## 4 Design Example: The High-Speed Press
### Comparison with HAD  
The HMADM model constructed in Section 4.1 was also solved by the HAD method proposed in our previous work [22], which calculates the total information contents of alternative structural configurations based on distance measure. Specifically, the common range of the \(i\)th attribute for the \(i\)th alternative is represented by its Euclidean distance to the \(j\)th NIS while the system range is represented by the distance between the PIS and NIS. The total information content of the \(i\)th alternative is the sum of the information content for all of its attributes, which are calculated by taking the negative logarithm of the ratio of common range to system range. It is worth noting that both the total information content in HAD and the relative closeness coefficient in the proposed HTOPSIS are calculated based on distance measure. However, a larger distance of an alternative to NIS leads to a higher relative closeness coefficient but a lower information content. Therefore, the configuration with the minimum total information content should be chosen as the optimal design in HAD. The detailed implementation of HAD is not given here for the sake of brevity. The information contents and ranking results of the nine alternative structural configurations in Table 3 obtained by HAD are listed in Table 8. It can be seen that the 4 th structural configuration has the minimum total information content of 0.3669, and thus is still chosen as the optimum design according to the results obtained by HAD. By comparing Tables 7 and 8, it can be seen that the rank orders of the nine alternative structural configurations obtained by the proposed HTOPSIS are similar to those obtained by HAD.  
The small difference between the ranking results of the proposed HTOPSIS and HAD comes from their different treatment of the relative importance of heterogeneous attributes. Specifically, the proposed HTOPSIS represents the relative importance of different attributes by their corresponding weights, while HAD represents the relative importance of different attributes by their corresponding system ranges. Moreover, the interdependency among attributes \(a_{3}\) and \(a_{4}\) (indicating the natural  
Figure 4: High-speed press developed from the optimum design obtained by the proposed heterogeneous technique for order preference by similarity to an ideal solution (HTOPSIS).  
frequencies of press slider closest to the punching frequency of 1.33-4 Hz and working frequency of 50 Hz) as well as attribute \(a_{1}\) (indicating the maximum deformation of press slider) can also lead to differences in the ranking results.  
The proposed HTOPSIS has the following advantages over HAD in solving HMADM problems with deviation and fixation attributes. Firstly, it relaxes the strict requirement of independency among different attributes in HMADM problems, and thus it is more suitable for solving HMADM problems with large number of attributes than HAD. Actually, it can be applied to any HMADM problem, because there are no prerequisites for its application. Secondly, the ranking of different alternatives is more efficient in HTOPSIS than in HAD because the calculation of relative closeness coefficients in HTOPSIS is much simpler than the calculation of information contents in HAD.