## 3 Results and Discussion  
GRA is applied for optimal machining tool selection based on categorical and numerical parameters such as machine type, cutting speed, and workpiece thickness to obtain the best characteristics in terms of machining time, dimensional accuracy, kerf width, and surface roughness. Therefore, the first step is to measure and systematize the output parameters as shown in Table 4. After the measurement of the physical quantities according to which each machine tool is evaluated, the second step of the grey relational analysis follows, namely normalization. It is well known that raw experimental data cannot be used for GRA. Therefore, these data should be processed in a quantitative way that is suitable for grey scale analysis. Then, the experimental data are converted into values between 0.00 and 1.00. The third step is the calculation of the GRC, which consists of several steps. First, the signal-to-noise ratio must be determined, which indicates how the response changes relative to the nominal or target value under different noise conditions. There are two signal-to-noise ratios that are of general interest to GRA: Smaller-the-Better and Larger-the-Better. Since all output parameters tend to a minimum, the target value of all input parameters (MT, DA, KW, and SR) is the-lesser-the-better, then the normalized values of these parameters are calculated according to Equation (2). The results of normalized values, deviation sequences, grey correlation coefficients, and grey correlation degrees are shown in Table 5.  
In the preceding methodology, each output parameter is classified as a \"smaller-better\" quality attribute. The results presented have a certain degree of uncertainty. It is such data that lends itself to further processing using fuzzy logic. Thus, the complicated multi-objective problem of machine tool selection can be solved by integrating GRA and FL. According to previous research, Mamdani inference system is the most commonly used. Apart from the fact that the rule base is intuitive and easier to interpret, there are two main reasons for its use. The first is that it allows manual adjustment of the input functions, and the second is that the output is also in the form of a fuzzy set. It is capable of processing numerical data and linguistic knowledge simultaneously. The Mamdani inference system was used to determine the grey fuzzy relation coefficient. The methodology is divided into four phases. Since fuzzy logic uses linguistic variables, the first phase involved the selection of input/output variables represented in the linguistic format. The selection of fuzzy intervals is an intuitive procedure that depends on the experience of the fuzzy modeler. It has been shown that it is best to divide an input variable into three intervals, for example, low, medium, and high. The linguistic variables for input and output with their fuzzy intervals are listed in Table 6.  
The selection of membership functions for input and output variables represents the second phase. Fuzzy intervals are determined based on the intuition and experience of the creator of the fuzzy model. A more accurate model can be generated by using more MFs. However, the time needed to create the rules increases and the interpretability of the model deteriorates. An example of such a function is a Gbell function. In modelling the GRG in this research, the Gbell type of membership functions is used. The membership functions of GRC for MT are shown in Figure 5. The same form and membership function