# Two criteria in a problem that involves multiple-criteria decision-making

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?