Dear: Jean Dezert , Albena Tchamovag, Deqiang Han, Jean-Marc Tacne

Reference is made to your paper :

The SPOTIS Rank Reversal Free Method for Multi-Criteria Decision-Making Support

My comments as follows:

It is a very good news to have a method without Rank Reversal (RR)

1- In my opinion you use the phrased ‘score matrix’ to indicate what in reality is the initial matrix, composed by performance values. This induces to confusion to readers for who score matrix is a matrix with different scores or results derived from applying a MCDM method.

2- You say in page 3 “The score matrix S = [Sij ] is sometimes also called benefit or payoff matrix in the literature.”

What happens if the matrix, as is most usual, also calls for minimization, using ‘cost’ values?

3- I don’t think that an initial decision matrix (IDM) can be considered incomplete because it does not have bounds for criteria. A matrix is incomplete when there is no indications of the quantity of resources for each criterion, procedure unfortunately followed by most MCDM methods, except PROMETHEE and those working with Linear Programming.

4- I agree with what you say about validations.

5 – You say “Classical MCDM problem becomes a well-defined MCDM one, where all scores values for each criterion are between its bounds”

6- “SPOTIS method will provide the best multi-criteria decision-making solution with preference ordering of all alternatives.”

Are you sure it is the best? On what grounds do you assert that?

7- In page 3: You consider criteria independent from each other. This s is a serious drawback, since in most projects criteria are interrelated. According to this, if you have two criteria like ‘Sped’ and ‘Fuel consumption’, that are interrelated, you can’ use SPOTIS? Why not?

8- How do you determine an ideal solution a priori? Based on what? Of course, if this solution is say very high, is does not matter what alternative you add, because it will be always above the maximum.

I grant you that it is a very elegant procedure.

9- I don’t think is correct to work with difference types of distances in the same problem?

10 - Where does weights come from? Are they subjective or objective?

11 – In page 5 “Once the MCDM is well-defined thanks to the specification of the bounds values of each criteria, the SPOTIS method does not suffer from rank reversal because the evaluation of each alternative is done independently of the others”

I agree 100% with this statement, because I also believe that the only way to avoid RR is evaluate each alternative independently. There is another method that applies this same principle and does not produce RR, but is not based on distances to a fixed point.

12- In page 7 “It could be argued that the SPOTIS method is more difficult (or risky) to use because of the freedom left in the choice of min and max bounds of the criteria”:

More difficult, risky? I don’t think so. It looks as a transparent method and very easy to understand. In my opinion its only drawback is using subjective weights.

Do you have a software for SPOTIS?

I hope my comments may be useful to your paper.

Nolberto Munier