# 101
Dear Nik Muhammad Farhan Hakim NikKu; Muhammad Naim Ku Khalif; Nor Izzati Jaini
I read your paper
Analytic Hierarchy Process based on the magnitude of z-numbers
My comments:
1- What is Z-numbers? You don’t explain
2- In the aabstract you ay “The integration of the AHP with fuzzy Z”
Did you know that Saaty, creator of the AHP, said that fuzzy should not be used in AHP, because it is already fuzzy?
3- “Judgment is followed by a degree of certainty or sureness”
Where did you get this from? A judgement is never 100 % reliable
4- “Most of the existing decision-making models based on Z-numbers transform the Z-numbers into regular fuzzy numbers by integrating the reliability parts into the restriction parts, causing a significant loss of information”
Could you demonstrate this assertion?
5- “The Analytical Hierarchy Process (AHP) is one of the most powerful of these methods”
As a matter of fact, it is the opposite. It is one of the most elemental of MCDM methods, only good for simple and trivial problems, since it is unable to solve medium complex problems., because its lineal hierarchically structure
6- “Construct the pairwise comparison matrices to represent the decision maker’s preferences on the restriction and reliability of each criterion”
And what happens if another DM thinks differently?
7- In addition of what Saaty said, where is the logic in using fuzzy to refine invented values?
8- Page 8. A re you sure that in Figure 3 all criteria are independent as requiredby AHP?
Don’t you think that a criterion may be affected by another?
9- Page 13 “In fact, the ranking of alternatives will not be affected as much when a sensitivity analysis is performed and consistent criteria weights are obtained”.
Sensitivity analysis is not related to consistent criteria weights. It is related with the degree or range a criterion can change without altering a solution. By the way, criteria weights do not define alternatives ranking; this is reserved to objective weights
10- “C3 and C4 were increased by 40%,”
And how do you know that you can increase those criteria in a 40%? To do than you need to
know the allowable range of variation of each criterion and you don’t have that in AHP, and by the way, both variations must be considered not separately, but jointly
I hope that these comments may help you.
Nolberto Munier
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