# A Credit Rating Model in a Fuzzy Inference System Environment
## 4 Data Analysis
We utilized numerous IF-THEN rules to evaluate the input variables as shown in Table 5. These rules are based on input variables and their membership functions. We extracted the data of each company by considering the practical variables we obtained via the Delphi method. We then identified the highest percentage, average, and the lowest percentage of the triangular fuzzy membership function of each variable. As specified above (Equation (1)), a triangular membership function uses the parameters \(a\), \(b\), and \(m\). The percentage values are denoted as alpha-cuts and are calculated according to [63]. An alpha-cut corresponds to the set of elements whose membership grades are greater than or equal to the specified value of alpha. Equation (3) shows how the alpha-cut is calculated:  
\[[\mathrm{A}]^{\alpha}=[a-m(1-\alpha),a+b(1-\alpha)]. \tag{3}\]  
We combined them based on the FIS and separated them into seven categories based on their levels of risk. This study helps managers make decisions and decreases the probability of a company defaulting. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Range** \\ \hline  & very poor \\ \cline{2-3}  & poor \\ \cline{2-3}
**quality and transparency of reporting** & average \\ \cline{2-3}  & good \\ \cline{2-3}  & very good \\ \hline  & enemy \\ \cline{2-3}  & aggressive \\ \cline{2-3}
**competitiveness** & average \\ \cline{2-3}  & suitable \\ \cline{2-3}  & without threat \\ \hline  & starter \\ \cline{2-3}  & small performer \\ \cline{2-3}
**company position** & middle performer \\ \cline{2-3}  & main performer \\ \cline{2-3}  & market leader \\ \hline  & highest risk \\ \cline{2-3}  & almost high risk \\ \cline{2-3}  & often risk \\ \cline{2-3}
**country risk** & middle risk \\ \cline{2-3}  & low risk \\ \cline{2-3}  & very low risk \\ \cline{2-3}  & no risk \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
In Table 5, all variables which are extracted from the model and their data are transferred to fuzzy data. The change from crisp data to fuzzy data is based on Table 4. Based on the FIS logic and following an OECD (Organisation for Economic Co-operation and Development) rating concept based on seven categories or classes, the data is classified, that is, the rankings of customer companies are determined. The membership function of each class is shown below in Figure 1. The figure presents an overview of the seven individual membership functions which are mathematically specified in Equations (4)-(10). Some researchers believe that the use of the Mamdani and Sugeno methods yields the same results [64; 65]. \[\mu_{\overline{A_{7}}}=\left\{ \begin{array}{c}\frac{x-16.67}{2.97 +16.67},-16.67\leq x\leq-2.97\\ \frac{16.67-x}{16.67+2.97},-2.97\leq x\leq 16.67\\ 0,\quad\quad\text{otherwise}\end{array} \right. \tag{4}\]  
\[\mu_{\overline{A_{6}}}=\left\{ \begin{array}{c}\frac{x-0}{16.67 -0},0\leq x\leq 16.67\\ \frac{33.33-x}{33.33-16.67},16.67\leq x\leq 33.33\\ 0,\quad\text{otherwise}\end{array} \right. \tag{5}\]  
\[\mu_{\overline{A_{5}}}=\left\{ \begin{array}{c}\frac{x-16.67}{33.33 -16.67},16.67\leq x\leq 33.33\\ \frac{50-x}{50-33.33},33.33\leq x\leq 50\\ 0,\quad\text{otherwise}\end{array} \right. \tag{6}\]  
\[\mu_{\overline{A_{4}}}=\left\{ \begin{array}{c}\frac{x-33.33}{50 -33.33},33.33\leq x\leq 50\\ \frac{66.67-x}{66.67-50},50\leq x\leq 66.67\\ 0,\quad\text{otherwise}\end{array} \right. \tag{7}\]  
\[\mu_{\overline{A_{5}}}=\left\{ \begin{array}{c}\frac{x-50}{66.67 -50},50\leq x\leq 66.67\\ \frac{83.33-x}{83.33-66.67},66.67\leq x\leq 83.33\\ 0,\quad\text{otherwise}\end{array} \right. \tag{8}\]  
\[\mu_{\overline{A_{2}}}=\left\{ \begin{array}{c}\frac{x-66.67}{83.33 -66.67},66.67\leq x\leq 83.33\\ \frac{100-x}{100-83.33},83.33\leq x\leq 100\\ 0,\quad\text{otherwise}\end{array} \right. \tag{9}\]  
\[\mu_{\overline{A_{1}}}=\left\{ \begin{array}{c}\frac{x-83.33}{10 -83.33},83.33\leq x\leq 100\\ \frac{116.7-x}{116.7-100},100\leq x\leq 116.7\\ 0,\quad\text{otherwise}\end{array} \right. \tag{10}\]  
Figure 1: Membership function of output variable.