## 5 Results and Evaluations
These rules are essential for the proper functioning of the fuzzy model and to describe the behavior of the fuzzy system. The antecedent part of fuzzy rules includes all the actual combinations of language values of the input variables. The result is the evaluation of all combinations, i.e., the assignment of linguistic values to the output variables. The created fuzzy inference model is necessary to verify whether the presented outputs are sufficiently accurate and applicable in practice. For this purpose, several evaluation metrics are selected, which are used to verify and evaluate the error rate or accuracy of individual illustrative models of fuzzy logic. Specifically, the Root Mean Square Deviation (_RMSE_) indicator is selected, which compares the original data \(y_{t}\) and the data obtained from the output of the model \(\dot{y}_{t}\). RMSE assigns a relatively higher weight to large prediction errors. This is especially useful when high error rates are undesirable. In the case of predicting the development of the stock index, this indicator can be considered the most appropriate. This indicator is also applied in many equally focused studies such as [16; 17; 23]. In addition to the above indicator, Mean Absolute Percentage Error (_MAPE_), Mean Absolute Error (_MAE_), Mean Squared Error (_MSE_) indicators are also applied and calculated. _MAPE_ is suitable for comparing forecasts between different time series because it is expressed on a relative scale. The _MAE_ indicates the size of the data set prediction error regardless of the direction of its development. It basically gives a linear error rate, which means that the differences have the same average weight. _MSE_ is a suitable indicator to determine whether the examined data set does not show more outlying prediction values showing a high error rate. Unlike _MAE_, it places more weight on outliers due to the quadratic part of its calculation. However, this means that a single bad prediction can significantly increase the error rate. In particular, _RMSE_ can be reported together with _MAE_, because the larger the size of the deviation between the two indicators, the greater the variance in the error rate of the examined data set. Based on the outputs of these indicators, it is then possible to evaluate which fuzzy model, or which type of fuzzy function and  
Table 3 shows the evaluation of accuracy and error rate for triangular MF IT2 FL. A total of nine models were examined, which differed in the degree of uncertainty involved in the membership functions. The RMSE indicator was used to compare the quality of models. A lower RMSE value indicates a better model. The table shows that model 8 had a value of 0.1512, which indicates a better model compared to another model form triangular IT2 MF. The value of the MAPE indicator is a dimensionless characteristic by which different models can be compared. The highest value was reached by model 1 with a MAPE indicator value of 90.32, while the lowest value was shown by model 7 with a MAPE indicator value of 74.74. Thus, in terms of this indicator, model 7 achieved a lower error rate and deviated less from reality in comparison with all other models with the same MF. The shortcoming in the MAE indicator was eliminated by first converting each error to a positive value using an absolute value, and the errors from all observations were then averaged as in the first cases. The MSE indicator converted negative error values to positive ones by amplifying them. The result is a large number and because large errors, i.e., large deviations of the forecasts from the actual situation, were given a large weight, while small errors were given much less weight. For both of these indicators, model 8 achieved the lowest error rate with a value of 0.1456. The trapezoidal MF IT2 FL in Table 4 can be evaluated similarly. The same indicators as for triangular MFs were used for evaluation and comparison. The lowest RMSE is in the last model examined with a high level of uncertainty, namely with LowerScale 0.6 and LowerLag 0.4.