I would like your valuable opinion on one issue:
I created a decision matrix considering two criteria and 10 alternatives, as below. My problem involves determining the optimal number of clusters from a dataset that has information about rural properties. So, basically, I use two criteria to know the ideal number of clusters. The alternatives are the number of clusters it can be. This decision matrix, I obtained using agglomerative hierarchical clustering algorithm.
nclusters(Alternatives) Criterion1 Criterion2 3 427.7037 1216.07483 4 2067.8457 315.11427 5 1797.6554 295.33840 6 1797.6554 295.33840 7 1798.7378 229.82400 8 1468.3216 229.82400 9 942.4955 229.82400 10 937.1313 229.31030 11 937.1313 229.31030 12 629.0550 29.85698
After obtaining this matrix, I used some multiple-criteria decision-making(MCDM), which are the weighted sum method (WSM), TOPSIS and VIKOR, to generate rankings of the alternatives. Then, I compare the rankings of both MCDM methods, and manage to generate a final ranking. So by chance, if rank = 1 is in the first row, it means that the ideal number of clusters is 3.
Now, I would like to know your opinion if it makes sense to use MCDM using only two criteria, even though there are 10 alternatives? I know that to be MCDM, you need to have more than one criterion. Of course, more criteria would help, but I only got those two.
What do you think?