Dear Ram Kumar Dhurkari

I have read your paper

MCDM methods: Practical difficulties and future directions for improvement

My comments:

1- In page 1, you say“The paper also emphasizes why a benchmark decision situation is essentialin assessing the capabilities of any multi-criteria decision-making method”.

In my opinion, it is impossible to have a benchmark decision situation. To do that you need a certain result to compare your results to, and you don’t have it. If you had, you wouldn’t need MCDM!

“The capability is in terms of accuracyin modeling the human decision-making process”

I also believe that the capability of a MCDM method is not related with accuracy in modelling the human decision-making process. What you need, first of all, is to model accurately the problem, that is, reproduce in a matrix all its characteristics. If you don’t have it, it does not matter the accuracy of the DM, because results will be based on incomplete information, derived from his personal estimates.

2- In page 1 “However, if the prescriptions of multi-criteria decisionmaking method do not resemble actual or real decision of the very same decision-maker, then multicriteria decision-making method failed in either capturing the true preferences of the decision-maker or in aggregating these preferences as per the expectations of the decision-maker”

It is difficult to understand your sentence due to the use of the word ‘prescription’. What do you intend to say with that? Do you mean a result using MCDM?

Why the method has to capture the preferences of the DM? You cannot solve a problem, other than a personal or trivial one, by preferences. You can incorporate some justified preferences, and the method must consider them, but it does not mean that the result must adjust to those preferences.

Why?

Because there are many relationships that can offset this preference in one criterion relative to others. For instance, you can establish in the initial matrix that criterion ‘cost’ has a preference value of 8, out of 10, and criterion contamination a maximum limit of limit of CO2 of 45ppm.

The method has to consider that, and may find that with that cost it is impossible to have a contamination of 45 ppm, and then, the problem is not feasible.

And how do you determine the ‘actual or real decision of the very same decision-maker’?

On what basis? Using what procedure?

3- “The multi-criteria discrete alternative problem and the multicriteria optimization problem”

Normally, it does not exist a multicriteria optimization problem, because you cannot have the highest benefit and the lowest cost at the same time; they are opposite. MCDM problems aim at finding a compromise or balanced solution, not an optimal one

4- What do you mean by “feasible alternatives”? If you consider them is because they are feasible.

What may be unfeasible is the problem as a whole, as exemplified above.

5- “The decision-making process relies on the DM’s judgment on the objective values of the alternatives”

I don’t see how the DM may judge about the cost to build a building for instance, something that was computed by engineers and financial studies. The DM only may judge on the relative value of each criterion, and, in my opinion, it could be very arbitrary.

6- Page 2 “however, it is likely that the prescribed decision is optimal but may be far from reality.”

Again, there is not an optimal decision, except if you use Linear Programming and with only one objective, which is not our case.

7- In page 2 “The foremost objective of MCDA is to reduce the complexity of the MCD problem by breaking it into multiple and single-criterion problems”

This is NOT the main objective of MCDM.

It is to find the best alternative satisfying all criteria as best as possible. It has nothing to do with complexity. It applies the same to a problem of 3 alternatives and 6 criteria, that to one with hundreds of alternatives and criteria. This is not complexity.

“These problems are approached independently and the solutions are aggregated to produce an overall solution to the MCD problem”

Most probably you took this concept from AHP, and it is false, according to Systems Theory, common sense and many researchers. You can’t partition a problem, solve each part independently and that add-up results. The total is not always equal to the sum of the parts, at least in MCDM.

As in the human body, there could be a disease but you cannot cure it if you don’t also find and treat its cause

8- “Therefore, it is highly desirable that the MCDM method must not exceed the capabilities of the human information processing system”

If this were true, mankind never would have reached the Moon.

What are the computers for? The trick is that the DM must know what to input in the computer, using a rational algorithm, and let the software make the computations. The DM is totally responsible and fundamental in both ends of the process:

1) Furnishing correct data, and

2) 2) Analysing results. not for computations.

It is impossible to perform and combine thousands of operations. The DM must not interfere in the processing of the data. What he MUST do, is analyze the result, and there, he can modify data in accordance with his experience and know-how, not by intuition or feeling

9- In page 2 “Similarly, very few studies have used any MCDM method for rank order calculation in an informed multi-criteria decision situation”

You are ill informed, since there are thousands of articles solving this kind of problems since the 80s. Your comparison with AHP is invalid, because it was not designed for problems with criteria interrelations

10- Page 3 “They compared the rank order generated before and after adding a new alternative into the problem”

What you mention is a phenomenon called ‘Rank Reversal’, probably the most analyzed problem in MCDM, still unsolved, and that was discovered by Belton and Gear in the 80s.

11- Page 3 “The actual decision can be arrived at without using any MCDM method”

Wrong, normally you can’t, because an alternative does not have the best value in all criteria

12- In page 3 “This is because as the size increases, the cognitive burden on the DM to remain consistent in judgment and decision-making also increases”

It appears that you refer everything to the AHP procedure where you need consistency of the DM estimates, but 99% of MCDM methods don’t use this approach, and they do not need to keep any consistency

Complex problems involve more issues than number of elements and they need to be solved using multiple relationships, something that is not allowed in AHP. Apparently, you ignore the realities of AHP, that is only good for trivial problems. The reason?

His lineal hierarchy.

13- Page 5 “However, if the customer finds brand B more attractive, it is likely that the MCDM method failed to either capture the true preferences of the DM or process them as per the expectations of the DM (the customer in this case).”

I don’t share this opinion. The failure is not attributable to the method, but to the client, since he did not input his preference in the decision matrix. Consequently, the method assumed that there are not preferences, and evaluated alternatives using the other criteria

14- In page 5. “The complexity does not end here. Suppose the customer notices another brand D that is different from brands A, B, and C. On comparing the features of brand D, the customer finds brand C as the most attractive option. It is paradoxical”.

No, it is not paradoxical. I have studied it, and in my reasoning, it is rational, because by introducing a new alternative the whole problem is changed from three dimensions or three alternatives problem, to one of four dimensions or four alternatives problem. This change can modify everything or not.

“How the introduction of a new and a different alternative can cause rank reversal?”

Find my answer above.

“Surprisingly, many studies have reported such rank reversal phenomena [12, 31, 97, 98, 108]. To understand and explain such phenomena, it is necessary that the MCDM methods connect the objective measures of alternatives on various attributes to the observed choices. Various descriptive theories of decision-making, primarily from the fields of economics and psychology, can be used to understand the choice behavior of individuals.”

What do you mean by ‘connect’? The original objective values do not change, unless the DM change them, but it is the matrix which is spatially changed by adding a new alternative. Please leave psychology out of this, we are talking mathematics, and most especially dimensional geometric spaces. The number of these spaces is equal to the number of alternatives. In my hypothesis, rank reversal may occur when the slope of the hyperplane corresponding to the alternatives, changes in such extend, that it is no longer tangents the polytope that contains all feasible solutions. This is linear algebra, not my invention.

15- In page 6 “Valuation involves elicitation of preferences from the DM for the criteria weight and on the performance of alternatives on various criteria”

If you use subjective weights, coming from the DM intuition, this is not evaluation but invented values, and that everybody can refute or change

16- On page 7, it is evident that you equal criteria to attributes. Criteria are the conditions that must be satisfied by the alternatives, while attributes are the characteristic of the data within each criterion. Thus, attributes may be: positive or negative, integer or decimal, formulas, degree of dispersion of values, etc. Objective weights like those obtained by entropy, determine the weight of each criterion regarding the dispersion of its values. (Shannon, Theorem)

17- In page 7 “The problem formulation is important because, when the axiomatic rules or the principles of the MCDM method are not attuned to the DM’s psychology, the prescriptions will diverge.”

From where did you get this fantastic assertion?

18- In page 9 “In addition, there is also a lack of work describing the means to verify the potential of an MCDM method using simple decision-making problems where the DM can make decisions with relative ease and without using any MCDM method.”

Did you realize that this is the second or third time you express the same concept?

19- “The philosophy of MCDM methods is to split the MCDM problem into multiple single-criterion problems”

I already expressed my opinion and reasons on this wrong concept. Suppose you have alternatives A, B and C that are evaluated by criteria C1 and C2. What happens if there is a cause-and-effect relationship between C1 and C2? For instance, in a mountain road C1 is speed and C2 is snow. During an intense snowfall, the snow makes mandatory to reduce speed for alternative A and perhaps B. How then, can you evaluate alternative A by C1 and later by C2? Where do you consider the influence of C2 on C1?

20- On page 10 “Many of the extant MCDM methods have normative foundations leading to rational decision-making, which often differs from the actual decision. Theories that have evolved from the field of psychology and behavioral sciences can explain these departures. Recent developments propose new models and concepts that can better explain the decision-making”

Therefore, according to your own words, only normative methods, not precisely AHP and ANP, are rational. And this is true.

It is irrational to think that what is in the DMs’ mind can be applied to real-life. It means that if the same problem is solved by two different DMs, reaching different results, then, there could be TWO real-worlds Please, think about this.

I hope my comments may help you

Nolberto Munier