In AHP, this is not an issue. Because you compare the values per criteria using the Saaty scale. In your case, if the Criterion1 is criterion of benefit, then

- in pairwise comparison table you compare a1 and a2, a1 dominates over a2, let's say 5 times, to (a1, a2)=5 and (a2, a1)=1/5=0.2

- in pairwise comparison table you compare a1 and a3, a1 dominates over a3, let's say 4 times, to (a1, a3)=5 and (a3, a1)=1/4=0.25

- in pairwise comparison table you compare a2 and a3, a2 dominates over a3, let's say 2 times, to (a2, a3)=0.5 and (a3, a2)=2

..........a1....a2......a3

a1.|.....1......5........4..|

a2.|...0.2.....1......0.5.|

a3.|..0.25....2........1..|

After then you follow regular AHP procedure (normalization by the sum of pairwise comparison table and then power...).

I also worked with Electre, and it seems to me that negative values in the decision table do not change method implementation.

This is my opinion.

Dear Fatih

It can never happen in LP or SIMUS. You can have in the decision matrix a mix of positive and negative values, you can even have all the values in the matrix being negative, but the result, if it exists, will also be positive

Why?

Because when the system of equations is solved you express the condition that the values of alternatives must be positive.

However, in the solution, you can have negative values for the criteria marginal values.

If you are maximizing a criterion, a negative marginal value means that increasing the criterion value will produce a decrease in the result and vice versa.

This is the information used for a rational sensitivity analysis

Dear Nikola,

Yes you are right. Yet, it is problem when we are not conducting pairwise comparisons. That is, we'd like to use original data set. How can we analyse with real data in MCDM methods such as TOPSIS, EDAS, ARAS, MABAC, CODAS etc.

Dear Munier,

I agree but what can we do when we have to use the real data set containing negative values in MCDM methods such as TOPSIS, EDAS, CODAS etc?

Dear Faith.

I believe that you can use negative values in TOPSIS, but I don't know about the other methods. In TOPSIS, if you have negative values and you are minimizing you have to choose the most negative. Even if you are maximizing a criterion with negative values, the best will be that with the least negative value

However I am sure that you can do that using Linear Programming

In AHP it is not an issue as other researchers mentioned. However, in surveys generally the fragments of the Saaty-scale are difficult to understand for layman respondents. That is why we offer negative values for expressing inferiority, these are certainly re-transformed in the eigenvector calculation. But your case is different as I understand, you have a ready dataset that should be transformed to an MCDM method. For this, I would say that you should separate the importance and the influence of the decision elements. The importance cannot be negative in any case, however, the influence can be. Consequently, I recommend the ANP or AHP-ISM hybrid technique if you want to stay in the AHP/ANP area for your problem.

I am facing the same problem. One of my initial criteria has negative values. In my case, I am using a carbon footprint for four options.

Option 1: -2.0 CO2e/kg;

Option 2: -1.17 CO2e/kg;

option3: 0.28 Co2e/kg, and

option 4 : 0.5co2e/kg

I would be glad if anyone helps me out in this.

Salman

Dear Faith

I am answering to your initial question of why some performance values in criteria may be negatives.

I am attaching a file showing an initial decision matrix (in black) with 8 columns as projects and 20 rows as criteria.

It is an actual analysis performed by Laura Tasca, University of Milano, more than ten years ago. It refers to selecting the location for domestic garbage incinerators, and all values are negatives because they refer to negative aspects of such undertaking such as air quality, noise, odors, wildlife, soil contamination etc.

Two consecutives rows correspond to the same criteria, for instance, minimize the negative effects of contamination, and, at the same time, establish minimum levels of contamination, since zero contamination is impossible.

You can see the result reached by SIMUS in the solid blue row and the ranking in red. I hope this can help.