Reality or fiction?

Nolberto Munier

Dear people working in MCDM.

This is not a quiz, a test, and there is nothing to answer to anybody. They are only some few questions aiming to make people to think, meditate, analyze, and reach a conclusion valid only for him/herself. It aims at determining how happy or satisfied is each of us with MCDM methods, all methods.

I believe that it could be valuable to know how the MCDM discipline impacts in our knowledge, and perhaps asking ourselves why and how we are applying MCDM methods. Since I already went through this exercise, I want to share how it was for me, and that it might be also for others.

There are more than 200 MCDM methods, based on different platforms, using different algorithms and assumptions, and with different procedures.

I think that it would be not only interesting but also an eye opener to learn how students, practitioners, professors, academics, and stakeholders think about these methods and if they are able to model a problem close as possible and solve it.

With this purpose, I formulate here a set of questions only as a guide line, and thus pointing out some characteristics of real-life scenarios. I am not here to judge the rightness or wrongness of what other people think about a method, only to know how this fundamental discipline is seen in its current state, in general, not on a particular method.

Along many years in RG I believe that my opinion on this subject is known, however, it is only that, an opinion, and as that, it can be correct, wrong or badly biased, but based on the genuine purpose of helping people in this very important matter as is MCDM.

My questions are:

1- Assuming that a practitioner chooses one of the MCDM methods to solve a problem. On what basis selects the most appropriate for his /her problem? (From now on I will use only the pronoun ‘his’ to avoid repetition). Is it because a method is simple, or the only one that he knows, or suggested by a professor, of for he has its software? In other words, how does he select it?

2- Does it happen to you that the chosen method is able to model and solve all the nuances of the real case, but you realize it does not, but decide ignore that ‘small’ detail and use it?

3- Do you think that the DM can solve a problem, that is, getting a solution, and then claim that he reached the optimal one? What would be your reaction on this? Do you think that by applying an algorithm you get a guaranty, because it followed an algebraic procedure?

4 – Did you realize that you can get a solution, with any method, but that it could be only cosmetic, or useless, because the problem is unfeasible and the algorithm did not detect it? To solve a problem, a method must satisfy each one of the criteria; if it fails, it means that the problem is unfeasible.

For instance, you can select an alternative, a method finds a ‘solution’, but this is incorrect, because there is no enough money to comply with all objectives, therefore, it is unfeasible. This normally happens, because most methods do not consider resources. Logic says that you cannot developed a method without people (a resource), or fabricate a product without raw materials (a resource), or

ignore the maximum contamination limits you are permitted to generate (the limited permission granted is a resource)

5- Criteria weights represent their relative importance, and intuitively it appears reasonable that there must be an ordering of criteria in decreasing order of importance. Nothing wrong with this, but do you think that they can evaluate alternatives?

Why this question? Because subjective criteria are normally used without considering the alternatives they must evaluate, and this is weird, since you cannot measure something if you do not know it is. It is not the same to have a set of criteria to evaluate sites for a fac tory, than the set you have to evaluate a government policies

As a trivial example, consider an engineer asked to evaluate three different medical procedures to treat a particular disease, when he does not have the faintest knowledge about it. However, this is the method that have been used for decades, and continues been used.

Employing objective criteria, is a completely different history, because their relative importance lies in the evaluation capacity of each criterion, computed considering the dispersion of values within each one. There is a very well-known theorem about this, which in addition, is the foundation of Information Theory, that these days is fundamental in our lives

6- Do you think that it is correct to assume that subjective criteria weights, a hundred per cent human decision, based on intuition, moods or wishes, instead of weights based on reasoning, experience, consultation and research, may be applied to real-world projects? If yes, please think if this acceptable.

7 – Do you think that it is correct to modify real data like a price, a volume or a contamination value, by affecting them with subjective criteria weights?

8 – Do you consider that resources are intrinsic to a problem? If affirmative, why about 99% of methods do not take them in account? It would mean than a manufacturer can get a product fabricated out of nothing, or assuming that the resource is infinite.

9- What is. from your point of view regarding MCDM, to follow the descriptive approach where the initial matrix is filled with numbers representing wishes and personal subjective opinions, or the normative one where subjectivity is absent since the matrix is formed by real numbers?

10- If the entropy weights represent objectively the ‘weight’ of a criterion, why most methods continue using subjective weights?

11 – Do you think that whatever the method you use, results will be different depending of the normalization method employed? If yes, why?

12 – What is for you the reason for rank reversal?

13- Do you believe that there are methods that claim to be immune to rank reversal?

14- Criteria are also objectives or goals; how do you measure if they are satisfied by a solution, and in what extent or degree?

15- Do you think that it is correct to breakdown a problem, solve its parts independently, and add up the partial results?

16 – Most methods consider real variable values and find a solution, however, there are external or exogenous variables like demand, international prices, stocks, earthquakes, etc., that depend entirely of the market or Nature, and that no method can consider. Do you think that these variables should be taken into account, and by who?

17 – is there a limit for the number of criteria, or it depends of the problem?

18- How would you consider to model a problem establishing that alternative A must proceed alternative D?

19- it possible to have a criterion with maximums and minimums limits at the same time?

20- DM and experts’ opinions are paramount, how can we incorporate them in the problem

without changing the real values?

21- SWOT analysis determines strategies considering Strength, Weakness, Opportunities and Threats, using existent exogenous conditions and reasoning. Do you think that is possible to match the advantages of SWOT with MCDM, and thus having a symbiosis and synergy between man and machine?

Thank you for your attention.