## 4 Experiments (Application to [PERSON]'s Airline Passenger Satisfaction Data) and Discussion
\(ACC_{1}^{(st)}\) is the test-data-accuracy of the system exclusively based on the most significant input attribute (attribute \"Inflight entertainment\", system (solution) No. 1, accuracy 75.2%). \(\Delta ACC_{j}^{(st)}\), \(j=2,3,\dots\) is the accuracy increase following the inclusion of 2 nd, 3 rd,...most significant attribute into the system. For instance, the inclusion of \"Seat comfort\" (2 nd most significant attribute) yields +2.0% increase in test-data accuracy and is related to system (solution) No. 2. In turn, the inclusion of \"Type of travel\" and \"Inflight WiFi service\" (3 rd most significant attributes) gives further 3.2% test-data-accuracy-increase and is related to solution No. 3, etc. The above presented reasoning is correct provided that there is no \"overlapping\" of some of input attributes over the other ones in the airline passenger satisfaction data. In order to verify that aspect of airline data, we remove from the original data set the so-far most significant attribute (i.e., \"Inflight entertainment\") and we repeat, in an analogous way, the learning experiment. Its results are presented in Part B of Table 6 giving \"Online boarding\" attribute the most significant place. Clearly \"Online boarding\" which occupied a low position in experiment of Part A was \"overlapped\" by \"Inflight-entertainment\". In the next step, we remove \"Online boarding\" from the present data set and repeat the learning experiment--see Part C of Table 6--obtaining \"Ease of online booking\" as the most significant attribute at this stage. It occupied second position in experiments of Part B. Therefore, we can conclude that it was not \"overlapped\" by \"Online boarding\". We repeat analogous experiments several times, i.e., removing the most significant attribute at a given stage and repeating the learning process on the reduced data--see Parts D, E, F of Table 7, and G, H, I of Table 8. In such a way, we arrive to the final hierarchy of input attribute significance from the perspective of the airline passenger satisfaction. It is shown in the left part of Table 9. \(\Delta CC_{1}^{(st)}\) of Table 9 means the same as in Tables 6-8, i.e., the test-data-accuracy of the system exclusively based on a single attribute (listed to the left of \(ACC_{1}^{(st)}\) in Table 9). The right part of Table 9 presents the results of alternative approach by [PERSON] [24]. The paper [24], to our knowledge, is the only available now reference addressing the considered data set (most probably due to the fact that the data set has been published most recently). The approach of [24] uses SAS system to calculate the mean values of particular input attributes separately for both classes of passengers (satisfied and neutral or dissatisfied) and to build decision tree to determine the attribute importance hierarchy. Figure 5 summarizes, in a graphical form, details of our approach (the left part of a block scheme of Figure 5) and the alternative [PERSON]'s method [24] (the right part of that block scheme) for the purpose of their comparative analysis regarding the determination of the final hierarchy of input attribute significance. Data preprocessing, data partitioning, learning process, selection of the most significant input attributes, and determining the final hierarchy of attribute significance are the main stages of performing that task. Since 9 most significant input attributes were selected in the alternative work [24], we also select the same number of the most significant attributes. Although both approaches select \"Inflight entertainment\" as the most significant attribute (as shown in Table 9), our approach provides much deeper insight into the mechanisms encoded in the considered airline data set (see collections of easily-interpretable linguistic, fuzzy classification rules presented in Tables 4 and 5). An important part of our work is the cross-validation experiment with 1:9 learning-test data split ratio. Each single learning experiment starts with generation of a Pareto-frontapproximation.