### Table 1 Interval-valued distances estimated by the human subject.

"... In PAGE 12: ... Because of the difficulty of precisely assessing the distances, the sub- ject was allowed to express his evaluations using intervals. These intervals are given in Table1 . The results obtained from both methods are given in Fig- ures 4 and 5.... ..."

### Table 2: Relation Rain+ with intervals of values.

### Table 2: Fats and oils data: interval-valued distances from Table 1.

2000

"... In PAGE 12: ... The objective of the analysis is to nd a meaningful feature space with reduced dimension, allowing to reveal the underlying structure of the data. In order to apply our approach, an interval-valued distance matrix was rst computed using Eqs (19) and (20) ( Table2 ). Results obtained with the metric hyper- sphere and hyperbox models are shown in Figs (3-4) and (5-6), respectively.... ..."

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### Table 9 The interval-valued dissimilarity matrix given in Example 2 D

in Interval

"... In PAGE 5: ... Next, we use another numerical example to demonstrate how to apply the proposed method for the situation of only one decision maker. This example has six objects and the dissimilarity value is given using the interval- valued data as shown in Table9 . The last row represents the degrees of pessimistic index.... ..."

### Table 5: Interval-valued solution resulting from the computational process recorded in Table 7

"... In PAGE 8: ... This strategy was applied to the solution from Table 5. Before this, however, all probabilities from Table5 were cut to 2 decimal points, since all the input densities were also given with this precision, so the resulting tight dis- tribution, which is contained in Table 9, has all the probabilities with two decimal digits. pi x1 = 0 x1 = 1 x2 = 0 x3 = 0 0.... ..."

### Table 8: Tight interval-valued solution received from the solution in Table 4

"... In PAGE 8: ... Table8 presents the result of the simplest version of the tightening process when applied to a distribution from Table 4.... ..."

### Table 9: Tight interval-valued solution received from the solution in Table 5

"... In PAGE 8: ... This strategy was applied to the solution from Table 5. Before this, however, all probabilities from Table 5 were cut to 2 decimal points, since all the input densities were also given with this precision, so the resulting tight dis- tribution, which is contained in Table9 , has all the probabilities with two decimal digits.... ..."