# How to create a final ranking considering four multi-criteria methods

The dataset below presents the rank of four multicriteria methods (MCDM), which are Promethee, WSM, TOPSIS and VIKOR. Note that some methods give similar results and others do not. In the case for the alternative with 2 clusters, both presented the same result, however for the alternatives with 5 clusters, for example, both presented different results. Therefore, I would like to know what metric I can use to choose the best rank for these cases. The idea is to create one more column with a final rank based on the four multicriteria methods for all alternatives.

``````df1<-structure(list(nclusters = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25), Promethee = c(1L,
6L, 4L, 5L, 2L, 3L, 23L, 24L, 22L, 21L, 20L, 19L, 17L, 18L, 9L,
10L, 11L, 12L, 13L, 14L, 15L, 16L, 8L, 7L), WSM = c(1, 24, 20,
19, 18, 17, 23, 22, 21, 16, 15, 14, 13, 12, 7, 6, 5, 4, 11, 10,
9, 8, 3, 2), TOPSIS = c(1L, 24L, 20L, 21L, 18L, 19L, 22L, 23L,
17L, 16L, 15L, 14L, 12L, 13L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L,
3L, 2L), VIKOR = c(1L, 24L, 19L, 20L, 17L, 18L, 22L, 23L, 21L,
16L, 15L, 14L, 12L, 13L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 3L,
2L)), class = "data.frame", row.names = c(NA, -24L))

> df1
nclusters Promethee WSM TOPSIS VIKOR
1          2         1   1      1     1
2          3         6  24     24    24
3          4         4  20     20    19
4          5         5  19     21    20
5          6         2  18     18    17
6          7         3  17     19    18
7          8        23  23     22    22
8          9        24  22     23    23
9         10        22  21     17    21
10        11        21  16     16    16
11        12        20  15     15    15
12        13        19  14     14    14
13        14        17  13     12    12
14        15        18  12     13    13
15        16         9   7      4     4
16        17        10   6      5     5
17        18        11   5      6     6
18        19        12   4      7     7
19        20        13  11      8     8
20        21        14  10      9     9
21        22        15   9     10    10
22        23        16   8     11    11
23        24         8   3      3     3
24        25         7   2      2     2
``````

An example that can better illustrate what I want is what the `MetaRanking` function does in the MCDM package which can be seen here: https://cran.r-project.org/web/packages/MCDM/MCDM.pdf

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