if/then). The fuzzy mapping rules (if/then) decide a given condition using linguistic variables, and, then, the fuzzy sets convert to a set of fuzzy outputs [34,35]. All 25 rules and membership functions for the IT-2 FLC are selected and given in Figure 4. Fuzzy rules are written as follows: if (input1 is membership function1) and/or then (output is output membership function).

Mamdani systems have widespread acceptance, are well suited to human input, and are intuitive. Therefore, the Mamdani system was used in this study.

The defuzzifier is the third stage in applying fuzzy logic control. The defuzzifier converts the fuzzy output available into the control objective. The output of the inference engine is still a linguistic variable. This linguistic variable is transformed into the crisp output by the defuzzifier stage. This stage is regarded as a conversion from the fuzzy output to the crisp output needed for real applications. The mean of the maximum technique, a center of gravity technique, and height techniques are commonly used in defuzzification. The Karnik–Mendel algorithm was implemented in this study as the defuzzification method. The Karnik–Mendel algorithm identifies the largest and smallest elements among the centroids [36]. This method converts fuzzy values into crisp system output values, expressed as

$$y(\mathbf{x}) = \frac{y\_1 + y\_r}{2} \tag{8}$$
