# 126

Dear Alessio Ishizaka · Enrique MU

I read your paper

What is so special about the analytic hierarchy and network process?

My comments

First of all, I want to congratulate you for your extensive bibliographical search about AHP and ANP. I am impressed by the number of authors you mention in your paper, and by your comments.

However, it is only a bibliographic search enumerating papers written on AHP and ANP, but there is not a single line that justifies these methods, other than mentioning the large number of papers published, which is undisputable, and by far more than other MCDM methods

Obviously, you are an advocate of the method and wanted to make its virtues known, but you do not even mention its drawbacks, that outperform several times over those good attributes it may have. You mention multiple applications of AHP, the same as other methods that are not ‘special’, and no mention is done on AHP abundant limitations. Therefore, your analysis is biased.

Technically, AHP is a descriptive process, and as that irrational, considering that it is based on intuitions, very useful in many aspects of life, but normally useless when applied to serious MCDM scenarios, and thus, assuming that the DM judgements are applicable to real-life, and to thousands or millions of persons, against common sense and something that nobody can accept.

AHP is based on the wishes and moods of individuals pursuing what they perceive or feel, without reasoning, which is natural in many instances of our life, instead on addressing on what it ought to be as in normative rational methods, which not coincidently constitute the largest number of MCDM methods. In my opinion, AHP may be appropriate to personal decisions like selecting a restaurant or a site for and you say that it is due to easiness of uses and a vacation, but it has no place in complex scenarios. Simply, it cannot manage them.

However, as you mention, it is the most used MCDM method, due to its easiness, which is true, and to its rigorous mathematical base, which is false.

AHP is probably the easiest MCDM method to learn. The DM determines the criteria, alone or with experts, but curiously, without considering the alternatives they must evaluate, and then compares two criteria at a time and assign a value according to his intuition, and that is all.

Even if he does not reason ‘appropriately’, that is, transitively or consistently according to percentage, the software refutes him and -suggests’ a correction. The DM has no alternative but accept, as a robot, it does not matter if he agrees or not.

What the DM does not realize is that a decrease, for instance from 7 to 6, is not minor, due to the ratio or logarithm scale, the method remains silent about that. Please, correct me If I am mistaken.

In addition, one wonders, and AHP does not explain it, why the DM must be coherent or consistent in his/her estimates? As an example, if you must select among three restaurants A, B and C for dinner and comparing quality and price, and you already determined that for you, quality is three times more important than price, and for that reason, close A, that is, you prefer to lose some money to get a gain in quality.

Now you compare A and C and finds that C has also a good quality, but at a considerably lower price, and you decide that you prefer to lose a little quality, to get a gain in price. That is, you reversed your priorities.

Finally, comparing B and C you reach the conclusion that both have good quality and good price, so it is indistinct what you chose

Consequently, A>B=C>A, there is not transitivity here. And what is wrong with this analysis? Nothing, just human decision. This elemental example also shows two AHP errors.

First, it considers that weights are constant. As you can see, they could not be, and

Second, criteria depend on the alternatives, not the other way around. If you do not have alternatives, it means that always, and for everything, i.e., houses, trips, careers, cars, food, furniture, etc. you prefer quality on price.

A>B=C>A, does this mean that you must respect transitivity?

In AHP, it does not matter that the DM must judge on items on what he may not have the faintest idea, like comparing cost with contamination, cost with public health, or cost with manufacture, and thus, assuming that he must be an expert or knowledgeable in each area, or posses the expertise each stakeholder has in the company that owns the project. I think that you will agree that this is something hard to digest.

In my opinion you should explain which were the advances in AHP that you mention. Which advances, using fuzzy, or becoming hybrid with other methods like TOPSIS or DEMATEL, to name only some of them?

When you consider these serious hidden shortcomings. it is natural that people select AHP; it makes practitioners believe that complex problems can be solved by intuition. Reasoning, researching, consulting, examining? What for? That is unnecessary as per AHP standards. One of the things that bother the most in AHP it is the lack of rational explanations.

What happens if the scenario demands using Boolean notation, i.e., 1 or 0, or if there is precedence between alternatives, or if criteria are interrelated, or if some alternatives are exclusive and other inclusive, or if a criterion establishes conditions on another? According to AHP the solution is easy: Just disregard all of these irrelevant and annoying characteristics of the problem.Don’t worry, simply, ignore all of them; nobody will notice, because the results cannot be validated, since there is not a yardstick to compare to, and also because many journals’ reviewers will accept that and approve the manuscript, something extremely frequent.

Just read the abstracts of problems ‘solved’ by AHP in Scopus on in the Web. The most common is that they disregard something that Saaty said very clearly and in writing: AHP works only - and with reason - with independent criteria, something difficult to find in most real-life projects. Just for that simple fact most AHP solutions are invalid. By the way, it is very easy to prove that Saaty was right in this.

This is the reason of the ‘success’ of AHP. Nobody will discuss it, as nobody rebutted me when I denounced these things along my eight years in RG, and after 270,380 readings of my questions and answers, and 2,277 contributions as of today, according to metrics from this platform.

Curiously, along these years nobody rebutted none of what I assert. Extract your own conclusions.

AHP was useful back in the 70s, but now it is history, ANP, based on the same principles and arbitrariness of AHP, is however a little better, because it is more realistic although very difficult to understand, and also assuming some inexistent concepts such as impact and feedback, and that were never explained by Saaty.

AHP violates System’s’ Theory by claiming that one of its greatest advantages is the decomposition of a problem. True, for understanding it, but not for solving.

You cannot maximize or minimize a criterion independently of the others, because a problem is a system, and as that, it must be solved considering everything at the same time. It is as studying the performance of a car selecting independently the best engine, the best transmission, the best tires, and the best style. It cannot be done separately, due to the fact that the aerodynamics of the car, its tires, its transmission, electronic and electric system, etc. are input to design the best engine. Sounds reasonable?

However, this is what AHP does, and that ANP improvedby using a network.

I guess that Saaty understood that AHP was faulty on this regard, and then decided to correct it by developing ANP, and in so doing burying AHP, and this took place more that 30 years ago.

AHP is the most used MCDM in the world? Absolutely true, but why?

Because it has managed to convince people that real-life problems can be easily solved by intuition, as for instance complex problems like regional planning, or deciding by intuition that photovoltaics cells are better than wind turbines to generate electricity.

They are only technical issues, why to bother with them?

AHP is a system based on false assumptions such as:

1- You can compare two different criteria, that is legit, but what you cannot do is assign a value to those preferences. How for instance, do you decide that tenderness is say three times more important than love? This comparison is fantasy.

2- AHP assumes (Saaty words), that trade-offs are equivalent to weights. Both are completely different concepts and not interchangeable.

3- AHP assumes that what is the mind of the DM, can be applied to the real-world. This may be true only in his / her imagination, and convinced because AHP quietly equals them.

Explanation? No, what for?

4- On what grounds AHP assumes that criteria weights are constant? This misjudgement can be easily demonstrated, as I have done many times in RG

5- To say nothing that the DM is reduced to the role of a robot, when a formula instructs him/her to correct him or herself

6- Where is the rational in using compensation, that means that increasing in 0.5 human health is compensated by a proportional decrease in land use or in paving roads? This is a disparate.

7- Who says they these trade-offs are lineal? Only suppositions and because they were normalized to sum 1.

8- What axiom says that the DM may vote for hundreds or thousands of people? Quite the opposite, the Arrow ‘s theorem just addresses this issue and of course denies it, calling this action a dictatorship.

9- Even the so-called fundamental table is dubious, because it is a poor imitation of the Weber and Fechter law relating incentives increases with log responses. AHP happily assumes that the value in criterion C1 on C5 or ratio importance, equals to incentives increases.

10- Can you imagine using AHP or ANP in simulation where you have to change parameters hundreds of times? It would be a nightmare.

11- How useful can be a method where the criteria must be independent?

I can continue, but this is enough to prove the falsehood of AHP.

I have been many years in RG and since the very first date I commented AHP, mentioning these very aspects. If I were wrong it would have been natural that scientists and practitioners would have rebutted me. Again, I never received a rebuttal. Why?

For obvious reasons: There are not responses to them.

I want now to address some specific points of your paper:

1- In page 2 you say “development of the theoretical foundations of the AHP”

A researcher may have as many theories as he wants; the problem is to demonstrate a mathematical as well as common sense foundation, both absent in AHP, other than the Eigen Value and geometric mean. All other are only assumptions like results from pair-wise comparisons, trade-offs equivalence to weights, need of transitivity, weights that can evaluate alternatives, sensitivity analysis using the ceteris paribus principle, existence of feedback in ANP. etc.

None of them are mathematical, and many rejected by scientists

2- Using fuzzy AHP? What for? To improve arbitrary values?

3- In page 3 you speak about modelling, possibly the most important aspect to be considered in MCDM. It appears that the meaning and importance of modelling is absent in AHP, where it reduces to putting values in a matrix.

Modelling means to represent as close as possible a project or scenario in a mathematical format or matrix. Since I speak based on facts, I will put some examples:

a) How do you model in AHP, that alternative A4 must precede only alternatives A1, A2, A3, A9?. This is applied anywhere as in manufacturing, construction, health cate, etc.

b) How do you model in AHP, that considering alternatives A2 and A7 they are exclusive, i.e., it is one or the other, therefore, one of them must not be in the ranking. This is usual in road projects, for instance determining the best route between two cities.

c) How do you model in AHP that a criterion such as heavy snowfall may alter another criterion as maximum speed in a road, or in other words, the speed criterion depends on the heavy snowfall criterion, only when a certain value is reached. Used in hgh mountain highway is comparison with lower-level routes, of in modal transportation.

d) How do you model in AHP that an alternative must comply with a certain number of criteria? For instance: A6 and A8 must satisfy at least these four criteria C5, C7, C8 and C14. A common question when analyzing urban planning

e) How do you model in AHP, that if alternative A7 is selected, also A1 must be selected?

Found in sewerage networks

f) How do you model in AHP that a certain alternative must forcefully be in the ranking? Typical of projects already initiated or for pollical reasons.? For instance, a promise made by a candidate to major before elections

g) How do you model in AHP that out of 89 environmental indicators, the DM wants as a result only 25 to analyze. Used in selecting indicators

h) . How do you model in AHP, that when you reduce indicators, the resulting indicators in the final result must incorporate as much as possible the information contained in the alternatives not considered in the ranking? Used in urban and regional planning

i) How can you use the same criterion with two different means? For example, in providing water to a housing complex you need to establish a minimum and a maximum limit simultaneously, in such a way for the software to work within these limits?

I have many more questions like these most of them encountered in real-life problems in my life and all of them addressed using MCDM methods. Could you please consider answering how would you model them in AHP or even in ANP?

I will be grateful for your answer

I my humble opinion, it is evident in analyzing these real-world scenarios that AHP was not designed to solve complex problems, but perhaps I am mistaken of did not understand the power of AHP, and for this reason I ask for your answers. Using your own words, which are then the morphological ways used in AHP to solve real problems?

4- In page 7 you cite “I get it, it is like going to the optometrist who asks you whether you see better with one lens or the other; except that there is the additional question of how much better can you see?”

This known example reminds me another from Saaty relative to determine areas of geometrical figures. Both examples are biased because in both cases you know the real result which allows you to make comparisons. As you know, this situation ss inexistent in MCDM

5- In your page 8 you make references to rank reversal in AHP

Yes, it was discovered in AHP, but later it was discovered that it is common practically in all MCDM methods.

In my opinion it is an unavoidable phenomenon related not with the MCDM methods but due to geometrical reasons. It was nothing to do with inconsistencies.

I would love to discuss this subject with you publicly or privately, either in RG, email, or WhatsApp.

Nolberto Munier