I agree, and I believe many people in the OR/MS community have no particular affinity for this approach. I guess using these methods is somewhat better than making decisions based on gut feeling, so if that is the alternative, then it may be great. Against any other alternative, I am not so sure.

Dear Joachim

I totally agree with your comments, and you were very polite when stating that they do not have a 'particular affinity'.

May be many people follow their feeling that 'this method, even if it is not good, es better than nothing'. It is an old saying, which is not always true.

Unfortunately, I believe that this feeling is common, and because of that people is free from study and using another method, to say nothing of the cost.

I agree with you that many people in the OR/MS community do not agree with these very popular methods, as we have seen here in RG, when reputed scholars establish and prove the drawbacks they have, both AHP and ANP .

The problem is that these methods are not match for methods such as PROMETHEE, VIKOR, TOPSIS, and many others, which if not perfect either, they are at least based on solid mathematical grounds, and logical assumptions.

I hold a very great respect for our colleagues, however, I can't understand, as I have said several times, that nobody came to support these two methods, using of course, documented information, other that they are the most used and popular methods, which is true.

Thank you for your comments.

Some parents tend to have a decision tree in their daily dealings. (Picture from my lecture hall)😁

Since after 10 days from posting this discussion, there are no answers that support usage of AHP/ANP nor giving rationale about appropriateness of their use (e.g for what kind of problems, with what kind of data...) I would like to turn this discussion in another way. There are some issues raised here, that are not related exclusively for AHP/ANP but rather general ones. I would really like to here some answers on the following issues (derived from questions of Nolberto Munier and asked in general manner):

* Which methods can consider complex problems, that involve a very large number of criteria/alternatives?

* Which methods take into account interdependence and/or correlation between criteria/alternatives?

* Which methods have weights or some other means for determining importance of criteria that are flexible to change based on specificity of alternatives that are compared?

Thanks for your answers in advance!

Dear Nenad

Thank you for your answer.You are right, there were no answers and probably never will. The simple reason is that AHP and ANP are indefensible.

Let me mention something that for me was very illustrative:Two years ago, I prepared a paper where I mentioned 19 aspects related with real scenarios that in my humble opinion should be contemplated in MCDM, and sent it to about 40 scholars and researchers around the world. This paper is since then, in RG in my profile, under the number 265.

I only got two answers and to my great surprise and satisfaction, the first one was from the late Dr. Thomas Saaty, and the second from a known Chilean scholar, an expert and staunch defender of these methods and with a solid practice. He expressed his agreement with some suggestions and disagreement on others, but unfortunately without explanation or elaboration of his rebuttals.

Mi greatest surprise with Dr. Saaty’s answer is because most of my suggestions are absent in AHP and ANP, and possibly they can’t be implemented in these methods because their structure. However, this scholar had the honesty, the candor and the decency to accept them, acknowledging, against his own work, that they were in reality needed, and expressing his desire to collaborate, as I requested.

Further, I was privileged enough to interchange some correspondence with Dr. Saaty - who always answered me - on the same subject, and especially about some weakness of AHP that I had pointed out, however, I did not receive answers from him substantiating his methods.Unfortunately, his passing away in August 2017, interrupted this healthy interchange of opinions.

I was and still am in disagreement with his methods, but I think that he deserved among other aspects, to be known for his integrity.Now, if the same creator of these two methods implicitly acknowledged their drawbacks, and did not haves answer for me, I believe that the chance that we receive response form other scholars is very slim.

In my opinion, the reason is that there are no logical and mathematical justifications to support these systems. The idea of working with preferences is good, however, it is not applicable to the problems most of practitioners face every day. Regarding to your conclusion that there are issues in my letter that are also general ones and then not only applicable to AHP and ANP, I wholly agree with you, since this is something I have been fighting for years in RG, in international fora, and in discussions with colleagues, when I maintain that at present NO MCDM heuristic method is able to represent reality even approximately.

As a matter of fact, two colleagues and I found the necessity of diffusing our ideas and suggestions, and to that effect we wrote a book where we extensively address this issue, examining the actual MCDM status, followed by enumeration and discussions using examples, of the main drawbacks of present-day methods, without pointing out any of them in particular. This is followed by our opinion about what should be done, and ending with a set of complex and actual examples solved. The book, was just on the bookstore’s shelves about a week ago, and published by Springer NY. Of course, it is also as ebook.

In it, we don’t work with formulas or assumptions. Every theme both as a drawback and as a suggestion, is analyzed considering common sense and using solid arguments, with also reference to the opinion of other scholars. It finishes with the development and solution of six complex scenarios.

Therefore, your liking to turn this discussion in another way, is more than welcome.

Now, you request answers for several important questions that I am happy to comply.* Which methods can consider complex problems, that involve a very large number of criteria/alternatives?

I am not sure that we can consider complex problems those with a large number of alternatives and criteria. In my opinion, complex problems involve more than that, such as including many restrictions among alternatives as well as correlation among criteria, or involving especial circumstances, as for instance, a portfolio of projects that do not start and finish at the same time and with changing performance values foe every year of construction, which is the reality.

Some time ago, I challenged in RG to solve a problem that I proposed, under the title of

‘Can you model and solve this real-world scenario with a MCDM method?

Answers: Not even one

Coming back to your question I believe that methods such as ELECTRE, PROMETHEE, TOPSIS, VIKOR, etc. are very well suited to address projects with a large number of criteria and alternatives. Even if they use assumptions, these are based on sound reasoning such as the preference statistic functions in PROMETHEE, or the selection of type of distance in TOPSIS. They are subjective, but not arbitrary, and the same applies to other current methods.

However, unfortunately, most of them work with weights derived from AHP, which of course are completely subjective and which, in addition, are not fit to evaluate alternatives. Of course, there is always the option of using objective weights as in methods ‘STEP-WISE WEIGHT ASSESSMENT RATIO ANALYSIS’ (SWARA), or ‘PREFERENCE SELECTION INDEX’ (PSI), or using entropy derived or statistic derived weights.

Your second question: ‘* Which methods take into account interdependence and/or correlation between criteria/alternatives?’

I understand that your word is ‘interdependence’ and not ‘interrelationships’. If it is the first the answer is: No method, as far as I know, consider that there can be dependencies among alternatives and dependencies among criteria, or correlation, and this is exactly my point when I said that these features may appears in real-world scenarios, and that no MCDM method can tackle them. However, LP and SIMUS, without a doubt, can tackle them, and of course, I can prove it.

Which is the secret of these two methods?

Very simple: They work with linear inequalities, which allow for making many different comparisons, dependencies and have the ability to replicate, albeit not perhaps in a 100 %, real-life scenarios.

If you mean ‘interrelationships’ between criteria, yes, many methods can handle it, including ANP, but as far as I know none method can handle interrelationships among alternatives. Again. LP and SIMUS can handle them without problems.Your third question: ‘* Which methods have weights or some other means for determining importance of criteria that are flexible to change based on specificity of alternatives that are compared?’

LP, as you know, as well as SIMUS do not use weights. However, it does not mean that they do not consider relative criteria importance. As a matter of fact, examining the LP Simplex algorithm it can be seen that in each iteration using the most important criterion is paramount, because it allows for determining which alternative must be eliminated from the former solution, to keep the dimension of the problem constant. If you wish I can explain this in detail using the Simplex algebra, and as did some time ago in RG when a researcher asked why LP is immune to rank reversal.

The last part of you question is exactly what LP and SIMUS do at each iteration, where a new set of criteria importance are computed based on the just selected alternative. Alternatives are selected in each iteration using the economic concept of opportunity costs, and compared with each other.

As mentioned above some other methods use objective weights which are legitimate for alternatives selection.

Thank you again for your questions, and please continue with them since they benefit us all.

Nolberto

Dear Nolberto Munier

can you see this questio?

https://www.researchgate.net/post/How_significant_the_Analytic_Hierarchy_process_AHP_used_in_CSR_supplier_selection

Dear Ali

I tried several times to open the file you mention to no avail, and in addition, what is it what I have to see?

If I consider the title of this paper it is weird for me to relate Corporate Social Responsibility with AHP, but of course, I have not read the paper, and then I can't give you an answer.

I would say that CSR should be a mandatory requirement in suppliers selection, but I don't see that it is a matter of personal preferences

Your clarification will be greatly appreciated

Dear prof. Nolberto Munier

Contents of the link:

Colleague Law Chong Seng asked the following question:

How significant the Analytic Hierarchy process (AHP) used in CSR supplier selection?

Questions about the best method in decision making for CSR supplier selection. AHP is the best or alternative choice?

Thank you Ali

It is difficult to say which MCDM method is the best for some specific problem

In my humble opinion I don't think that AHP is the best for CSR.

Without too much analysis, just think, that criteria for CSR are normally interrelated, and that AHP only works with independent criteria. And this is only one of the several drawbacks of this method.

Dear Nolberto,

Thank You (=U) for this fruitful discussion!!!

I'd like to say, I consider You as one of the most experienced specialists in the field of MCDA with a system approach to the theory and practice of applying methods for Decision Analysis of this class! Thanks so much for that!

Concerning your question.

0. Yes, followers/users of AHP consider this method as a very convenient one.

It's very easy to indicate preference of an alternative against others in the ratio scale. It's much easier than thinking about swing weight coefficients in MAVT or the choice (calculation) of objective weights (using entropy, eg) for TOPSIS, etc...

Drawbacks of AHP (U also wrote ...) !? ....- they don't think about....

Why besides that....!?

1. AHP was implemented in a good software, ExpertChoice (and it was the 1st good system with an MCDA method) and in many others...

2. Consider the following situation.

Decision Maker asks an analyst:

- Which of the existing MCDA methods you are going to use for our problem?

Analyst: - There are several ones....

DM: - But, which of them is the most popular!?

Analyst: AHP, according to different statistical analyses!

DM: - So, use AHP !!! -))

( this is so called positive feedback)

3. You know, I teach my students different methods, including AHP.

And AHP was included in our DecernsMCDA system, and students use it. However, I never use AHP in my research/ case studies (!!).

And my points is here as follows.

AHP is one of the MODELS for decision analysis... Each model approximately reflects a source process.

E.g., they use ecological/economic models, despite some

relations/functions/assumptions/ structures are not (fully) correct, and experts understand that...

However, those model are often useful or have the right to be used.

Thus, AHP may be used for some scenarios (where it is convenient..., eg, with small numbers of criteria and alternatives)... AHP ranking often (in robust cases) coincides with ranking by other methods (eg, with MAVT, especially if linear partial value functions are used).

So, I am not an active opponent of the AHP

[it seems to me, I wrote something close before, and T.Saaty sent me email with his thanks..., it was about 3 years ago....].

4. I plan to develop with my Team a new version of DecernsMCDA, with different MCDA methods

(including Objective (entropy) and subjective/experts' weighting, with many classical, 1 probabilistic, and several Fuzzy MCDA methods).

That for education purposes and applications...

I don't have many developers and financing..., and it would be good to use Decerns and your method/system, SIMUS, for complex and comprehensive analysis of important Case Studies.

=Boris

Dear Boris

NM-Thank you very much for your answer. As of today, 111 colleagues have read my question and only Joachim Arts, Nenad Medic and you answered. The first two friends supported my question and you provide some sort of justification for using AHP. Many thanks to you people.

BY - Thank You (=U) for this fruitful discussion!!!

I'd like to say, I consider You as one of the most experienced specialists in the field of MCDA with a system approach to the theory and practice of applying methods for Decision Analysis of this class! Thanks so much for that!

NM- Thank you Boris for your words, however, I am simply a researcher that instead of looking at the mathematics of a method, prefer to analyze it from the point of view of its utilization and especially using common sense. Precisely, as you say, ‘a system approach to theory and practice’ I have found that normally, in most methods, there is no room and no will for trying to reflect reality. They all work with simplifications and sometimes assuming facts that reflect their own convenience.

You and I aim at the same objective; to improve the MCDM process. Your target is improving data, while my goal is improving modelling.

Just as an example:

Years ago, I wrote to the authors of a published paper and criticized it, not because they used AHP, but because there was clear evidence, looking at the data of the scenario, that there were undoubtedly relationships between criteria, which as you know, AHP can’t handle. When I asked why they ignored the fact that AHP works only with independent criteria, and consequently their problem was inappropriate for AHP, I assumed that probably they did not know that restriction, however, to my surprise their answer left me astonished, because they said “Oh, because we consider that it was better to assume that there are not relationships”.

I asked again ‘On what grounds’? I got no answer.

Let me tell you that this response was from one of the authors who was a professor of OR. That is, they agreed to adapt the method to their convenience. This procedure is more that usual, and it is what I am against of.

And do you know what really worries me? That the peer review process did not realize the undue use of a method, and happily approved it. This is what made me aware of the necessity of a quality control of work done for practitioners, irrelevant if they are published or not.

Great progresses have been made in the field of improving reliability of data, and you and your collaborators are probably one of the groups that most have contributed in this aspect, especially in using fuzzy environs. However, if we consider the spectrum of papers, almost nothing has been done to design and process a mathematical model that reflects a scenario as it is, or at least nearly.

We are still using simplifications and getting results according to them, however, as the results can’t be checked, we assume they are correct, which of course, is very handy. Unfortunately, AHP is ideal for these manipulations, while other methods involve reasoning, and then, it is more difficult.

I already proposed to the MCDM society the convenience of installing, under their leadership, and probably from a joint effort grouping many practitioners, a quality system similar to those already existing in many areas and in different fields, since long time. Silence was the answer.

BY- Concerning your question.

0. Yes, followers/users of AHP consider this method as a very convenient one.

It's very easy to indicate preference of an alternative against others in the ratio scale. It's much easier than thinking about swing weight coefficients in MAVT or the choice (calculation) of objective weights (using entropy, eg) for TOPSIS, etc...

NM- As you say it. It is more convenient and easier than other methods, especially in MAVT, where you need a function, but it does not necessarily mean that it is effective and correct, especially when the scale is arbitrary, and in my opinion irrational.

For instance, where is the rationality by stating that happiness is 3 times better than say quality of life? You are entitled to say that you prefer happiness, fine, but assigning a value at this preference borders the absurd.

Regarding subjective weights, AHP ‘computes’ them by intuition. Can you imagine deciding by intuition how a very large undertaking, such a very large dam construction will affect people that have to be displaced because their land will be flooded?

If proofs of this irrationality are needed just look at the suffering of thousands of people that were relocated for the construction of the Three Gorges Dam in China and in the Itaipú Dam in Brazil. Google has a lot of information about it. That is, in AHP the DM or DMs re taking decisions that affect the life of thousands of people, without consulting them, of course, not about technical issues, but as how they see the dam will affect their lives. In addition, as you know, this voting system violates Arrow’s Impossibility Theorem, which defines this procedure as a dictatorship. Please correct me if I am wrong.

I posed this same example to Dr. Saaty two years ago, and his answer was: “People need to be taught”. By respecting his memory, I prefer not to comment on his answer.

In addition, remember that objective weights do represent criteria importance, while subjective weights are only trade-offs, and then, can’t be used for alternatives evaluation. Consequently, why are some methods still using them? This is a question that I asked many times in RG. Answers: NONE

BY -Drawbacks of AHP (U also wrote ...) !? ....- they don't think about....

NM – Most possibly you are right, but then the attitude of these practitioners is not very professional indeed. I prefer to think that most practitioners are using it acting in good faith, but not realizing about its drawbacks. Who is going to tell them that the result is incorrect?

BY-Why besides that....!?

1. AHP was implemented in a good software, ExpertChoice (and it was the 1st good system with an MCDA method) and in many others...

NM- A software does what the algorithm of a method indicates, and I agree with you that Expert Choice is a good software, but it just processes data, as the software of other methods do. They can use as much reliable data as possible, using perhaps fuzzy environs, but the effort is sterile if the mathematical model is biased, incomplete or faulty.

A useful analogy is the test of a model of a car (mock-up) in the wind tunnel. You can improve the diverse parameters, wind speed, condition of the road, acceleration, car speed, etc., and use diverse software to simulate different conditions, but if the wooden at scale model is faulty, if it does not fully represent what the designers have in mind, the results will be false.

BY - 2. Consider the following situation.

Decision Maker asks an analyst:

- Which of the existing MCDA methods you are going to use for our problem?

Analyst: - There are several ones....

DM: - But, which of them is the most popular!?

Analyst: AHP, according to different statistical analyses!

DM: - So, use AHP !!! -))

NM – Precisely! In other words, the analyst uses it because it is the most popular method.

What kind of analyst is this? Where is his analysis?

BY -( this is so called positive feedback)

NM - With all respect Boris, I would call it an irresponsible feedback.

BY - 3. You know, I teach my students different methods, including AHP.

NM - Of course, you must, as I also explain the AHP method in my books, but I also warn the reader about its drawbacks, not only for AHP, but for other methods too. Let me illustrate a situation that relates to teaching these methods, not only AHP.

Some years ago, a friend of mine, professor of OR told me that when she was explaining the pair-wise comparison and preference decision in AHP, a student raised his hand and ask her which was the purpose of this comparison, because according to his understanding the DM was making a comparison, quantifying it and even correcting his own judgement, because a formula instructed him to do so.

He said “I believed that we were studying a method to select real options, but here in AHP, the DM is analyzing his own scenario, since he does not even consider the options, therefore, where is the connection with the real one, or why we have to accept that his approach represents reality’? And he added:

‘The DM is looking for a transitive result to his preferences, but what if the scenario that he is trying to model is intransitive?

My friend told me that she was a little embarrassed with these questions because she could not find a rational answer.

BY -And AHP was included in our DecernsMCDA system, and students use it.

NM- Of course they are using it, as I had to do when I was taught this method, but it does not mean that students really understand it. It would be interesting to make an anonymous poll with students about what they think about the method. I still remember that at that far away time, I was questioning the lecturer and arguing about this method since he started. I never received a rational answer.

BY -However, I never use AHP in my research/ case studies (!!).

NM- There you are my friend!

If you never used it, you probably had very good reasons. Probably you had to teach it because it was in the university curriculum for OR, apparently not because you believe on it. Am I mistaken?

BY-And my points is here as follows.

AHP is one of the MODELS for decision analysis... Each model approximately reflects a source process.

E.g., they use ecological/economic models, despite some

relations/functions/assumptions/ structures are not (fully) correct, and experts understand that...

However, those model are often useful or have the right to be used.

NM- I agree that those models, including AHP and ANP are useful for better analyzing and understanding a problem, but other than that, it does not necessarily mean that they can model correctly a problem and solve it.

BY-Thus, AHP may be used for some scenarios (where it is convenient..., eg, with small numbers of criteria and alternatives)...

NM-Yes, I agree. However, what is the purpose of using it when people may know that AHP is mathematically and conceptually flawed?

Just a simple example. If you have, say four alternatives to be selected subject to a set of criteria, AHP makes a pair-wise comparison regarding the main objective. However, in that comparison it completely ignores the alternatives. In so doing it assumes that criterion A is say 4 times better than criterion B, and granted, it could be, however, it considers that those preferences are constant. Then, when in its second step compares pairs of alternatives, it assumes that this preference holds for all of them, which could be certain or not. Do you think that this procedure is correct?

BY-AHP ranking often (in robust cases) coincides with ranking by other methods (eg, with MAVT, especially if linear partial value functions are used).

NM- This is true, and I have seen it many times, however, you certainly know that most models use weights derived from AHP in a known hybrid combination. Now, in so doing, if you are introducing these supposed weights, in say for instance in Promethee, most probably you will find both results coincidental, because you are introducing in the second a partial result of the first.

BY -So, I am not an active opponent of the AHP

[it seems to me, I wrote something close before, and T.Saaty sent me email with his thanks..., it was about 3 years ago....].

NM- I wasn’t either, and I have said several times in RG, that AHP was for me the best method for trivial problems. However, after investigating more in depth, I think that I should reverse my opinion, based on what I said before about constant preferences, since it may not even be useful for trivial problems.

BY 4. I plan to develop with my Team a new version of DecernsMCDA, with different MCDA methods

(including Objective (entropy) and subjective/experts' weighting, with many classical, 1 probabilistic, and several Fuzzy MCDA methods).

That for education purposes and applications...

I don't have many developers and financing..., and it would be good to use Decerns and your method/system, SIMUS, for complex and comprehensive analysis of important Case Studies.

NM- It will be an honor for me if you incorporate SIMUS in the next version of Decerns, and you know that I am at your complete disposal to help you and your collaborators if need be.

One again, my friend, thank you for your answer.

Nolberto

Dear Boris

Thank you for your words. I really appreciate them. However, I don’t think that I deserve your compliments. My work is in a modest scale, I am only trying to improve the way in which MCDM is performed to day, nothing remarkable indeed!

However, is a hard fight since it appears that many practitioners and researchers and MCDM associations are happy as the MCDM as it is, and then, except from your support and that from a handful of colleagues, I work alone. People don’t even defend their positions by challenging what I say, and you can measure it by the lack of response from more than130 people that read it. There is none.

Regarding my new book, and your interest on it, let me think about how I can get a free copy for you; I have to talk with Springer New York about it. Just in case give me your postal address in Obninsk. You know my email address.

As I told you my knowledge of the fuzzy environs is very limited, but I know enough to understand the importance, and especially the significance of the development that you and your students are doing, in ranking fuzzy numbers, but I don’t have an idea at what you refer in ‘Violation of the basic axiom in diverse fuzzy MCDA methods’. Which is this axiom, and why is it important?

In my opinion you selected three very good methods for in-between comparison. That is a very interesting research, and its conclusion may be very enlighten. If I may, I would suggest to include SIMUS in the test, considering that it does not use weights, although of course, as you know, considering criteria relative importance and computing it at each interaction. Naturally, I can send you the SIMUS software. It is in Visual Basic, and also in Python, but the latter is still not sufficiently tested.

However, I have a question: These three methods use weights, therefore what type of weight are you going to use? That is, in my opinion, you can get different results not due to your alternatives, but to the system of weights you use.

Probably you already know it, but there is a very interesting paper published by Reggiani and Janic ( An Application of the Multiple Criteria Decision Making (MCDM) Analysis to the Selection of a New Hub Airport’, EJTIR, 2, no. 2 (2002), pp. 113 – xx), where they compare the results of using different types of weights in three different methods (AHP, SAW and TOPSIS). They are: 1) No weights, 2) weights determined by simulation using uniform distribution, and 3) weights derived from entropy.

According to this author 'AHP, like SAW and TOPSIS, produce different results when they use different methods for assigning weights to criteria', therefore it appears that in your case it would be convenient to choose only one weighting method, and according to this author SAW and TOPSIS have some coincidence in results when entropy weights are used.

Of course, in the AHP case these different weighting methods do not apply, since the system generates its own.

Thank you for your very last sentence, but in reality, our friendship of years is extremely important for me.

Best regards

Nolberto

Dear Nolberto,

thank U VM for your answer and deep comments!

I'll write U email with my answers and details.

=Boris

Dear Nolberto Munier

in some problem that we can neglect interrelation between factors ( neglecting its impact on results) I think Its better to use simple method i.e. AHP

In more complicated problem which interrelation between factors more impact I think we use ANP

Dear Mohammed

I really appreciate your answer, thank you. You are one of the very few that makes your opinion known. Unfortunately, not many colleagues follow your example in defending what they think is a good method, even when they acknowledge its drawbacks.

It is a shame, because if more users would decide to give answers, posing different points of view, sharing their own experience, letting us know how they understand the drawbacks of AHP, that could be an excellent teaching tool for all of us, me included, of course. We always can learn from others and from their experience and reasoning.

But it appears that it is easier and more comfortable not to think about AHP shortcomings, it is better to ignore some troubling facts and assume that the AHP method is reliable, because if so many people use it, it must be dependable and solid.

Yes, I agree with you that possibly in some cases you can neglect the interrelationships. The problem is, how do you know that no interrelationships exist?. On what grounds you decide that? By intuition?

In addition, as you properly assert, you talk about 'impacts', that is a cause-effect relationship. If it exist, how you consider it? I remind you that ANP does consider interrelationships but not impacts

Dear Tasneen

NM- Thank you so much for your answer.

TBM- I absolutely understand your concern towards AHP method.

NM- Yes, I am concerned, but in addition, I am astonished as how educated and prepared people, even MCDM professors, don’t see the deficiencies of the AHP and ANP methods, and continue using them, or keeping silent.

TBM- However, I believe (still my personal opinion) that the "easiness of use" has way more profound dimensions than the effort made to obtain the results. Where easiness to use could mean that the analysis is more consistent and therefore of a higher quality.

NM-Yes, I agree, there is no doubt that ‘easiness to use’ is an important concept, and it is rooted in many people, however, I don’t think that it is healthy to choose a MCDM method, simply because it is easy or because its diffusion.

Regarding the second part of your sentence, in my opinion, I don’t see how easiness to use is related with consistency and quality. Topsis, is by far more scientific than AHP and it is also very easy to use, and its purpose is crystal clear: To find the alternatives with the shortest distance to de ideal and the largest to the non-ideal. What is the purpose of AHP?

Just think, why there are more complicated methods for MCDM, developed inclusive before AHP, such as Linear Programming, SAW, Electre, Pomerthee and Topsis? In my opinion, AHP makes selection easier just by not even attempting to contemplate aspects of the real-world that other methods consider, for instance, the necessity to take into account resources. For AHP the world is full of infinite resources.

How can you select a project among others, if you don’t consider the cost of each one and the total amounts of funds available? It is like going to a supermarket and filling the shop cart with different goods, and without an inkling of what they cost or how you are going to pay for them. Is this rational? Of course not; well this is similar to the AHP approach.

As you can see, I am neither using mathematics or psychology, only COMMON SENSE.

TBM- So let's rephrase it this way:

I think you might agree that an expert is more capable of comparing precisely and consistently, two elements at a time than multiple elements at a time.

NM- I don’t know, I am not a psychologist; this is Miller argument, and in addition, it is only a theory, that can be refuted in the future. Remember that some of the notions introduced by Freud, are no longer considered valid.

I don’t believe that pair-wise comparison is a wrong method; the DM can make a comparison between equipment A and B and decides that he prefers A over B, and that is absolutely legitimate; for me, which is very debatable is to put a cardinal value to that preference by using a fabricated scale, the ‘Saaty’s Fundamental.

Let’s see another issue:

The DM compares for instance criteria ‘Performance’ and ‘Reliability’, two intangibles. Remember that the poor guy is blind, because he does not know the projects, since in AHP, they are the last to be considered, and after the criteria weights are determined.

The problem is: Since each element may have several meanings, to what pair is he referring to? For instance, for performance, there could be many, such as production/hour, electricity consumption, maintenance costs, etc. For reliability, there could also be several such as number of rejects, unscheduled stops, overheating, etc. My question is, which pair of these two criteria is the DM comparing? Since in AHP it is supposed that he knows nothing about the two equipment, he makes a general – good for all – comparison.

In all honesty, do you thing that it is correct establish a preference without identifying to what it refers to?

TBM- I still understand some of the scholars' concerns regarding the used scale (e.g., Saaty's linear scale does not ensure a balanced dispersion of weights) and the uncertainty in expert's judgment. However, such a kind of problems can be addressed by using other types of scale (e.g., the balanced scale, geometric scale) given the type of the problem and the aim of using AHP. Regarding the uncertainty in expert's judgment, this is another problem that can also be addressed.

NM- But what is the purpose of applying a MCDM method? To identify the ‘best’ alternative based on existent information, or see how well the DM performs?

Where is the DM analysis with reality?

Suppose that the selection consists in choosing one of three equipment, all of them to produce the same product or function, which prices, quality, performance, delivery time, etc. are perfectly known and documented, and suppose that the SAW method is used and that this ranking was obtained: C>A>B

Assume that the DM, using AHP, determines that the ranking, as per his preferences is: B>C>A.

Which of the two rankings do you think should be considered? One, obtained by a mathematical procedure and with reliable values, or the other obtained by following the DM intuition?

Tasneem, you are a nuclear engineer. Assume that you have to select on a major issue such selecting between a Light Water Reactor or a Heavy Water Reactor, subject to hundreds of criteria.

I don’t believe that if you are one of the DM you will use AHP, and dare to decide on undertakings like this valued in hundreds of million of dollars

TBM- I'll come back to you soon to discuss this issue

NM- I will very much hope so, and I will be looking forward for your next.

Thank you for your collaboration.