## 4 Experiments (Application to [PERSON]'s Airline Passenger Satisfaction Data) and Discussion  
First, we would like to reveal some details of the operation of our approach to design FRBCs from the considered [PERSON]'s airline data. For this purpose, the MOEOA-based genetic learning and optimization experiments for a single learning-test data split are presented and discussed. The ratio of split of the original data was 1:9, i.e., only 10% of the whole data set (preserving the class proportions) was used as the learning data to build the system whereas the remaining 90% of the original data were used for testing purposes. The learning-test data split applied in our experiments is widely used in processing data sets with large number of data samples (in our case, we dealt with as many as 259,760 data samples). Such a data split not only reduces the computational complexity of the learning procedure but, more importantly, formulates much higher demands for the classification technique since \"generally, the larger the training dataset, the better the classification performance regardless of which classification algorithm is used\" (quotation from [27]). Therefore, the assumed data split poses a significant challenge for the system's design technique. For comparison purposes, Figure 3 presents two 10-element collections of non-dominated solutions (i.e., optimized FRBCs) obtained in a final generation of a single run of our FRBC's design technique using, independently, our SPEA3 and SPEA2 methods. Both collections represent the best available approximations of Pareto-optimal solutions generated by our SPEA3 and SPEA2, respectively. Particular solutions from a given front were characterized by different levels of optimized accuracy-interpretability trade-off \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Environmental Selection Procedure of SPEA2:** & **Our Original Environmental Selection Procedure Implemented in SPEA3:** & **Our Original Environmental Selection Procedure Implemented in SPEA3:** & **(a) gradually (i.e., in the subsequent generations of the optimization process) fills the archive with only such non-dominated solutions (if their number is lesser than the archive size, the best dominated solutions from the current population are also selected and copied to the archive to fully fill it), & **(b) truncates overfilled archive by removing from it solutions which have been dominated by any new solutions that have appeared in the current population, & **(b) truncates archive by removing from it solutions which have been dominated by any new solutions that have appeared in the current population, & **(c) gradually exchanges some non-dominated solutions between the archive and the current population in order to maximize the sum of distances between the nearest neighboring solutions in the archive.** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Differences between environmental selection procedures of SPEA2 and SPEA3. allowing the user to select a single solution (a specific FRBC) characterized by a desired level of compromise between the accuracy and interpretability. Figure 3 shows that our SPEA3-based approach outperforms the SPEA2-based one by generating the collection of solutions characterized by much-better-balanced distribution in the objective space (the solutions are distributed along the front in a much more even way). The accuracy- and interpretability-related numerical details of all SPEA3-based solutions from Figure 3 are collected in Table 3, in which \(n_{INP/R}\) is the number of input attributes per rule, \(ACC^{(lrn)}\) and \(ACC^{(lst)}\) are the percentages of correct decisions in the learning and test sets, respectively (the remaining parameters were defined earlier in the paper). Fuzzy rule bases of the first seven solutions from Figure 3 and Table 3 are presented in Tables 4 and 5 (membership functions of fuzzy sets used in those rule bases are shown in Figure 4). The remaining three solutions Nos.