Hi
I saw you've listed TODIM as one of your TO-Dos in README.md. I'm willing to implement it. However, I have some ambiguities in some steps of it. The method has originated through this study: https://www.academia.edu/download/56873871/1991_TODIM_Basic_and_application....pdf

My ambiguities are as follows:

• They claim that a score of 0-9 can be assigned to each alternative with respect to criteria. However, they should have mentioned how they chose the scores. For example, how did they figure out (or assign) a score of 1 to $i'th$ alternative in the $c'th$ criteria?

• I'm confused about how did they finally find the weight of each criterion since they mentioned two approaches:

  the scale from 1 to 9 is employed for relative comparisons between criteria. The use of this 1—9 scale relies on the latest formulation of the AHP method [17, 18].
  [17] Saaty T.L., Multicriteria Decision Making, The Analytic Hierarchy Process, Thomas Saaty (ed), 1988.

  And in a bit further, they mentioned:

  the weights of criteria are computed by averaging over the normalized columns.

  As far as I know, In the AHP, the importance of each criterion is entered by the user, and the relative importance matrix over the set of given criteria is calculated:

  julia> foo = [1, 2, 3]
  3-element Vector{Int64}:
  1
  2
  3
  
  # the following is the pairwise comparison of criteria
  julia> compar = foo./[foo foo foo]'
  3×3 Matrix{Float64}:
  1.0  0.5  0.333333
  2.0  1.0  0.666667
  3.0  1.5  1.0

  Afterward, the importance weights of the criteria (which tells how much each criterion will factor into the decision) are calculated using Geometric Mean:

  julia> imp_weights = reduce(*, compar, dims=2).^(-1/length(foo))
  3×1 Matrix{Float64}:
  1.8171205928321397
  0.9085602964160698
  0.6057068642773799

  Finally, the weight of each criterion can be calculated using the following equation:
  $W_c=\frac{imp\textunderscore weights_c}{\sum_{j=1} {imp\textunderscore weights}_j}$
  where $c$ is the $c'th$ criterion, $imp\textunderscore weights_c$ is the importance weights of the $c'th$ criterion

  julia> weights = imp_weights./sum(imp_weights)
  3×1 Matrix{Float64}:
  0.5454545454545454
  0.2727272727272727
  0.1818181818181818

  But in this process, we do not have an operation like "averaging over normalized weights". So a clarification about whether they achieved the weight of criteria using the same approach in the AHP is needed.

• The last ambiguity is where they used a parameter named $a_{rc}$ in determining the dominance of the $i'th$ alternative over the $j'th$ alternative:
  $\delta_{(i, j)}=\sum [a_{rc}(w_{ic} - w_{jc})]$
  They didn't mention what's $a$ in the above (or maybe I haven't grasped it). But I guess it should be the relative importance of the reference criterion over the $c'th$ criterion.