Dear Bruno,

I would recommend you to find papers that support the usefulness of AHP over other methods for your specific research. AHP was initially developed in the 1970s, but many people still finds it useful for their research. Your professor makes the point. However, it does not mean that AHP is not suitable for your research.

Good luck.

Hi, How are you Dear Bruno,

I agreed with Mr Didik, you need to find some related papers. I wanna use too for my research topic, which mean that AHP is still useful. However, you can add also need idea too. By doing so if many others find also useful then you are welcome.

Best regard Didi

Hi Mr Didik

Thanks for the feedback. Perhaps there is need to use multi methods. Suggestions would be welcome though i am looking a tried and tested decion tools.

I have recently used AHP for assessing supply chain performance in my paper. it is very useful to convert people perceptions in to quantifiable form. No doubt fuzzy AHP would be a better option but it depends on the application.

You can find much more details on the Capabilities & Limitations of AHP in the provided links:

https://entwicklungspolitik.uni-hohenheim.de/uploads/media/DP_09_1999_Hartwich.pdf

http://www.sciencedirect.com/science/article/pii/0895717788904815

http://www.palgrave-journals.com/ori/journal/v22/n4/full/ori200910a.html

Certainly not because , it's a refinement and a practical implementation of the weighted sum, which finally is one of the more instinctive aggregation method. It has the advantages and inconvenient of weighted sums no more no less (see Pomerol and Barba-Romero, Kluwer, 2000). 

Dear Bruno;

as some of the comments already mentioned: AHP is still among the dominant methods within MCDM. One of the reasons for that is its transparency and simplicity, which makes results defendable and also understandable to laymen. Thus, I recommend that during your selection process for the method (which is a MCD process in itself) you take into consideration your goals. If you need to present results to a broader or non-academic audience, e.g. in a public hearing, you might want to use a simple method that renders useful results (such as pure AHP, DEA, GP, or the like). If you only move in an academic environment or you can assume that your target audience are experts in the field, you might want to step up to more complex methods, such as ANP or hybrid approaches.

I echo some of the previous comments: Conduct a literature review with a specific focus on your area of research and limit the time period for scientific articles to the last 5 years.

Good luck;

Simon Musaeus   

Dear Bruno, 

AHP is a method that suffers from several reported

flaws. In fact, there are several articles that report AHP problems, for instance:

C. A. Bana e Costa and J.-C. Vansnick, "A critical analysis of the

eigenvalue method used to derive priorities in AHP," European Journal

of Operational Research, vol. 187, pp. 1422-1428, 2008.

Therefore I would not recommend you to use this approach in your research. Please let me know if you have any question.

Regards,

Teresa

No, the AHP is not old or outdated. In fact, there is also the ANP which is a generalization of AHP, which can be used for almost any kind of discrete problem, no matter how complex. (By the way: remember, new is not always synonimus of good).

One more thing; There is an index of closeness called (Compatibility Index G), that can be used to measure how good is the final outcome (the priority vector), compared with actual values. This index has shown that the AHP (and ANP still better) are obtaining very good results, very close to actual results (when the last are possible of being known).

Teresa;here 

the cristicism of Bana e Costa and Vansnick has been contested here: doi:10.1016/j.ins.2008.10.001

Until today, I have not seen any study of real world problems in which the supposed shortcomings of AHP (and the above article is not the first and not the last one), would have had any practical impact. AHP/ANP are useful and reliable tools.

Best regards

Dear Mrs. Teresa, I participated in an article rebutting the criticism of Bana e Costa, and Vasnick (and also from Watson 1982 and Belton and Gear 1983). "A Systemic Rebuttal to the criticism of using the eigenvector for priority assessment in the AHP for decision making"2010. This article shows that, from a systemic point of view, the eigenvector is a very good mathematical operator to be applied in this kind of systemic problems, (based mainly in graph theory to measure the intensity of paths). And we found that when you try to enforce the system with some arbitrary condition (like COP condition or Bana e Costa's condition), normally the result is the lost of the emerging properties of the system, jeopardizing the whole system behavior.

Dear All

Thanks so much thus far for the feedback though i am somewhat more confused. I am quite new in this area of operations research as my background is development finance. But i note that much as the flaws for the AHP are reasonable especially the pairwise comparisons and consistency ratio issues, the emerging alternatives appear to be more academic than practical and their use has not been as dominant as the AHP. Somewhat, in my literature review, i have been able to connect with the AHP with much ease but that is not why i appear to have a bias for it. If there is something out there that is more practical and more widely used than AHP, thats what i am looking for.

What i seek to develop is a model that is meant to evaluate risks in public sector investments hence the modality must not be too academic but must have a strong semblance for reality and easily understood by non technical staff so that it stands a better chance of being adopted for actual implementation. I do work for a policy research institute and from experience, the moment a politician smells some 'crazy' models (we mostly use econometrics) , they usually end up rubbishing the model as being academic. At that point, what a researcher ends up with is research for research and not for practical implementation.

Dear Bruno;

have you seen this article? The authors present some options.

http://file.scirp.org/Html/4-9900078_5167.htm

Best regards

http://file.scirp.org/Html/4-9900078_5167.htm

AHP is deeply flawed.  The primary issue is that it relies strictly on pairwise comparison and ignores critical information about the relationship to other alternatives.  One work that you should consult is: Saari, D.G. and K.K. Sieberg. 2004. "Are partwise comparisons reliable?" Research in Engineering Design 15: 62–71.  Don Saari has written extensively on these problems and has proven important theorems about the unique benefits of the Borda Count and on how it deflects issues raised by Arrow's Theorem.

There are many other problems with AHP but the most fatal is that it ignores critical information.

Not outdated but simply not good.

AHP reads the decision matrix horizontally and even consider the objectives two by two, being  in that way a victim of the Condorcet-Arrow Paradox. Then weights have a double meaning of normalization and importance. The information is a mixture of verbal statements and quantities, creating a poor stability,far from simplicity and nevertheless with a maximum of calculations and a high computer time.

Hello Colleagues

Many thanks to you all for the various views. 

Given the lack of agreement on this matter as expected, may i rephrase the question as follows:

What would be an ideal MCDA tool to develop a risk assessment framework with more than 7 criteria each having 5 sub criteria or attributes?. Based on feedback from many, i note that the pairwise comparisons for a problem with more 7 criteria can be too daunting to respondents hence issues of consistency can surely arise. If there is an appropriate online analysis tool like Expert Choice for AHP, kindly advise.

Hi Wald

Thanks a million for the feedback. I have since sent you an email to seek your further input.

There are many critics about AHP, like the few showed here. Most of them easy to rebut as comments show poor AHP understanding.  For instance, lack of use of critical information clearly indicates low modelling skills under feedback conditions (where ANP might be the right method). Similarly, reference to Arrow's theorem claims for need on clarification of difference between ordinal and cardinal numbers (and the properties of its scales), or to understand that geometric mean, eigenvector operator and optimization process are different concepts for different purposes (sometimes complementary but never opposite). Also, learning about Order Topology and Graph Theory (including Cesaro'Sum important contribution) to build measurement in decision making might  be of help too.

Being thousands (if not tens of thousands) of practical, real, examples of good applications of AHP (and ANP), as reference, and being tested in calibrating situations in economic and physic problems, it is simple to sustain that, as any method, AHP/ANP provide valuable results when used properly by knowledgeable actors. Nevertheless, it is true each methodology sustains results within its framework of indicated assumptions, and the practitioner should verify before applying a method mechanically, for the sake of testing and publishing.

No matter how many times the needs of solid knowledge of AHP is recommended, it is also true there is no worse deaf, that who does not want to hear. And that is a personal decision, no doubts about it. 

use MULTIMOORA (for bibliography see GOOGLE or Web of Science). I used this model for 27 objectives with 15 alternatives and 22 objectives with 28 alternatives (the European Union Countries) .You can apply it for your 35 objectives. In fact there is no limit. 

Hi Claudio

Thanks for the feedback, appreciated. One alternative i have so far found in one of Saaty's papers (2008) is to use rating scales as an alternative to pairwise comparisons though under this method, one has to define the finer rating scales for each attribute. In the same paper, he indicates that pairwise comparisons yields better results but marginally so. Some readings i have done proposes use of pairwise comparisons at criteria level and use rating scales at sub criteria/attribute level.

Like i indicated, i foresee myself having

Hi Bruno,

When we are using human decision-making, AHP is the best way to go, since, we (human /people) cannot compare many items at the same time to make an effective decision. So piecewise comparison is a good approach- you could use this approach when asking your participants to compare a few items as well.

However, if you are using mathematical modelling or computer simulation et cetera you could use many other multi-criteria decision-making (MCDM) approaches.

Hope it helps.

Regards,

Sev

Hi Bruno,

Yes, you can use rating model (knew as absolute measurement in AHP), this is a good alternative when you have many alternatives and wish to keep the ranking unaltered by the alternatives (no feedback between alternatives and between terminal criteria). For each terminal criteria you have to build a rating scale, this is an important step of the modelling process. The scale is not the Saaty's scale, it is a specific scale for each terminal criteria, built by pair comparison or provided for some external process (at the end it has to be a cardinal scale that represent the real intensities ratio among the levels).

Hint: an important consideration when structuring the AHP model is to check the 4 Axioms in which AHP was built on, specially Axiom 2 about homogeneity between criteria belonging to the same level of the hierarchy.

Any perception based decisions best tool is AHP or fuzzy AHP. it is very powerful today also. yes there are some drawbacks but if the user has enough knowledge and full understanding of the basic concept and its application. every thing in the world has some drawbacks but one has to overcome that by due intelligence and knowledge about the domain. i think that is the true job of a researcher.

The AHP is the only accurate and rigorous mathematical way known for the measurement on intangibles. It is not going to get old for a long time.

There might be newer techniques, simpler methods but what stands out AHP is that it provides a measure of the consistency of the decision-makers in the pairwise comparison of criteria. I'm not sure of any other methods that offers this

Dear Bruno,

Simplicity is an advantage. Outdated - I do not know, but please note that "invented long time ago" does not mean automatically obsolete or bad, vide: Pythagorean theorem. I would say, that anybody who want to use AHP/ANP (as well as any other decision method) should know theirs strengths and places where one may encounter problems. Condition of Order Preservation mentioned by Teresa Rodrigues is just another argument for this thesis (See: Kulakowski, K. Notes on Order Preservation and Consistency in AHP, EJOR 2015, http://dx.doi.org/10.1016/j.ejor.2015.03.010)

BTW: The best decision method will not help you if you say to the common sense - goodbye ;)

best regards,

Konrad

Once again, the lack of knowledge about AHP (coming now from using the eigenvector operator), it shows the misguided counterposition between optimization analysis and system analysis.

In the optimization extreme visions, you may have the absurd idea that every value has to be precise and consistent with every other, like the condition of order of preference (COP). But, this is some kind of "terroristic vision" if viewed from a systemic point of view. I mean, if you apply COP in a complex system you may have your optimization but, I can assure you, your system representation is dead long ago.

This is not the intelligent way to do things, your system do not have to die, it has to grow up and represent all the possible interactions at every level (not just in the first level), and that is what the eigenvector operator does (a system operator), once your system is well covered (in a steady point) then (and only then), you may think in optimization process.

By the way, in sismic analysis (a clear example of a complex system), first you have to calculate the steady point and only then you may apply an optimization process. (Make a guess about which system operator has to be used to establish that steady point).

Some authors don't seem to know about the thirty year old proof  that the eigen-vector is necessary when the matrix is inconsistent. Also that the Fundamental Scale of the AHP is not a guess but is derived from the Weber-Fechner stimulus response theory. In addition and by way of validation,  if one replaces the numbers of the Fundamantal scale by other numbers from some other scale, in a matrix for which the answer is known on a measurement scale, one finds that the answer is no longer close. 

Finally, there are now many papers that show fuzzifying the AHP does not improve on the eigenvector result. This should tell one that with one such counterexample, there cannot be a theorem which says that fuzzy is always good to use. There is no such theorem and one needs to tone down the boasting about how good fuzzy is. It is an act of desperation to maintain this attitude. Future generations will ask why? Where is the proof? 

When a matrix is consistent all proposed methods give the same correct answer. No need to do any statistical experiments. The mathematical proof is sufficient and trivial.  

I am rather reluctant to be a member of the large group of scientists working on PC matrices, although, of course, as all of us,  I have been  using some methods of pairwise comparisons for years. In my case, mostly not in a professional way. I do not always agree with prof.  Waldemar Koczkodaj nor with other scientists working on PC methods, however, I agree with prof. Koczkodaj that I have never met in my entire life a man more devoted to science than prof. Koczkodaj who pays very little attention to making money by twisting science... This is certainly  prof. Koczkodaj who has been working on turning my attention to scientific pairwise comparisons methods and inconsistency indices. This is why we wrote together with J. Szybowski an introductory paper about inconsistency indicators maps and their connections with G-metrics some time ago this year. Some knowledge of group theory is necessary to understand this paper. Of course, generalizations and development  of this approach are still possible. What troubles me is that I am affraid that I do not read fast enough to be able to become an expert in this field for I am unable to read so many articles of other authors that have beed published so far. Therefore, unifying approaches are needed. 

•The lesson of history is that a bold and plausible theory that fills a scientific need is seldom broken by the impact of contrary facts and arguments. Only with an alternative theory can we hope to displace a defective one.

     ---- S. S. Stevens, On the psychophysical law, Psychological Review, 1957

I am searching for applications of reciprocal and consistent-shaped  matrices in physics and, unfortunately, I am unable to find any such  non-trivial matrices that can be really useful to  explain some problems of physics. However, some interesting matrices of consistent shape appear naturally  in mathematics, especially matrices that take values in not necessarily abelian groups are interesting. Hermitian and skew-Hermitian matrices can be considered as satisfying a kind of reciprocity with respect to a suitably chosen mapping. However, no reasonable kind of consistency is visible in the matrices of size at most three that are applied in physics and are known to me. Of course, a physicist may want to create a matrix  of results of measurement to get a consistent matrix in physics  but it does not seem to make any sense to create such a matrix because it cannot explain a law of physics.  Perhaps, experts in PC-matrices know what such matrices are for in physics. I do not want to think  that they are certainly needless in physics. I would be grateful for a professional help of experts in PC-matrices. 

if $\sigma_i$ denotes  the 2\times 2 Pauli's matrix, then the matrix $[a_{i,j}$ where $a_{i,j}=\sigma_i\sigma_j$ is a consistent matrix over the multiplicative group of 2\times 2 matrices whose elements are complex numbers. This is one of consistent matrices formed naturally from matrices applied in physics. The scale used here is a subset of the set of 2\times 2 matrices over the set of complex numbers. I think that this is a new observation, not an outdated one. I wonder what interpretation of it could be the best, 

Hi Eliza, waiting for your new findings ...

Since I am a beginner in PC-methods and applications of PC-matrices, many discoveries from the past are new for me. To get a more appropriate applications of consistency conditions, I have generalized a notion of a consistent matrix to the notion of a consistent mapping defined on X\times X and taking values in a group. Matrices are also mappings.  The consistency condition for a mapping F:X\times X\to G is as follows: F(x,y)\odotF(y,z)=F(x,z) where \odot is the action in the group G=(G,\odot). When X\subseteq G is non-empty and such that each element of X is its own inverse in the group G, then (and only in this case) the mapping  defined by $F(x,y)=x\odot y$ for $x,y\in X$ is consistent . Pauli's matrices \sigma_i satisfy the condition $\sigma_i\sigma_i=I$. Some other matrices met in physics satisfy it, too. Unfortunately, I know too little about matrices in physics to say more at this moment.

The Analytic Hierarchy Process-Is it old and Outdated? - ResearchGate. Available from: https://www.researchgate.net/post/The_Analytic_Hierarchy_Process-Is_it_old_and_Outdated#view=569afc895dbbbd61528b4567 [accessed Jan 20, 2016].

http://www.sciencedirect.com/science/article/pii/0895717788904815

http://www.palgrave-journals.com/ori/journal/v22/n4/full/ori200910a.html

https://entwicklungspolitik.uni-hohenheim.de/uploads/media/DP_09_1999_Hartwich.pdf

You might find my latest paper useful.

Article Deflecting Arrow by Aggregating Rankings of Multiple Correla...

Dear Sir you may also find following article useful for developing risk model

Multi-criteria supply chain performance evaluation: An Indian chemical industry case study

O Vaidya, M Hudnurkar

International Journal of Productivity and Performance Management 62 (3), 293-316

Dear sir, you may use a multicriteria decision model called PCbHDM for your purpose.

The PCbHDM is a MCDM hierarchical decision model. It is proved mathematically that this model is immune to the rank reversal.

You can find its applicatioin framework (also the mathematical proof and some discussion) in the following paper:

Fujun Hou, Market competitiveness evaluation of mechanical equipment with a pairwise comparisons hierarchical model,

PLoS ONE 11(1): e0146862. DOI:10.1371/journal.pone.0146862.

Additionally, there are also some issues realted to some current MCDM models. They are approached in my work. You can get to know details from the

following paper:

Fujun Hou, A hierarchical decision model based on pairwise comparisons, Fundamenta Informaticae 144 (2016) 333–348.

Regards,

Fujun

There are very many papers relevant to AHP  and it takes too much time to read them.  I think that authors should not be in a hurry while writing their papers because readers do not want to waste their time on reading papers that are to be improved soon.. More complete, nicely polished  results should be published. I know that it might be hard or, perhaps, even impossible  for some authors to write papers without any mistakes and without too many words in them. However, I believe that all who write can try to be more careful and. before they submit their paper to a journal, let them read their text several times to catch all misprints and other errors.  

Methodology to be used depends on the needs of your problem. AHP cannot cater all the needs and hence other techniques are relevant.  Especially when there are a lot of factors to compare, paired comparisons are practically invalid, hence so AHP cannot be applied.  GRA can be used in such instances to get possibility values.  Many other techniques are also available.

Anyway, it is good to have a deeper knowledge about AHP and, more generally, about PC.

I agree with Eliza.

There is a lot of confusion and misunderstanding about AHP, scales of measurement and mode of measurement.

My free web-based AHP software (http://bpmsg.com/academic/ahp.php) has >4000 users, 600 of them active with more than 1000 projects and 3500 participants. My AHP exel template was downloaded nearly 21,000 times. Does not look like outdated!

Dear Klaus

No, I don´t think that AHP is outdated, but the fact that over than 1000 projects have been developed using AHP does not mean that their results are correct (which is impossible to check), or than the method is sound (which is easily challenged).

Remember that a method such as cost/benefit analysis was considered during decades the most for decision making. It only considered the economic aspect, but naturally, aspects such as the environment and society were completely ignored, and thus, for their users the method was correct.

The GDP, a method  used world-wide, is another example. Everybody knows that it does not represent a country growth, however continues being used in despite of effort for United Nations and other organizations to improve it.

 AHP has virtues, such as being simple, understandable and easy, but sometimes cumbersome to implement. However, that easiness normally does not go well with real life complexity, and this is for me it weakest aspect. It is without a doubt and by far, the most used model, but apparently your >4000 users did not take into account or probably did not realized its drawbacks.

Dear Bruno

Risk is defined as the product of probability of occurrence times impact.

If you can determine that product for each alternative, in a risk criterion, and calling for its minimization, you can use different MCDM models such as PROMETHEE. or TOPSIS.

 However, this a static scenario, if your probabilities and impacts may change as a function of time, you would need to perform a sensitivity analysis

If need help I will be happy to cooperate

Dear Waldemar

I had not seen your comments until today, however I agree with most of them about AHP.

1. Pair- wise comparison is far from new. It is not a development of Dr. Saaty, however  I don’t think or I have never read that he is claiming authorship of it. He just uses it. In fact it is credited to L.L. Thurstone that developed it in 1927.

2. I believe that AHP is a very good method, probably the best, for trivial problems, where comparisons are made for the direct beneficiaries of the consequences of a project, such as personal selection for purchasing a car or renting and apartment, as well as selecting new personnel for hiring in a company.

3. In my opinion, decision making using AHP for serious and complex projects may produce very wrong decisions and even with catastrophic results. I bear witness of one of them since it very badly affected a huge project I was working on, because following the preferences of ‘experts’ they did not pay attention to people claim that said project will hurt them. The Supreme Court of Canada ruled against the company, and it lost more that one thousand million dollars. I also know other cases such as this and therefore I am talking about something that I know very well. To those who are interested and can give full details of these several projects.

4. Even when AHP defenders say that the model can manage complex projects it is not true.

What perhaps they call ‘complex projects’ are projects with a large decision tree, but that is not complexity, that is complication, which is not the same. AHP is not able to handle complex projects because personal preferences have no room there. Just imagine applying personal preferences about the kind of fuel to use in a rocket, or deciding the best route for the under sea tunnel between France and England, or deciding what type of dam is better for the huge Itaipú hydro dam in Brazil.

In addition, it cannot handle complex projects simply because is not built for that. Just think that:

* It does not consider resources availability, and thus it assumes that they ere limitless, which of course is absurd.

* It does not take REALITY into account, since it ignores elemental facts such as: Existing conditioning between alternatives, correlation between criteria, annual budgets, it does not even take notice that in a portfolio competing for resources there are normally projects in different stages of development, and with different annual percent of completion, while some have not been started yet and with their own annual percentage of completion, and all of them have to be considered simultaneously. Can any of AHP defenders tell me how it can handle this issue?

Add the fact that normally projects underway cannot be stopped or that a project must forcefully be done other than for technical reasons. For instance, it happened to me than in selecting a project for a city five year plan I found myself with the IMPOSITION from the major of a city to include a project that had been no selected by a MCDM. Why? Because it was his campaign promise and he said that he did not care about what the mathematical models said; he wanted his project selected. This is reality.

How can AHP manage that?   AHP does not consider either when there is funds scarcity and that then not all projects can be developed, another reality.

* AHP, is not prepared in its second stage to evaluate alternatives because it uses weights that, on top of being subjective, only determine criteria relative importance. However, that is irrelevant to evaluate alternatives, because what is really important is criteria capacity for evaluation, and this is measured by the discrimination between its performance components, not by criteria weights. Another reality.

* Because its cumbersome wise-comparison system, it is generally recommended not to exceed ten criteria. NO COMPLEX PROJECT CAN BE EVALUATED ONLY ON THE BASE OF SUCH A SHORT NUMBER OF CRITERIA. Complex projects usually need hundreds of criteria, which is well far away of AHP capabilities, at least from the economical and practical point of view.

You state that only optimization methods give the optimal solution. It means methods using mathematical programming such as Linear Programming, Goal Programming, Epsilon restrictions, Genetic algorithms, etc. I completely agree with you, and in addition these methods are able to replicate reality not in a 100 %  of course, but with an approximation by far superior than other methods. However, they also have limitations that must be overcome, and that have been, although not yielding optimal solutions but a compromise one.

I also agree with you about the journals. They don’t care to publish revolutionary ideas about established methods, even when they are incomplete or wrong. Thanks to Research Gate we have the opportunity to express our ideas and be freely discussed by everybody.

I have written many answers to RG colleagues regarding AHP. I found a common denominator in all of them. While I put real examples, point out aspects, and I fundament mathematically and logically my concerns about AHP, very few responded. Only one person responded and addressed my issues; however, he limits to words and more words that in reality mean nothing and consequently without telling exactly how to solve a problem.

I cordially invite my colleagues to refute what I say about AHP.  Many people is using this method and they have the right to be informed about its possibilities and drawbacks..

I am not saying that I am right. What I am asking for is for somebody telling me that I am wrong, where and why.

Dear prof. Klaus,

Your tutorials are really interesting and I started my first step into research solving a decision making problem using the excel sheet provided by you.  Still, when there are too many factors to compare, pairwise comparisons and the consistency comes out to be risky measures and the validation of the results are practically impossible.

Dear prof Waldemar and prof. Nolberto,

Thanks for sharing the above useful information.

Dear Nolberto,

yes, I agree, the numbers only show that AHP is not outdated (which was the original question). They don't show, whether the results are correct or incorrect, but they also do not show whether the users did or did not realise the method's drawbacks and limitations.

For me, as a practitioner, AHP is one of the supporting tools in decision making. The intention of a tool is what it does. A hammer intends to strike, a lever intends to lift. It is what they are made for.

From my users feedback I get often the impression that some of them expect a decision making support tool to make the decision for them, and this is not what it is made for.

In my practical applications AHP helped me and the teams a lot to gain a better insight into a decision problem, to separate important from less important criteria and to achieve a group consensus and agreement how to tackle a problem or proceed with a project. Probably, this could be achieved with other tools too, but as you say, AHP is simple, understandable and easy.

For sure, real world problems are complex. Therefore they have to be broken down and simplified, to be handled with the method, and I agree, over-simplification can be dangerous. On the other hand, what other approach than the break down of complex problems into digestable pieces is possible?

Finally, it's not the tool producing the decision, but the humans behind it. They will be accountable for the decision, and it's their responsibility to find the appropriate model of a decision problem and the right balance between  rational and non-rational arguments and potential consequences of their decision.

Just my humble opinion.

Klaus

Dear Rajesh,

thanks for your feedback; glad to hear that my work was helpful to you.Yes, I agree, beyond 7 to 9 criteria for most people pairwise comparisons become difficult to handle in a consistent way.

Dear Klaus,

K- yes, I agree, the numbers only show that AHP is not outdated (which was the original question). They don't show, whether the results are correct or incorrect, but they also do not show whether the users did or did not realise the method's drawbacks and limitations.

There is no method, except Linear Programming that can assure the DM that the result is correct, provided the data is correct. And that is my point with AHP. Data is not correct because it is manipulated in the preferences stage.

Some months ago, here in RG somebody asked how quantitative values are managed in AHP. Only one AHP defender replied, but not explaining anything, but proposing some general norms to be followed that I am sure left the asking colleague in the dark. The reason is simply; nobody can give a rational explanation of why the DM is allowed to modify data which is truly reliable, as can be for instance homologated values for performances from manufacturers in a case of equipment selection. On what grounds the DM can modify those figures and why? I have never received an explanation by this strange procedure.

 Regarding your second point you are right, users don’t realize that because they do not have to. They do not have to know the intricacies of a method to use it, as you do not need to know how the engine of your car works to drive it. It is our function as researchers and professors to point out the deficiencies for people to be aware of the risks that they are taking using some methods, and this is my aim.

I am not against any method, all of them incorporate good, bad and questionable procedures, and I don’t think that there is an exception on that. Linear Programming for instance was very much restricted because it deals with only one objective, unless you use Goal Programming, but also both have another drawback such as accepting only quantitative criteria.

K- For me, as a practitioner, AHP is one of the supporting tools in decision making. The intention of a tool is what it does. A hammer intends to strike, a lever intends to lift. It is what they are made for.

Agreed, both tools are very useful indeed, provided that you use them properly and for their intended use. I have said several times that for me AHP is the best tool for decision making for trivial problems, not for complex ones, and also have shared this opinion and many others with his creator.

K- From my users feedback I get often the impression that some of them expect a decision making support tool to make the decision for them, and this is not what it is made for.

This is very true. People often do not realize that these are only tools. Their only function is to process data not to decide for the DM. However, in general MCDM models do not give the DM enough information for him to take actions. An example is the so called sensitivity analysis. The only thing that the DM can get from it is to determine when the ranking changes because a criterion changes. Not very useful data indeed!

K- In my practical applications AHP helped me and the teams a lot to gain a better insight into a decision problem, to separate important from less important criteria and to achieve a group consensus and agreement how to tackle a problem or proceed with a project.

There is no doubt about your assertion. Even if I do not approve the preferences scheme, it is true that it may lead to a healthy discussion that provides insight into a problem, but it does not mean that said procedure has to be used for providing unrealistic and biased data as AHP does.

This discussion may be extremely valuable when examining the results given by a model, not before, as is done in AHP. That is, you process thy quantitative and qualitative data you have, run a model and get results. Then, and only then, you can dissect the solution and inspect it from different angles, including of course your knowledge and know- how, and even, because of that, reversing the ranking. This procedure is a universal practice, such as producing models and testing them and then extracting conclusions. You can see this in the aeronautical, automobile, food, fashion, etc., industries.

K- Probably, this could be achieved with other tools too, but as you say, AHP is simple, understandable and easy.

Yes, this can be achieved by other tools too, with the difference that normally decisions taken in modelling are supported by mathematical tools, such as statistics, Monte Carlo, Regression, etc.. It is not a guarantee of rightness but I believe that you will agree that this is more reliable that the arbitrary system used in AHP.

K- For sure, real world problems are complex. Therefore they have to be broken down and simplified, to be handled with the method, and I agree, over-simplification can be dangerous. On the other hand, what other approach than the break down of complex problems into digestible pieces is possible?

I don’t share your opinion that complex problems must also be broken too for their examination.  May be in some cases, but this is not a norm, and possibly its application may lead to inaccuracies in results because events are not independent, quite the opposite, they are linked in an intricate fabric, even with feedbacks, where many times an action depends in the results of others. The ‘Divide and rule’ policy may be good for politicians but may not work well in engineering.

Answering your question, I do not know other procedure that uses that system. I have worked in several large projects, complex by nature, and never felt the need to dissect it in pieces.

K- Finally, it's not the tool producing the decision, but the humans behind it.

Without the shade of a doubt!

K- They will be accountable for the decision, and it's their responsibility to find the appropriate model of a decision problem and the right balance between  rational and non-rational arguments and potential consequences of their decision.

The problem is that it is very difficult to determine if the job done according to certain procedure could have been bettered by another, since do not know which the best is. However, some times, as I mentioned it in my last comment, you can tell without a doubt that the decision taken was wrong, and the mathematical model has nothing to do with it.

It is also my humble opinion Klaus, and thank you for your invaluable input

Nolberto

Dear Norberto,

nothing to add. Thanks for your detailed reply.

Klaus

There are many interesting mathematical problems relevant with AHP, so even some mathematicians can find it interesting to study the mathematical side of AHP.

Dear Eliza,

You are right; there are a lot of interesting mathematical problems to be solved with AHP. In fact, I have used AHP/ANP for real and complex ones (not just academic).

After many years of application and working on some extensions on the methodology, I believe the following 3 topics are important to keep in mind:

1.      The art of modeling:

Modelling is an art not a technique. AHP needs good models to obtain good results (this is especially valid in complex problems). This art of modeling is based in the analysis and synthesis process, analysis to break down complex problems and synthesis to recover the properties (including the emerging properties) of the initial system. So, this is not just applying software as a tool from a tool-kit by someone with no understanding on how AHP/ANP work; I have seen many wrong models which (of course) return wrong results. Although it seems obvious, the MCDM is a decision making modeling process. Hence, the user needs to understand what is behind the method. Next, just a couple of examples:

·         Checking method’s axioms and/or hypothesis. (By the way, if a method does not explicitly present its axioms and/or hypothesis, it is a direct call to run away from it).

·         Checking the mode of measurement; You may use absolute or relative measurement modes depending of what you are looking for and what degree of dependency between criteria and alternatives you will allow within the model (this includes the old “issue” of rank reversal).

So, using AHP (and making complex decisions) is not like driven a car in a week-end where you can be “blind” about how the engine works; you must know what is happening and how to control the modeling /decision process. (Most of the times this is one of the main reasons that makes the difference when be hired as an expert).

2.- Proving results:

Some people claim that AHP/ANP has not provided proof about its ability to return acceptable results. I totally disagree. There are some very simple examples available for verification purposes, as the classic Area problem, the Perimeter problem (which involves feedback and hence rank reversal issue), and one that I find very nice, related with the physical problem of the inverse square law of optic (the intensity of light decays with the inverse square of the distance). AHP, with a very simple model, can obtain very close (compatible) results to the real set of distances, and nobody can argue that this is a linear problem; the only requirement is to have a good sense of deepness (just like when making the test for the driven license). To better understand this issue, I suggest the book “The Number Sense”. How the mind creates mathematics, by the great mathematician Stanislas Dehaene.

 I have tested several times all these examples with students and professionals during training and consultancy activity and for almost all cases I got the right results (right in the sense of been close/compatible enough to the actual results). By the way, there are many others examples (several designed and conducted by Dr.Thomas Saaty), which can be replied anytime. There is also a book (by Rozann Whitaker) including a lot of examples like these from simple to more complex ones to be conducted in AHP and also in ANP.

There is also a new compatibility index (created especially to be used in weighted environments), to establish if two priority vectors are close enough to consider them compatible. This index can be used also to establish what MCDM method get closest results to actual data, or for pattern recognition in a weighted environment, or to measure if the consistency index of Saaty is an acceptable index in terms of the priority vector obtained for the limiting case of consistency index, compared with the actual or expected results.

 3. - Combining different methods:

AHP and ANP may be combined with other OR methods (linear programming, integer lineal programming, Control Path Method, etc...), and this is because AHP is, at the end, a metric engine, creating a ratio scale metric that has the properties required by the classic methods of OR.

Dear Bruno;

Do you think a2=b2 +c2 is old?  I think anyone can say no. So math never die.

Dear Kerin

That's right, math never die but processes and reasoning might do or change

Einstein dramatically proved with his General Relativity Theory that Newton's Laws cannot be applied to all cases

AHP is very good for small personal and corporate wise problems because it reflects what the interested people know and want, and for me it is still very valid. However, it cannot be applied to all cases

 The AHP process was never good for complicated problems because it is unable to reflect reality, when DMs put their values in lieu of recognizing true values produced by polls and surveys comprising thousand of people and actual values.

The AHP process is wrong from the realistic point of view, except when used as personal or corporate projects, because weights are used to select alternatives and that is incorrect, since they only reflect, and subjectively, the importance between criteria.

If you are dealing with a risk assessment project remember that risk is Probability of Occurrence times Impacts; therefore, those are real although not exactly known issues. Sometimes experts can appreciate the probability of occurrence when there is no information, but usually it exists, in form of statistics or similar circumstances, and impacts can be normally appreciated with some reliability. It is not a matter of guessing.

In my opinion you can use TOPSIS but without weights.

Dear Nolberto,

you are very wrong in your statament. I have applied AHP in large problems with very good results.

Two more things:

1.- Probabilities is a subset of priorities, so you can use probabilities in a AHP or ANP model. (I'm working in risk assessment for natural disaster management, and as you may know, management is strongly related to priorities).

2.- Weights are absolute necessary to build priorities, and get a reasonable answer. Perhaps, what we really need is to know more about measuring in weighted environments, in order to have a better understanding in how to apply this (or any) cardinal MCDM method.

At the end, maybe, the problem is not in the method but in how is applied.

Dear Waldemar

You expressed it very well

I have said the same as you state many times. You can reach a reasonable answer when you work with problems which result you know before hand (as the AHP example with geometrical figures), but that is not a guarantee that you can assume certain results as valid  when you don't know the true value. 

Dear Claudio

A) I appreciate your answer; however I work with facts not with words. It remains to be seen what is that you call ‘large problems’; just because they respond to a large decision tree? Please notice that I refer to complex and not to large problems. The latter are just a matter of patience by performing large amounts of pair comparisons, while the former are a matter of difficulty in  modelling reality. Let me put some examples

1. There are problems in river basins with hundreds of criteria and no less alternatives.

How can you model in AHP or in ANP that a town located down stream demands receiving quality water that is without too much salt, from undertakings that take place upstream, or chemicals from a paper plant?

2. In problems calling for supplier’s selection in large projects such as chemical plants, how do you consider the possibility of joint venture?

3. In a construction plan and with a budget for the next five years, where there is a portfolio of say seven projects, how do you select the most adequate when there are not enough funds to build them all, when one project is already under construction, another finishing in six months, and five projects that have not started yet and will scheduled to start at different times?. Consider in addition that there is an annual budget to be satisfied and which cannot be surpassed, and of course with each project at different annual percentages of completion

4. Have you cane across with selection when one of the projects must be selected without discussion, because political reasons? How do you solve it in AHP or ANP?

B) How many times  have I asked you to tell me how you can affirm that in applying a MCDM method (ANY, not only AHP), the results are good, if you don’t know which the true result is? Please, could you answer this question?

The result may be satisfactory because it satisfies the DMs, but it does not mean that it is correct

If we solve the same problem, you using AHP, and I  using Promethee, Electre , Topsis and SIMUS, and we got five different rankings, as it can happens (and if you need an example I can provide it), all of them according to you are very good? And if they are, which of them do you think is the best? And then which result do you adopt?

C) In analyzing risk for several alternatives probabilities are independent, so there are not priorities there. For a risk  criterion probability for alternative A can be 65% and probability for criterion B can be say 40%, they are not related as you suggest and with your ratio system.

D) Sorry, but it is not true that you need weights to build prtiorities .It appears that you are not aware that there are several MCDM that do not use weights

E) I agree with you in your last statement. I am not against AHP when used for trivial problems because I think that the method is good for that kind of problems, however, I insist that AHP is not prepared to handle complex problems. If you think that I am mistaken, please try to solve one of the problems that I proposed in A). Of course, I can reciprocate, choose a complex problem amongst them or another of your choice and I will be happy to send you not only the result but also the procedure for you to criticize.

I disagree that 'AHP is a valid method' at all. I do not just criticize the AHP but suggest an alternative to it. The interested people could have a look at the following article and make a comparison.

Hou, Fujun. "On the hierarchical model PCbHA: a more general case." Soft Computing (2017): 1-12.

Dear Fujun

I said that in my opinion AHP is s good method for trivial and simple elemental problems  and that it is not prepared to MODEL, let alone to solve, complex problems.

If somebody think that I am wrong, I would very much appreciate it that he/she demonstrates it with an example representing reality and complexity  and solved by AHP.

Dear Nolberto,

Thanks!

It's permissible even preferable to allow people having different opinions on a topic/method in social science.

When you use the AHP in your research/application, you could also give the PCbHA a trial.

Best,

-- Fujun

I agree with TL Saaty that AHP ia an accurate and rigorous technique. Like every other technique, AHP is not perfect and any improvement to make it more practical and versatile should be very beneficial

"    The problem is with ' I have used so-and-so and it works ' since it does not provide a proof and a different so-and-so  may produce even better results.    "

----- Professor Waldemar W. Koczkodaj

Dear Fujun

I am not sure that I understand you when comparing AHP and PCbHA

I agree with you about allowing people to have different opinions on a method in social science, however MCDM methods do not below to  social science, even when they can (and MUST) consider social issues, because projects are built to serve society, in one way or the other. It is their main purpose.

Even in social sciences, although they are not mi field, I understand that people inclination to judge if something like a project  benefits or might hurt them, have to be taken into account over any other consideration. 

This is the reason by which I say that a decision-maker cannot have preferences on this same issue, because he/she is not entitled to override people's decisions.

A person or a group of persons cannot decide for many thousands or even millions of people, and in addition to be something that cannot be rationally discussed, this point of view is mathematically supported by the Arrows' Impossibility theorem

When I say that AHP is valid I refer for its use on simple problems such as deciding to buy a car or an apartment or to select personnel, because the DM knows what he or his company needs, and he or his company will be the receptors of the benefits and potential drawbacks. But this is not the case when the project involves many people who are the ones that will be the receptors and will suffer or benefit with the undertakings, and then their future welfare cannot be decided by a person or a group of persons.

I am not saying that this particular example constitutes a complex problem but obviously reality is complex  and AHP does not represent reality.  Of course there are many other  issues in complex scenarios that need to be modeled, an activity for which AHP or ANP have not been designed for.

Dear Adebayo

'I agree with TL Saaty that AHP ia an accurate and rigorous technique'

It would be very interesting and very useful for me at least, if you can demonstrate what you affirm- but more than with words - that AHP is an accurate and rigorous technique.

Dear Nolberto,

I have used AHP in construction research. In my paper published in an ICE journal,I applied AHP to contractor selection in a case study project in Nigeria. The project participants found AHP rather "complex" but agreed the outcome was very transparent and useful especially for locations where bid rigging is common.

On publication of the paper, a UK-based engineer with vast experience in construction procurement commented saying he found the approach very practical and transparent  but found the matrix algebra too academic. I explained to him that with appropriate software  the algebara was not necessary. I demonstrated the use of the software to him and we together published a discussion paper on the original paper (See second paper below). That is the basis of my conviction that AHP is a powerful tool for MCDM

References

Oladapo, A.A., 2011. Multi-criteria contractor selection–a practical application of analytic hierarchy process. Proceedings of the Institution of Civil Engineers-Management, Procurement and Law, 164(2), pp.79-88.

Oladapo, Adebayo, and Richard Patterson. "Author's reply." Proceedings of the Institution of Civil Engineers-Management, Procurement and Law 166, no. 1 (2013): 47-48.

Dear Adebayo

You are confirming what I expressed before; in the sense that AHP is good for this kind of problems because it is the owner or consultant who will live with their decisions. They know exactly what they want and what to expect.  Naturally, not knowing your problem it is difficult for me to talk about its complexity. Normally, these type of problems - and naturally I am not referring to yours - are quite straightforward since you have a roster of potential contractors that are subject to a set of criteria. Where is the complexity?

I guess that you are referring to selecting the main contractor, normally doing the civil work, and leading the job in the sense that all other contractors and sub contractors input to him. In this scheme, the main contractor is responsible to the owner or consulting firm about the development of the work. He has to coordinate the whole job and produce the master schedule for the owner or consultant approval.

There are however  problems of this type of problems where there are more constraints, such as:

1. Most probably in large and expensive undertakings you have two or more construction companies that submit together, forming a joint venture. This means that their scores should be the same. How do you do tackle this issue with AHP?

2. It is also frequent that the MCDM method, whatever it might be, gets the same or very near scores for two bidders. How do you select the one which is more convenient?

3. How many criteria do you consider adequate for selecting the main contractor as well as the others? I would say that more that 70. How long it takes in AHP to perform all the pair-wise comparisons, assuming for instance that 8 companies are bidding? I cannot imagine the workload if it is necessary, as usually happens, to modify some values. Not very flexible indeed.

4. Most probably a project for selecting the main contractor has mixed quantitative and qualitative criteria. How do you manage in AHP with the quantitative criteria, for instance years of experience, number of works done in the last 15 years, type and age of equipment, liability, etc.? Is the DM going to override these actual and reliable data - according to AHP methodology - to put  his/her own values? On what grounds?

5. What about criteria that are expressed in percentages, such as people opinion about the undertaking? How do you do that in AHP? Does the DM also override people’s opinion and wishes?

6. Each bidder, irrespective of its importance and prestige has its weak spot. It may be its lack of  expertise in a certain type of work, or because the company does not own the equipment or that it has some negative history of not finishing projects in time. How do you detect which the weakest spot of each one is and how can it affect the job in the future? Do you think that AHP or ANP can give you some information, and if so, how?

I hope that this illustrates what I call complexity in projects, even when this type of projects are not very complex, unless we are talking of very large projects such as undersea tunnelling, determining the best use of water in a river basin or building a large hydro electric dam, involving dozens of subcontractors, where are a lot of aspects to consider,  for instance precedence of alternatives, uncertain geology, bad weather, etc..

By the way, if you are concerned with bid rigging, AHP is not precisely the best method, since it paves the way for a dishonest DM to favour one specific bidder.

The AHP mode is very simple and understandable, I have to grant it. There is not complex algebra, and as you say the DM does not need to know it, and for course its software makes computation easy.

You talk about transparency. In my humble opinion this is something that you see and do not have doubts about it, because everything follows clear paths and everything has a clear and clean explanation. How can this UK-based engineer talk about transparency in AHP when decisions are taking according to PREFERENCES? How the DM justifies that criterion B is six times more important that criterion C, and than that this value is the most close to the truth? What happens when a second DM does no share the opinions of the first? Of course, from the actual, not mathematical point of view, the fact that B is six times more important than C does not mean that C is only a one sixth of B.

You speak about a rigorous technique. In all honesty I fail to see it.

I greatly respect your opinion, of course, but let me ask you a question: How many of the questions that I put here can be answered by AHP?

Regards

Dear Nolberto,

Sorry haven’t aswered you before, I was busy with my trivial and low complex problems of my clients (lucky me that they still haven’t found how trivial are their problems).

About your questions to me and to Mr. Adebayo Oladapo, those questions shows your lack of knowledge and experience solving real problems using AHP/ANP. Anyway, most of the questions that you have arised have been solved long ago. (some of them are quite described in the literature). As I told you before, this is your problem not of the methodology.

About the correctness of the results. When I said "good results", of course I’m not saying “close to the true or known results”, that's would be absurd, since you never know what is the correct answer because most of the times correct doesnt even exist. But, there are ways to discover if your results were good or not (again this just shows your lack of knowledge/experience).

About your comments about probabilities “In analyzing risk for several alternatives probabilities are independent, so there are not priorities there”, these words are just showing a very narrow view about priorities and measuring.

Finally, your comments about weights and priorities, it is showing that measurement in decision making is a field that totally escape from you.

I’m sorry that I cant take your invitation to solve your problems (I’m enough busy with my trivial and low complex problems).

Regards,

CG. Dear Nolberto,

CG. Sorry haven’t aswered you before, I was busy with my trivial and low complex problems of my clients (lucky me that they still haven’t found how trivial are their problems).

NM. May be they don’t realize how trivial their projects are

CG. About your questions to me and to Mr. Adebayo Oladapo, those questions shows your lack of knowledge and experience solving real problems using AHP/ANP. Anyway, most of the questions that you have arised have been solved long ago. (some of them are quite described in the literature). As I told you before, this is your problem not of the methodology.

NM. In my answer to Mr. Odabayo during my elucidation of examples of complex projects I was asking questions in general sense, not addressed to him in particular, and I don’t remember formulating a question specifically to you. It looks like another of your ‘supported’ verbalizations.

You are right in one sense. I don’t’ have experience in solving complex problems in AHP/ANP simply because complex problems cannot be formulated in these two models.

As it is you style you use only words. In lieu of telling me that there is literature about this kind of problems and that have been solved long time ago, why don‘t you put examples of theses ‘complex problems’ you refer to, or give me the names of the projects or at least a brief description of one of them, and thus making me aware that I am mistaken? I am suspicious that what you call ‘complex problems’ are simple problems responding to several levels in a decision tree. Curiously, I said this before and you didn’t deny it. If you are convinced of what you say, please demonstrate it, as I do.

I understand that you are very busy, if not, I would suggest you to put forward a fake ‘complex problem’, and see how you ‘solve’ it using AHP/ANP. Sorry, I believe I am asking too much………

It would be better, and by far more useful,  if instead of denying and criticizing other people opinions just by using elaborated sentences  that say nothing, you could produce practical evidence. I believed that in my answer to Mr. Oladapo, I put some ideas about complexity. If you are convinced that AHP/ANP can solved some of them why didn’t you say a single word?

CG. About the correctness of the results. When I said "good results", of course I’m not saying “close to the true or known results”, that's would be absurd, since you never know what is the correct answer because most of the times correct doesnt even exist. But, there are ways to discover if your results were good or not (again this just shows your lack of knowledge/experience).

NM. Then, what is for you ‘good results’? Why don’t you elaborate?

I am genuinely interested in knowing which are the ways to ‘discover’?  if a result is good or not. I am always eager to learn, and really it would be positive for me to acquire new concepts (to compensate in part my lack of knowledge) and improve my proficiency (to compensate in part my lack of experience), especially coming from a knowledgeable and experienced practitioner like you; it would be very generous from your part.

CG. About your comments about probabilities “In analyzing risk for several alternatives probabilities are independent, so there are not priorities there”, these words are just showing a very narrow view about priorities and measuring.

NM. Really? Then show me that I am wrong

CG. Finally, your comments about weights and priorities, it is showing that measurement in decision making is a field that totally escape from you.

NM. Again my friend, you fight reasons with words

CG. I’m sorry that I cant take your invitation to solve your problems (I’m enough busy with my trivial and low complex problems).

NM. Another verbalization?

I did not invite you to solve the problems that I proposed. Instead I said: How many of the questions that I put here can be answered by AHP?

Answer: None

NM. Claudio: Are you attending the MCDM 2017 event in Ottawa on next July?

I will be there, and perhaps if your answer is affirmative, we can hold a fruitful interchange

Best regards

Nolberto

In 

Saaty, T. L. (1991). Response to Holder's comments on the analytic hierarchy process. The Journal of the Operational Research Society, 42(10), 909-914.

I read

'It would appear that familiarity with the latest literature on the AHP could avoid poor attempts at undermining a theory that many able scientists and mathematicians have found to be valid and useful. Holder is lagging the field a bit.'

Also, in

Saaty, T. L. (2015). Rank Preservation and Reversal in Decision Making. Journal of Advances in Management Sciences & Information Systems, 1, 34-37.

I read

'To maintain the established order we preserve rank. To allow the established order to change, we also allow rank to change.'

I'm not 'able' let alone a 'scientist and mathematician'. Is their anybody willing to give a comment on the above words? THANKS.

Fujun

There is an article from Holders, a response from Saaty and response to response from Holders, the three have been published

I have read the three of them

I am not inclined to judge the comments of these two distinguish colleagues. However, I side more with Holder observations. Let’s see:

Validation

Saaty argues about his example on better optic with chairs. I am not taking sides here, however what calls my attention is when Saaty says(referring to Holders)

 ‘His points are out of date. We can cite many references to refute them, as explanations of his points have already appeared in several places in the literature’2-6.

Which is curious is that the two mentioned articles are his……, not from other researchers. So he is citing himself as a proof

The ratio method

Since long time ago I wonder about the rational of the ratio method followed by AHP, because if A = 3 B, it automatically assumes that B = 1/3 A, true from the mathematical point of view but could be wrong from the actual point of view. As an example, if we say that a football team A is three times better than a team B, other people can say, yes, but team B is not as bad either compared to A to deserve only 1/3. B could be of lesser ‘quality’ but not necessarily the opposite of A. In addition, it remains to be seen how the DM can rank intangibles. He can say that A is better than B, but it he allowed to say how many times is it better?

Suppose that a criterion calls for people happiness for three projects A, B and C. You can get relatively reliable information by a survey considering each project as an independent activity, and this can be used in a decision matrix. Then, may be people in a 30 % is happy with project B, a 45 % not very happy with project C and 35 % very happy with project A.

Can we say that people is 14.2 % happier with project A than with project B? It seems to me that the people may show a preference for A over B, but are we entitled to gauge that difference in happiness in percentage? I don’t think so.

The same reasoning applies for other qualitative criteria such as sadness for instance. Can we say that John is 2.6 times sadder that Paul? Obviously not. I am not a mathematician; I am just using common sense and logic thinking.

Validation

AHP defenders say that the method can be validated, and to prove it they use different quizzes.

One of them calls for determining the size of different geometric figures; and he is successful using his method, but we do not have to forget that he is evaluating measurable and real things, things that he can see, and which true sizes are very well known. It is not the same when you measure intangibles.

Therefore, the fact that you can approximate in one or two or three examples to the real values, is not a solid argument for validation in other cases.

Holders response about validity says

 ‘Thus questions about the validity of the AHP are far from having been settled’

This was written in 1990 and is as valid today as it was 27 years ago. That is, AHP has not been able to prove validity, the same for all MCDM methods. There is an exception to this. There is a method where validity can be proved irrefutably and that is Linear Programming, provided that there is only one objective and all quantitative criteria. Even if you don’t know which the true value is, you can be sure that if there exist a solution, the method will find it.

AHP uses a contraption called  ‘consistency ratio’ to measure the consistency in preferences. If a DM acts in good faith, is knowledgeable and knows what he is doing, he assigns preferences. However, preferences have to be consistent, that is, they must comply with the transitivity principle.  If A is 3 times greater that B, and B is 4 times greater than C, then A must be 12 times greater than C. If this not happen, AHP allows for correction up to reach a 10 % error, then the DM adjusts his preferences until a consistency is reached. That is, he is forced to admit that his preferences values were no correct (but he thought they were!!). Is that orthodox? In my opinion this ratio may be considered a ‘licence to adjust’. If it does not fit, who cares, make it fit.

Rank reversal

 Saaty states that sometimes rank reversal is necessary and proposes two trivial examples to demonstrate it. I would like to see an actual case where RR is welcome.

Dear Nolberto,

Thanks for your explanation.

Best,

Fujun

Waldemar

Will you be attending the MCDM 20147 Conference in Ottawa next July?

I will be there and it will be a pleasure to have a chat with you, specially now that I have relocated in Kingston, Ont.

Nolberto

BJ: To AHP Discussion

 Dear Colleagues,

 it was my pleasure to read the Discussion about AHP…

So many years (~37) and so many talks about…!-))

That’s good! ….

All the main directions of discussion were covered, at least partly:

1. Prof. Thomas Saaty, as the Author of AHP, and AHP-followers stress that AHP was and is used in applications and  “…is the only accurate and rigorous mathematical way….”;

2. Prof. Waldemar Koczkodaj presents and proves in his papers the serious shortcomings/drawbacks of AHP;  and

 3. Prof. Nolberto Munier discuss the pros and cons of this method. I want to say (reading his works), I appreciate very much Nolberto’s  efforts concerning the use of MCDA methods within decision-making process and regarding correct implementation in applications.

Therefore, I’ll discuss some other questions around AHP.

1. I teach MCDA at my Uni for many years. My students (bachelors, undergraduates) ask me each year: Which MCDA method is the “best” and the most popular…

I say there is no the “best” method…! However, there is the most popular one…  In addition to other analyses, I mention my paper from 2015… I analyzed there the usage of different MCDA meth and software (using Scopus, WoS, and ScienceDirect data for 2000-2014) within the multicriteria problems associated with risk management. According to my analysis, AHP was the post popular meth … with big advantage (AHP>TOPSIS>PROMETHEE>MAVT/MAUT).

 2. Each year, I ask my students to vote for the one MCDA meth,  which they would use for analysis of a serious MCDA problem. The results is presented below.

[My students know 9 methods, and each year they make presentation at an open Seminar with analysis of their own multicriteria problem using several MCDA meth].

2.1 Ranking (MCDA methods) by IST students (for the last 2 years, 55 students): MAVT/MAUT (~45%)> AHP (~25%)>TOPSIS (~12%)~Promethee (~12%) [for the previous years the AHP votes were

Dear Bruno

I have tried two decision-making methods (AHP and TOPSIS). I have read many research results using the AHP method. But there are some researchers who use a more simple method of calculation such as TOPSIS. Maybe you need to try many methods so you can find the best method  for your research. Your professor's suggestion may be that way.

Best regards Bruno

The journals are mostly afraid of publishing criticisms to an existing popular method or algorithm.  AHP gives good results only when the size of the pairwise comparison matrix is small.  When the number of criteria increases, pairwise comparisons become invalid and making it a serious headache for the decision makers.  Likeways, TLBO is also one of the most popular but most criticized amongst evolutionary algorithms.   But for many problems TLBO provides good reliable results and many researchers use it as it is simple to establish.   On a counter argument, if any optimization problem solved using TLBO, and if review goes to the criticism teams, they will simply reject it saying the methodology is not up to the mark.  

Dear Rajesh

I agree with your first statement in a 100 %. It appears that journals are afraid to publish something that is against established procedures. I am afraid  that I have some experience on that.

However, your second paragraph leaves me puzzled, since how can you affirm that AHP (or any other MCDM method), produces good results when there is a small pairwise comparison matrix?

I wonder what paradigm you use to compare results when you don't know which the real result is?

In addition, if two different DMs produce different pairwise comparison matrices for the same problem, how do you interpret these two good results? Are there degrees of goodness?

I would very much appreciate it to have your response, whatever it might be, because this is an issue that I have been insisting over and over and never got an answer.

Dear Waldemar and Nolberto,

Thanks for the comments and responses,

As I said, AHP becomes invalid when the number of pairwise comparisons increases as of the following reasons,

1. Decision- makers find it difficult to remember all of the importance relations, as it is based on pure interpretation logic.

2. They have to think in such a way that "I have given second criteria 5 times important than the first and the third criteria 3 times important than the second, then there is a relation that the third criteria should not be at least 7 times important than the first.  This only makes the evaluation consistent.

3. When the number of criteria is more, it is impossible for a decision- maker to remember all of these relations and to make a consistent matrix.  In usual, researchers collect expert opinions and if they go wrong they modify the matrices to make it consistant.  This itself will end up with wrong conclusions.

4. Finally, it is all subjective that a 5 times importance and a 7 times importance may vary with individuals and be averaging the results without any fuzzy or grey aggregation can yield wrong conclusions. (Note: Saaty commented not to use any fuzzy or grey methodologies with AHP)

5.  Even when the results are unknown, we can use interpretive logic to analyse the results obtained from various methods and say which method outperform the other.

6. In one of my research problems, I obtained the results using Grey Relational Analysis and compared it with AHP and me got the results that GRA outperform AHP for the problem I considered.  http://www.sciencedirect.com/science/article/pii/S0959652614008774

7. Also, the concept of universal best methodology does not exist and AHP has its own drawbacks.  You may refer to No Free Lunch (NFL) theorem.

Thanking you,

Rajesh R.

Boris

Thank you for your contribution to this debate.

BY. 1. Prof. Thomas Saaty, as the Author of AHP, and AHP-followers stress that AHP was and is used in applications and “…is the only accurate and rigorous mathematical way….”; for the measurement of intangible’

NM. Let’s analyze this sentence

Accurate: The Dictionary defines ‘accurate’ as: ‘Free from error’ or ‘Carefully precise’.

Accuracy is related with consistency; a system may be accurate in some results, but to be credible it also needs to be consistent in all results; it cannot be accurate in some and inaccurate in others.  If Dr. Saaty says that his system is accurate, why then AHP includes the consistency ratio to compensate for lack of consistency or error? Doesn’t it involve a contradiction?

Rigorous?  Saaty’s fundamental scale of absolute numbers is an invention based on a psychiatric opinion; there many scholars that have criticized it. It might be reasonable, but not rigorous since it does not have any mathematical foundation.

Intangible. By definition it is something incapable of being perceived by the sense of touch, as incorporeal or immaterial things; impalpable.

I believe that this word is incorrectly used in this context. It appears that AHP can measure intangibles as human intelligence, or intangible effects such as erosion due to logging, or losing natural capital due to oil extraction, or people desperation when they are moved because a large project needs their land?

I would really appreciate it if somebody can explain me how AHP can measure them, because these are normal and current aspects that a MCDM problem should consider. My guess is that AHP cannot rationally address these criteria, because they are components of a complex scenario for which the model is not prepared for.

BY. 2. Prof. Waldemar Koczkodaj presents and proves in his papers the serious shortcomings/drawbacks of AHP; and. Prof. Nolberto Munier discuss the pros and cons of this method. I want to say (reading his works), I appreciate very much Nolberto’s efforts concerning the use of MCDA methods within decision-making process and regarding correct implementation in applications.

NM. Thank you Professor Yatsalo for your comment; that is in effect my goal. It does not matter what model we use, but it must replicate reality as much as possible

BY. Therefore, I’ll discuss some other questions around AHP.

1. I teach MCDA at my Uni for many years. My students (bachelors, undergraduates) ask me each year: Which MCDA method is the “best” and the most popular…

NM. Yes, I also got that question many times and even here in RG. My answer to my students was that they shouldn’t ask about which the best model is because it does not exist; they should instead ask: ‘Which is the MCDM method that best model my reality and satisfies my needs?’ irrelevant if it is popular, easy or complicated.

BY. I say there is no the “best” method…! However, there is the most popular one… In addition to other analyses, I mention my paper from 2015… I analyzed there the usage of different MCDA meth and software (using Scopus, WoS, and ScienceDirect data for 2000-2014) within the multicriteria problems associated with risk management. According to my analysis, AHP was the post popular meth … with big advantage (AHP>TOPSIS>PROMETHEE>MAVT/MAUT).

NM. I think that you are absolutely right. There is not a ‘best’ method, none of the existing models can replicate reality and probably never will, and certainly AHP is the most popular. Now that you mention risk management, I wonder how AHP can handle risks expressed in percentages. Or do we have to admit that the DM can establish that alternative A is say ‘n’ times more risky than alternative D, and if he can, on what grounds?

BY. 2. Each year, I ask my students to vote for the one MCDA meth, which they would use for analysis of a serious MCDA problem. The results is presented below.

[My students know 9 methods, and each year they make presentation at an open Seminar with analysis of their own multicriteria problem using several MCDA meth].

2.1 Ranking (MCDA methods) by IST students (for the last 2 years, 55 students): MAVT/MAUT (~45%)> AHP (~25%)>TOPSIS (~12%)~Promethee (~12%) [for the previous years the AHP votes were