Dear Nolberto Munier

This is and interesting question. I have felt some difficult in choosing the most appropriate method in several situations, mainly because there is a great amount of methods applied to the same objective, in other words, there are several methods that work in the same decision problem kind.

A lot of them are well disseminated, and most of time the choice falls on them, but I keep thinking if there is (or there are) other(s) (most) suitable method(s)

Some researchers and practitioners have tried to stabilish a formal protocol to the Multicriteria Problem construction, indicating that the method's choice must be concerned in define the ones that match with a specific decicion problematic but even this does not remove the my doubt, given what I have already mentioned before.

I like to compare it with another area (also related to the Operations Research): the Statistics. There are a lot of statistical methods that may be applied in different situations, but their choice becomes easy once there are specific tests that ensure their suitability to a given case, acordding to the available data.

I don't work on the basic development of MDCA methods, so I can't be conclusive about it, but may be a way to make the selection easier or more adjusted according to the application, following the example of the Statistics.

Well, this is just an insight I had, because of some difficulties I have felt.

Regards!

Dear Sir, you see more:

Multiple criteria decision-making techniques and their applications – a ...

https://hrcak.srce.hr/file/253067

by A Mardani - ‎2015 - ‎Cited by 213 - ‎Related articlesSep 11, 2015 - MCDM methods cover a wide range of quite distinct approaches. MCDM methods can be broadly classified into two categories: discrete MCDM or discrete Multi-attribute Decision-Making (MADM) and continuous Multi-objective Decision-Making (MODM) methods (Chauhan & Vaish, 2012; Zavadskas et al., 2014).[PDF]

5 MCDM Methods 5.1 INTRODUCTION The Multi criterion Decision ...

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MCDM Methods. 5.1 INTRODUCTION. The Multi criterion Decision-Making (MCDM) are gaining importance as potential tools for analyzing complex real ...

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https://www.sciencedirect.com/science/article/pii/S0305048315001243by E Mulliner - ‎2016 - ‎Cited by 84 - ‎Related articlesHere, a number of widely used MCDM methods – the Weighted Sum Model (WSM), the Weighted Product Model (WPM), the revised Analytic Hierarchy Process (AHP), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Complex Proportional Assessment (COPRAS) – applied for the assessment of sustainable ...

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https://www.sciencedirect.com/science/article/pii/S2212827115009403by D Sabaei - ‎2015 - ‎Cited by 14 - ‎Related articlesThe first section of this paper reviews MCDM methods in different literature, and then the second part develops a set of criteria to classify different techniques.

Dear Victor

Thank you for answering my question

VC. This is and interesting question. I have felt some difficult in choosing the most appropriate method in several situations, mainly because there is a great amount of methods applied to the same objective, in other words, there are several methods that work in the same decision problem kind.

NM.I believe that we should ask why there are so many methods. If a method works well, why to look for new ones?

First of all, in my opinion, it is because we do not have any way to decide how efficient or good a method is. The only way would be to know the result of the problem, but, if we know it, why would we need to use a method?

MCDM is not like many engineering problems where we have formulas, and we know for sure that whatever number we put in the formula the result will be correct, although may not necessarily realistic. The formula is simply an algorithm which does not care about the real meaning of the value inputted, and normally there is no subjectivity here, unless we use probabilistic values.

MCDM has a large component of subjectivity, and it appears that the different methods approach subjectivity in different ways. Some use Decision-Maker preferences like AHP and ANP, while others work with Decision-Maker assumptions about outranking between alternatives, like ELECTRE and PROMETHEE, and other work with preferences regarding the best distance to an ideal solution like in TOPSIS and VIKOR.

Which of them is the best? Hard to say. However most of them consider different approaches trying especially in improving information.

VC. A lot of them are well disseminated, and most of time the choice falls on them, but I keep thinking if there is (or there are) other(s) (most) suitable method(s)

NM. In my opinion, you have to look for a method that better replicates a real-life situation, for instance scenarios with correlations between alternatives, or negative values for the decision matrix performance factors, or considering that there could be multiples scenarios for the same alternatives, or assuming that different projects in a portfolio start and finish at the same time, or that criteria have restrictions.

And these conditions and many more, are common in real life projects. However, could you tell me which of the existing methods can cope with even one of these real situations, let alone with several at the same time

For sure there are better methods. Try Linear Programming, where there are not preferences or assumptions.

VC. Some researchers and practitioners have tried to estabilish a formal protocol to the Multicriteria Problem construction, indicating that the method's choice must be concerned in define the ones that match with a specific decicion problematic but even this does not remove the my doubt, given what I have already mentioned before.

NM. I am not sure of what you call a ‘formal protocol’, however you next words make a lot of sense to me if I read you rightly.

That is, for me the worst issue in MCDM is that methods do not represent the true characteristics of a certain scenario.

Why not? Because none of the existing method can MODEL reality even approximately

Surely you will be asking if Linear Programming can model reality when the other methods can’t? The answer is yes, although possibly not in its entirety, but by far more accurately than existing methods

Now, probably you will be asking why this particular ability of LP?

Because LP works with linear algebraic inequalities. For this reason, each criterion can be greater than, lower than, or equal to some value. Assume for instance that there are three independent projects. One (A) is tu build a housing complex on an island. The second (B) involves to build a bridge between the main land and the island. The third project (C) is to increase sewerage in the mainland.

To model this simple scenario, you have to establish that both projects A and B have to be forcefully built, since the complex can’t work without a bridge, and the bridge has no use without a destination. Since there is no restriction on project C, no restrictive criterion is needed, and it may or may not be selected.

This is simply done in LP establishing a criterion where A = B, therefore, both need to be selected.

Do you know an existing MCDM method that can do this?

What happens if you ignore this restriction? That the model may select only A or only B, which is useless.

Another example, suppose that engineering says that the bridge has preference over the housing complex, in order to transport materials and people during construction. How do you instruct the model? Simply, with a criterion that establishes that B > A, that is, B is more important and has preference than A.

In this case probably you have to consider both restrictions simultaneously, that is one criterion with A = B and another with B>A, and thus indicating that both must be selected, but B built before A.

In addition, LP is based on a rigorous mathematical development, there are not preferences or assumptions here, only real issues, which can’t be said regarding other methods, and it is the only method that provides optimal solutions.

If somebody is asking which is then the role of the Decision-Maker, I will be very happy to answer and document it

Of course, LP has also drawbacks, for instance it can only work with one objective at the time and only with quantitative criteria.

Most probably these drawbacks where the origin for researchers start looking, back in the 1950s, for other methods that could work with multiple criteria, and then appeared ELECTRE, PROMETHEE, TOPSIS and at least 20 more.

The SIMUS method based on LP, can solve these two hurdles and work with as many objectives you want, even in the hundreds, and solves simultaneously all of them. However, it does not deliver an optimal solution, but a satisfying solution, as all the other methods

VC. I like to compare it with another area (also related to the Operations Research): the Statistics. There are a lot of statistical methods that may be applied in different situations, but their choice becomes easy once there are specific tests that ensure their suitability to a given case, according to the available data.

NM. I agree with you VIctor, but Statistics is a science, while subjectivity based on personal preferences is not. As matter of fact you can use Statistics to solve many problems related with MCDM such as synthesizing the opinion of people affected by each project, or determining criteria importance using variance, of refining data using Monte Carlo simulation, or reducing the final number of selected alternatives using Principal Components Analysis, or using entropy, etc.

VC. I don't work on the basic development of MDCA methods, so I can't be conclusive about it, but may be a way to make the selection easier or more adjusted according to the application, following the example of the Statistics.

NM. Again, Statistics is a science, while MCDM uses some science but is not a science by itself. It is my opinion, which is not in agreement of what other researchers like Saaty said in one of his publications in 2008.

VC. Well, this is just an insight I had, because of some difficu lties I have felt.

NM. I hope these comments help. Of course, I can be mistaken, but until now, even when in the last 4 o 5 years I have said the same many times in RG, nobody came across and told me that what I said is not correct. I wish I had!

Nolberto Munier

Dear Nolberto Munier

This is and interesting and difficult question (differents methods, differents MCDM problems: technical, social, economical ...).

Sometimes I wonder too: how many lot of issues pertaining to a scenario are not considered?

You're welcome, Nolberto Munier .

Dear Marcin

You are the first person in rising this issue, and today I have answered my own question about it towards that title, as well as asking how a certain problem that I proposed, and that considers all issues pertaining a scenario can be solved

You really put the finger on a sore spot! Welcome to the club! Now, I am sure that I am not alone!

The fast and documented answer is that as per today MCDM methods are unreliable.

Probably many people will be asking how I dare to make such declaration

It is very simple: Just by reading lots of papers published, studying the scenarios and observing how the modelling fits the scenario requirements.

It is an issue for which I have be fighting since long time ago

There has been progress in improving the quality of data inputted, but none on modifying the structure of MCDM in order for them to consider real aspects and characteristics of a scenario

Apparently, you and I are the only persons concerned with this subject.

We, as practitioners, are in general ignoring reality. We are adapting reality to our needs and resources., when it should be the opposite.

We are not considering that reality is just more than inputting numerical values in a matrix.

For me the main culprit are the different MCDM methods which apparently were not developed to treat serious problems. And when |I say serious problems I mean those than consider reality.

The way they are structured forces the practitioner to ignoring facts, conveniently closing an eye to facts that are there for everybody to see, and dismissing aspects that are important.

In my mentioned answer I make a call to the MCDM community in join our efforts to develop a new paradigm that offers solutions more credible that those at present

I sincerely hope you can join this effort

Dear Dusan

Thank you for your response and for the abundant material mentioned

However, I was not talking about applications, which by the way there must be thousands.

I am concerned with the reliability that those methods offer.

In my humble opinion none of the methods in the market are reliable, because even if their mathematics may be sound and correct, and I believe they are, except AHP and ADP, that are flawed, they are unable to represent real aspects of a scenario. As our friend Marcin says ' How many lot of issues pertaining to a scenario are not considered? '

Consequently, their results probably are reliable considering the data inputted, however, since many aspects are ignored, dismissed or not considered, when they should be, their results are mere approximations of reality, therefore, unreliable

I agree with you, Mr. Nolberto.

Every mathematical model is true in itself. The basic problem is in the physical model and as much as a better description of the phenomenon or process. In how much of your mathematical problem you describe just such a process, you are closer to a scientific truth and have a more realistic model.

The whole life is reduced to the search for the scientific truth.

With respect and all the best

Dusan

Dear Dr. Regodic

Thank you for your response to my question.

You are absolutely right on what you say and I support your comments in a 100 per cent.

You mention something that is extremely important, when stating that: ' In how much of your mathematical problem you describe just such a process, you are closer to a scientific truth and have a more realistic model.'

That is exactly what I have been saying , and that was the reason why I posted my question.

In my opinion, if a mathematical model does not replicate reality, although probably it is not possible in a 100 %, the result it achieves is debatable, and the method solving said specific problem unreliable, even when the method as per itself may be reliable.

That is, the method may solve efficiently a certain problem, but if it is only a faint resemble or reality, then this effort is not very valuable.

This concept perhaps offers us the opportunity to answer a crucial question many times posted here in RG, and it is: Which is the best MCDM method?

I believe that the answer is: The method that can replicate reality more accurately

Dear Mr. Nolberto, I am treated with your approach. You're right in everything. If the tertiary model does not rely on correct research (which is expensive) then our model (physically and mathematically) is incomplete (incomplete). By introducing new assumptions (or new equations that describe processes more fully), we will have a more advanced model on the market that will describe the natural phenomenon more closely and will be able to give the same results in the repeated procedures. Who has a better model that more realistically describes succinct processes, it is more competitive and closer to the scientific truth. For example, the flight of a plane can be described with a material point, with three degrees of freedom, as a rigid body with six degrees of freedom (12 differential equations, three translations, three rotations). It is the best and most complex model with six degrees of freedom, because it describes the rigid body movements more realistically and gives parameters that can track speed, coordinates, rotation, flight stability, etc. at the exit. Thank you very much, Mr. Nolberto. Dusan

Dear Dr. Regodic

Thank you very much for your words. It is rewarding that somebody with your background and experience supports my ideas

What you say about introducing new assumptions represented by mathematical expression is exactly my thinking. Only that I would add that we need more that equations. In my understanding, we need to work with inequalities representing diverse aspects of the problem such as for instance, that there must be a precedence between alternative C and D, in the sense that you can't perform the second if the first is not selected first., a very common case in real-world problems

As you know, this simple restriction can be represented with an inequality in where the left term contains the common performance values for this criterion, and the left side the other aspect to be compared.

In the example above suggested it is very simple, since all we have to do is create a new criterion and establishing that C > D.

Or, if the scenario establishes that alternatives F and G are exclusive, we simple put F + G = 1.

This way practically any feature or characteristic of the scenario can be represented not only considering alternatives but also criteria.

For instance, some problems need to represent that for the same criterion there are two restrictions, for instance water consumption to population. These restrictions translates in an upper limit, say (12.8), in order for people not to waste water, and another the lowest limit, say (2.5), that guarantee a minimum necessary and established by health organizations

This is very easy to model since we can use the same performance values in two different criteria and the using > 2.5 and < 12.8. The method most probably will choose an intermediate value.

Of course this is no new for you, but I am taking advantage of the window you opened with your reasoning, to let people know how these characteristics can be modeled, and how they can be used to represent different aspects of an scenario.

It is then understandable that MCDM methods that are attached to a simple decision matrix, are unable to solve real problems.

As you know, this is the procedure followed by Linear Programming, and this is the reason for which I say that complicated problems that can not be represented in the modeling, can be solved by this discipline

My knowledge of aerodynamics is nil, but I guess that you also work with inequalities since I imagine that the are limits to translations and rotations and other parameters

Best regards

Nolberto

Dear Mudassar

Very interesting your problem.

I would say that if your algorithm produces the minimum time for completion of a model in the assembly line, or the maximum amount of mixed units, when compared with the actual system, then you have a winner

Therefore, the MCDM method that produces the minimum time appears for me to be the best, however, it does not mean that is the optimum, since there could be other algorithms or processes that can improve that time.

In my opinion, and since the time in each station is the same for whatever method you use, one measure could be to minimize the total idle time in each station, and for different combination of mix units.

Thank you, Mr. Nolberto, for the wonderful communication.

You are very convincing and radiate with warmth.

With respect and all the best.

Dusan

Dear Dr. Regodic

Thank you for your kind words

Best regards

Nolberto

Saying outright that MCDM method may not be correct. Of course there are merits and demerits.

Dear Prof. Singh

It is difficult for me to understand your first sentence, it appears that something is missing.

Let me express my judgement on MCDM methods.

In my opinion the way practitioners are using MCDM is similar - only similar- as inputting data in am algebraic formula and get a result.

Say for instance, the problem for determining car traffic between two cities and based on their respective populations. There is a model, called ‘Gravity Model’ where if well done, allows determining this traffic with quite accuracy.

The gravity formula is a simple one, that can represent reality pretty well, and affected by some exponents that are normally unknown. The procedure is then, using the population data of the two cities and the distance between them to predict the number of cars.

However, the model needs to be calibrated using actual results which are obtained through physical measures, such as counting the number of cars on a road and using pneumatic sensors.

There is similarity here with the MCDM methods because the DM introduces data and gets results; however, there is also a large difference:

It is not possible to calibrate the MCDM methods because the true result is not known. However, many practitioners fill the initial matrix with data, get a result, and happily declare that hey succeed, and which is worse, the paper they produce is approved by peer reviewers, who apparently don’t take into account that the model is far away from reality.

What the practitioner calls a success is because he/she inputs data, push the start key in the software, and gets a result, which only indicates that the software performed as expected, because it is based on mathematical principles.

It is similar that using logarithms to solve a multiplication, whatever the data you put the result will be correct. Now, if the multiplication represents a real fact, is another thing.

Present-day MCDM models follow a similar process, however, unlike the algebraic formula, they are not prepared to replicate reality, therefore the result may be meaningless because there are many aspects of reality that were not considered.

If in addition, when you consider that is a lot of PERSONAL subjectivity, it explains why different methods give different results for the same problem.

Does it mean that all of them are right?

Hardly!

After this introduction, and in my opinion, to gauge the goodness of a MCDM method you have to consider two things: The scenario and its characteristics, such as follows, which are only a sample of situations that normally happen in engineering projects:

a. Complexity, for instance where an alternative can be developed simultaneously in different places (multiples scenarios), or

b. If there is only one place, or

c. If you have to consider resources and their limits (low and high), and/or

limits for environmental contamination, or

d. That in a portfolio of projects not all then may start and finish at the same time, and have different rates of completion in different years, or

e. That is not enough funds for developing them all, or

f. That it is necessary for instance, that the alternatives comply with certain minimum number of restrictions, or

g All the above t thee same time.

That is what I call a complex scenario, and it has to be properly modeled.

The second thing is how the DM models this scenario.Dou you know any MCDM method that can model these very real situation?

Du you know any MCDM method that can model these very real situations?

This is what I call complex scenarios, while nowadays it is considered complex if it has many alternatives and many criteria and sub criteria, which is truly a minor issue and not even a problem.

As a conclusion, in my opinion the best MCDM model is which can represent a scenario the best and with minimum subjectivity.

I am talking about subjectivity when personal considerations are inputted in the model, as is done nowadays.

The DM is probably the most important component of a MCDM process, since he/she has to design a model representing reality as much as possible, but without any personal opinion that does not belong to reality. If he does he is distorting it!.

At the end of the process, when the DM knows the result from the MCDM method, he must then examine it, analyze its apparent contradictions and drawbacks, use his own expertise and knowledge to modify the result and even rejecting it, but he is doing this when he has a solid base on which to work.

He is not guessing or using his intuition, or making personal assumptions, but examining a sound result, applying common sense, making the necessary modification according to his expertise, and determining the robustness of the solution