#170

Dear Bartosz Paradowski, Bartłomiej Kizielewicz, Wojciech Sałabun

I read your paper:

Equal Criteria Influence Approach (ECIA): Balancing Criteria

Impact in Multi-Criteria Decision Analysis

My comments:

1- In abstract you say “Traditional approaches to weighting criteria often result in insufficient consideration of the varying influence of criteria on decision outcomes”

True, but in my opinion not in the sense you assert.

The main problem with criteria in MCDM methods is that from the beginning in the modelling the initial matrix, they are unable, in most cases, to model reality, and thus, are only coarse approximations.

As an example, they do not consider that resources are finite, nor that alternatives may be inclusive or exclusive, or that there could be dependency between alternatives, or that some performance values may be negative, or that criteria may be not constant since their performance values may change as a function of time, as happens very often in practice, in most real-life scenarios, etc.

It is also difficult to understand that criteria must equalize their impacts on alternatives. If all criteria have the same impact, how can they evaluate alternatives? This concept collides with Shannon Theorem that says that criteria must be weighted according to the discrimination or dispersion of the performance values each one contains

2- “It allows the selection of an appropriate decision option and the determination of the relevance of individual criteria”

I might agree with this, however, it appears that you neglect to consider that a decision matrix represents a system, and as that, all criteria values are related in greater or lesser degree, as Systems’ Theory claims.

3- “Conversely, the objective approach relies on using measures of information and analytical data to determine the significance of criteria. Mathematical and statistical tools are used in this case, such as determining weights using entropy, standard deviation, variance, or Pearson’s correlation measure”.

I am afraid this is partially incorrect, since entropy, standard deviation and variance are effectively well suited for weights to affect alternative, because they reflect dispersion, but not Pearson’s correlation, that only indicates, comparing two criteria, that their attributes have a certain degree of similitude, that is, both goes up and down at the same time.

4- “In particular, changes in one criterion may disproportionately impact the final solution compared to modifications in others”

True, but only because a change in theweight of a criterion displaces the line or plane representing it in a parallel form that may be different for the other criteria, but this is due to a geometrical construction, not to impact.

This unequal parallel displacement among criteria most probably may change a pre selected best solution, but simply because it changes the original position of each alternative, which, as you know, is formed by the intersection of criteria.

Since we are dealing with lineal expressions, we must adhere to the principles of linear algebra, which also explain why we need to work with intersections of criteria.

You also say “aggregating the influence of each criterion”

Many times, the sum is not equal that the sum of the individual parts. Why?

Because criterion C3 may be affected by criterion C2, and that contribution from C2 to C3 must be accounted for.

This is the reason by which working with sustainability for example, we have to consider the three legs, Economics, Social and Environment, and the solution is found when in a Venn diagram you can see the space where the three legs coincide generating different solutions; same here.

5- “This approach is based on MCDA sensitivity analysis; wherein individual criteria are systematically excluded from the decision matrix”

I am afraid you are confused, since sensitivity analysis does not exclude criteria from the decision matrix. In reality, some criteria are not considered or excluded before sensitivity analysis, because they have no influence in the alternative selected; sensitivity analysis is then applied to the subset of criteria that do participate in the selection.

This subset is mathematically chosen using the Simplex algorithm (Dantzig, 1948).

You can check this by yourself since the Simplex is an Excel add-in, under the Solver name (lock for it in Data).

Run a simple or complicated example, and you can verify that the algorithm shows which are the basic criteria that matter, the others are irrelevant and do not play any role in sensitivity analysis, because what is of interest, is how sensitive is the best alternative to the variations of the selected criteria taken at the same time.

6- Finally, and always in my opinion, it seems that in eliminating a criterion at a time, you follow in some way the procedure adopted by the MEREC method.

When I commented on that method time ago, I noticed that in so doing and in each iteration, it is working with different decision matrices each time a criterion is removed.

You are doing something similar, and as I commented in MEREC, I wonder if your method if correct, because in each iteration you are working with a different matrix. Hard to accept that results can be added up.

These are some of my comments, hope they can be of help

Nolberto Munier