# 210

Dear Andreas H. Hamel •Daniel Kostner

I read your paper:

Multi-weight ranking for multi-criteria decision making

My comments

1- In the abstract you say “A basic problem in multi-criteria decision-making (MCDM) is to find a ranking for alternatives which are not directly comparable with each other”

In my opinion this definition of ranking is incorrect, since MCDM also addresses interrelations between alternatives, for instance in cases where there are inclusivity and exclusivity. Your definition refers only to the latter

2- Page 2. ” New methods such as COMET and SPOTIS were recently proposed which are rank reversal free”

I am afraid that I do not concur with this assertion; as per my research in RR, I found all MCDM methods are subject to it, and it does not matter the sophistication. I can and I did demonstrate that RR is simply a natural consequence of changing dimensional spaces each time an alternative is added or related. It is an unavoidable geometrical consequence, as a fall of objects to a floor is, due to gravity.

3- Page 2 “The new ranking method is suited for this situation since it takes into account a set of predefined weights vectors at once and can therefore be interpreted as a ‘‘compromise’’ ranking with respect to multiple weight distributions”

Well, you can reach a compromise or agreement but it does not necessarily mean that it is realistic or allowable. You talk about pre-determined weights, by who? If they are subjective, what is their value?

4- Page 3 “A ranking function always comes with a loss of information”

Interesting concept and in my opinion correct, because if you select stay A >C>D you are leaving B off the picture. However, also consider that if there is interaction between alternatives, that in formation could be already be registered in another alternative

Dear authors:

In my opinion, your paper is mathematically heavy and I am afraid quite difficult to follow for most readers that are more interested in solving their problems than entering in the field of pure math, or in abstract concepts like dimensional spaces in MCDM, feasibility, cones and dual cones, but that need to be explained, which is not very difficult

Please, don’t get me wrong. I would not dare to criticize the work of colleagues. It is simply my opinion.

If this paper, as appears, reflects a complex mathematical analysis, it is hard to see it as a tool that can be used by practitioners.

Nolberto Munier