Dear Colleagues,

It is about the PARIS method.

I have found something illogical stated in every paper I have looked at that deals with this method.

It's about the determination of the reference ideal solution's elements (see Step 6, Eq. (11), in the attached excerpt from a paper).

Namely, if the normalized values of the decision matrix data are introduced for both benefit and cost criteria as done in Step 2, using Eqs. (2) and (3), the problem boils down to maximizing values, obtained using Eq. (9), by all criterion functions. Thus, the reference ideal solution from Eq. (11) should not involve any minimums.

I also use benefit and cost criteria as well as Eqs. (2) and (3), and after that I determine the elements of reference ideal solution as maximal values for each criteria function. It turns out I get the same final ranking of alternatives as in the paper whose excerpt is attached here, but with different values calculated using Eq. (12). However, the relative distances I obtained using Eq. (13) were the same as those in the mentioned paper.

Sincerely yours,

Darko Anđić