Dear researchers,
Are there any recent and better methods as compared to the old famous Analytical Hierarchy Process (AHP) for calculation of weights? Especially in the context of GIS analysis.
Dear Kamran
In recent years, several methods have been proposed to overcome the limitations of AHP (e.g. Analytic Network Process (ANP) and VIKOR). In this way, the best-worst multi-criteria decision-making method (BWM) is one of the latest MCDM model created by Rezaei in 2015 to overcome the inconsistency derived from pairwise comparisons by minimizing the pairwise comparisons as well as obtaining the weights of criteria and alternatives with respect to different criteria (Rezaei, J. Best-worst multi-criteria decision-making method. Omega 2015, 53, 49-57.).
Bests,
Amin Naboureh
Dear Muhammad
I will approach this subject from another angle, starting with this question:
Q: Which is the purpose of weights?
A: They are needed to rank criteria.
Q: Why do we need to rank criteria?
A: Because normally not all of them have the same significance or implication; all criteria have the same importance, if not, there would be no reason to choose them, but it does not mean that all have the same significance. They are two different concepts.
Q: Which is the purpose of criteria?
A: They are used to evaluate alternatives.
Q: Based on what?
A: Not certainly on preferences based on intuitions.
Q: But again, based on what?
A: On solid grounds such as using entropy or other procedures as ratios, or in other words, criteria SHOULD be weighted using rational, not invented data.
Q: Where does this rational data come from?
A: From the inputted data that constitutes the initial decision matrix.
Q: What are criteria?
A: Criteria are conditions that alternatives have to comply in greater or lesser degree.
Criteria are formed by a series of numbers that can be quantitative, that is, reliable values coming from sources such as vendors, costs, benefits, environmental contamination, percentages, etc. They can also be qualitative, coming from statistics, surveys, polls or crisp values obtained from fuzzy logic.
The DISPERSION of those series of values for each criterion, indicates the significance of each one.
Q: Why?
A: Because if the values are very close the power for evaluation is very limited. Think in casting a dice. The probabilities of getting any number from 1 to 6 is exactly the same: 1/6.
Q: What information does the player have before casting the dice, for setting a strategy?
A: NONE, because any number may appear. If the dice were ‘loaded’ in some way, there will be some dispersion of probabilities, and a player will now beforehand that there is certain probability that the chosen numbers will appear. That is, he now has some information, and may design his strategy. In other words, this dispersion of probabilities allows him to select a strategy.
Exactly the same happens in MCDM if a criterion has all its values equal. Its does not offer ANY information and then its capacity to evaluate an alternative is NULL.
However, AHP ignores this simple fact and happily assumes that the DM can measure at will the importance of a criterion regarding another. This is absolute negation of reality!
However, I am not asking to trust my words, I did not invent what I said, it is not my creation. This capacity to evaluate a criterion derives from a famous theorem enunciated in 1948 by Claude Shannon, which happens to be nothing less than the corner stone of Information Theory and Artificial Intelligence. Is there any other proof needed, in addition to common sense?
Q: Which is instead the back up of pair-wise comparison and arbitrary weighting?
A: There is one.
In addition, remember that in AHP, weights are computed without considering the alternatives they are supposed to evaluate. It is just similar of asking a blind person to evaluate the quality of a picture.
In the context to GIS it is the same, if say, you are selecting a route between A and B, all layers are important, but not all have the same significance. If one layer over a territory shows that the region between both ends has scarce and dispersed population, and then many empty spaces where the route can be built, it is more significant that a layer where most of the land is occupied by forests and protected areas and where there is no room for a road.
The different layers, all important, but with different significance for your project, is the equivalent to criteria. Therefore you have grounds to make a rational decision, but what base do you have by saying for instance that population is say 3 times more important than forested area. Based on what?
Q: Which would be the rational in deciding, without considering the route, that one area or criterion is ore important than the other?
A: That would be total absurdity.
Dear Prof. Nolberto Munier
Thank you for the useful answer. I hope you share it somewhere as an article as it will be very useful for students and researchers who are working in MCDM.
Very interesting message criticizing AHP, although I am one of AHP advocate!
I really appreciate your thoughts and perspective and need to find it as a reference not just an answer for a question that might be reached only by chance like my case.
Stay safe and let's enjoy more from your thoughts.
Thank you.
Regards
Mohamed
Muhammad Kamran
Regardless my above added answer mentioned Prof. Nolberto Munier ,
I highly recommend to have a look at the Fuzzy AHP, it's somehow an evolved approach from AHP.
I believe that AHP is one of the good approaches in MCDM where much uncertainty is accompanied with human decisions and the way human thinking is working.
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. You might find the attached paper useful as an alternative approach.
TOPSIS requires defining an ideal alternative which may not be possible.
A method that has been proven mathematically to be true based on a set of rational assumptions is valid. All others are suspect. Frequently methods are chosen on an ad hoc basis out of ignorance or because the outcome fits a preconceived notion of what should be correct. See attached presentation for a more detailed discussion.
According to Topsis method, the ideal solution is simply determined from the evaluations matrix !
Dear Dr. Salaheldin
Thank you very much for your comments on my writing in RG about AHP. I indeed value them when they come from somebody with your background and experience.
I firmly believe, in line with many other people in RG, not only that AHP is deeply flawed as Neal Hulkower says, position that he has maintained for years, but that from the practical point of view, AHP in inapplicable, because it is based on the false premise that the DM can make personal decisions when considering complex scenarios that involve perhaps millions of people, that did not ask for the DM to be the interpreter of their benefits or harms derived from a certain project.
You are experienced in the oil industry, a tough industry indeed, which is alien to me. However, and considering my ignorance of such industry, I would like to ask if you are able to solve a scenario that includes wells operation, transportation, processing, storage and transportation to the markets, using AHP.
Or put it simpler, can AHP or ANP determine the plan that makes a balance of final products related with refinery capacity, storage capacity and markets demand?
That is what I call complex scenarios. Do you think that this kind of problem, or even many simpler can be solved by preferences?
You support some of my points again AHP and honestly says that you are a supporter, and of course I respect that, since I am not the owner of the truth!
Then, for my information, I would like very much to have if possible, you authorized input regarding why you support AHP.
Now from my point of view, I believe that AHP is very good, and probably the only MCDM method available to address problems involved with personal or perhaps some corporate issues, in where preferences are paramount, and especially, scenarios where the benefits or failures of the project will fall on the people that made the decision.
But even in this case, you need to establish criteria preferences based on the available alternatives, something that AHP ignores. Really, for me that is incomprehensible.
Just as an example, assume you want to select for dinner some of the restaurants you know, and you decide that between quality and price of food you prefer quality, and this is perfectly right, but you can’t consider that said preference is constant, because it can work with restaurant A and B, but not with A and C.
You know that AHP does not determine criteria weights, it finds trade-offs, that are very useful to make a balance between gaining quality in selecting restaurant A against sacrificing price regarding restaurant B, because it is more economical.
What if comparing restaurants, A and C it is the reverse? That is, in this second analysis you prefer to gain in price in C, and then sacrificing a little quality in A?
My question is:
How is it possible to establish preferences between quality and price as AHP does, if you don’t have the restaurants and their corresponding estimates between quality and price?
This elemental analysis, is not related with AHP mathematical approach, but with the applicability of the method to real situations. For me, this is one of the many fallacies of the method, since it is based on a psychological ‘finding’, and ignores that real-world projects are based on facts, not on personal preferences.
Is my reasoning wrong? If it is, please correct me.
If you want to continue in private this interesting discussion my email is: [email protected].
Dear Dr. Salaheldin
Reference is made to your comment about using Fuzzy and AHP.
I am not in a position to discuss the benefits of using FAHP, because I am not proficient in fuzzy logic.
However, probably you know that a scientist that was highly proficient in both, the late Dr. Saaty, in one of his writings he declared his opposition in using Fuzzy and AHP, because according his own words:
"'It is unfortunate that there are people who use fuzzy sets without proof to alter
the AHP when it is known that fuzzy applications to decision making have been
ranked as the worst among all methods".
"The fundamental scale used
in the AHP/ANP to represent judgments is already fuzzy"
The Analytic Network Process
Thomas L. Saaty- University of Pittsburgh - [email protected]
Dear Neal
As always, along the years, I agree with you.
AHP is not only deeply flawed - you usual expression - but its main drawback is that it was designed only from a theoretical and psychological point of view, and then, without considering real-life scenarios.
Dear Zhor
And it is correct. TOPSIS is a rational method that considers maximums and minimums of each criterion, and then consolidates this CERTAIN data with a very rational formulation.
What is wrong with that?
Dear Nolberto,
I am just making it clear. Indeed in the privious comments, there is comment about the finding of the ideal solution,
Otherwise, I agree with you Topsis is a rational method providing an acceptable results,
I have one paper about an improvment version of Topsis, in wich I study the use of nadir solution at the place of anti-ideal solution, this is what is called TOPSIS Nadir : The impact of using new significant reference point with TOPSIS methods: study and application
Moncef Abbas; Zhor Chergui
DOI: 10.1504/IJIDS.2019.101139
Dear Zhor,
I'm asking if you can share this paper with us,
sincerely yours
Dear Muhammad Kamran,
There are several MCDM approaches that you may employ based on the requirements of you project. For instance, you need to consider if there is any relationships among the identified factors/criteria of which AHP is not capable to do so (in these cases, ANP is a better option).
In recent research, it is very common to adopt/develop hybrid MCDM approaches which might be of your interest based on your question while each has its own pros and cons. I give you some examples of these methods and you may use them if it suits to address your research problem. Fuzzy AHP/ANP, Cybernetic Fuzzy AHP/ANP, Parsimonious AHP/ANP, Express AHP/ANP. BWM, FBWM, etc.
I agree with most of the previous answers especially those of Prof. Nolberto Munier , having two very short comments:
1. The science (or even the art) of decision making is based on selecting the most appropriate tool
2. I support AHP because I used it in some of my previous researches and found it is applicable in many scenarios to an extent, also I appreciate the consistency index which is not common to find similar effective indicator in other methodologies.
It's really an interesting discussion. Thanks for all contributors.
Dear Professor Salaheldin
Thank your for your support
I 100 % agree with you with your first statement, and I would add that to select a method the DMs need to be well aware of the characteristics of their problems. It is completely useless to apply a MCDM method that can't model at least the main features of a scenario, such as people using AHP, when they perfectly know that their problem has relationships between criteria, as most of the scenarios. Or using a MCDM method that does not consider resources. Yes, they will get an answer, which most probably will be misleading, because it is not possible to examine a project, detect its features, and ignore those that do not fit a MCDM method that one has in mind, that is to fool oneself.
Regarding your second statement regarding supporting AHP, you are of course right, if you have had good experiences with that method.
I concur that for personal problems and for certain corporate projects such as hiring new personnel, or for the military, AHP is possibly the best, if not the unique method to solve that problem, but it is in my opinion unrealistic to apply it in complex escenarios that don't develop along a hierarchical structure, or have precedence between alternatives, or/and multiple dependencies, limits in resources, etc.
You are right about the consistency index, it is a nice feature, but what is its utility regarding the problem you need to solve?
It merely means that the DM has achieved a consistency or transitivity regarding his/her preferences, and this is important.... for him of for her, but what is its importance regarding a real-world problem? Where is the relationship? How can he apply what is a result of his mind to solve a real problem? It is only a mathematical trick, that even forces the DM to modify his preferences in accordance with what a formula says...Where is the logic in so doing? Where is the reasoning?
It is different when solving a personal problem, because in there the DM has a clear link with his problem. He knows better than anybody what he wants and which his limitations are, he can establish his own preferences, and he knows how his good or bad decisions will affect him, and perhaps his family, but to nobody else, and he knows that if a bad decision is taken, just for instance choosing a university career like engineering and he later realizes that it is not for him, he can change
Normally, you can't do that in most real-world projects such as building hydro-electric dams, dwellings developments or building a railroad between A and B. They are irreversible.
Of course, bad and very bad decisions can be and have been taken too, using other more rational methods such as PROMETHEE, ELE CTRE or TOPSIS, but in these methods, there is reasoning, analysis and work with reliable quantitative data and even statistically justified qualitative data, all of this absent in AHP.
It is for me clear that a person can't apply the same AHP procedure, when the project may affect millions of people. He does not know in what extent his selection will benefit or hurt those people, he does not know their problems. Am I right in my reasoning? Am I inventing a situation that does not exist in order to criticize a method such AHP or ANP? Believe me that I have, not invented examples, but real cases where the recipients of a projects had to pay the consequences of a bad decision. How a person can decide that criterion 'water' is more or less important that criterion 'manpower' , let alone put a value to that preference, as for instance in an industrial location problem?
Sorry for this lengthy answer and thank you very much for your participation in this subject.
Dear Amir
Your first sentence is THE answer to people that ask what MCDM method they can use
"There are several MCDM approaches that you may employ based on the requirements of you project"
There is not a method that can be used to solve all classes of problems, nor a method that is better than another.
I agree with you regarding that there are also several hybrid methods that can help, such as using fuzzy in AHP, or in TOPSIS or in other MCDM methods. However, they do not address the root of the problem, which is modeling difficult and conflicting scenarios, for they only improve data reliability but they don't modify their structure. Therefore, in my opinion, using FAHP, or FTOPSIS, for instance, don't change the structure of each method, and after the fuzzy application they maybe still unable to model properly a scenario
Dear Prof. Javed
According to you abstract your method generates weights. My question is: How do you get them?
Really, expressing that they are similar to those of AHP and SAW (although this last one does not generate any weights), is not very encouraging or promising, since the so-called 'weights' - which are in reality trade-offs - something that even Dr. Saaty, recognized in some of his books, express only preferences of a DM, and in addition, useless for alternatives evaluation.
Perhaps I misunderstood the meaning of you comment in the abstract, for that reason I would very much appreciate your clarification.
I recommend strongly MACBETH ( Measuring Attractiveness by a Categorical Based Evaluation Technique )
, much more consistent than AHP:
http://www.banaconsulting.com/site/PT/software.html
to Nolberto Munier
I agree with you, partially. Despite its limitations, AHP can be perfectly applied in many situations, and can help decision making in well delimited contexts.
Saludos desde la España confinada
Dear M.J.
I said that AHP is very good when applied to the military, to personal decisions or to some corporate problems such as hiring personnel, but only as a rough approximation.
AHP is conceptually wrong and mathematically flawed
For the first, consider:
* The limitation of criteria independence, which many practitioners prefer to ignore, because,..... why to bother, if probably the stakeholders or the reviewers of a paper will not notice about that transgression?
*The flaw in considering that preferences between criteria are constant (something that is clearly false),
* The absurdity of putting a value to preferences, without considering on what projects they will apply.
*The incongruity of conditioning and modifying a DM evaluation based on what a formula says, and then, giving priority to a mathematical contraption over the human mind. Where is the logic of this procedure?
What if the DM says that whatever the formula indicates he/she are convinced that their original evaluation was correct and they are not willing to change?
In that situation, wouldn't it be more rational to use simulation for the whole AHP process and allow the computer decide, and blindly accept it ?
* The limitations in the number of criteria. This is completely ridiculous when there are scenarios involving hundreds, if not thousands of criteria. However, AHP supporters say that it can solve complex problems...…..
* The use of a hierarchical structure that is good for the above mentioned uses, but completely unsuitable for most projects,...…… Should I continue?
I am not saying, and I never said, that I am right, not even partially; instead of that I give reasons, which can be rebutted of course (which, by the way, suggestively, in more than five years in RG, nobody challenged), when I state that AHP can't and should not be used in complex problems. This assertion it based on reasoning and on my practical experience, not on psychological theories. I also base it on my experience, because when I needed to solve some MCDM problems, I found that using AHP is impossible to even remotely represent reality.
I don 't enumerated the mathematical drawbacks since many mathematicians, more learned than me, have objected the method since de 80s.
Saludos desde Canadá, y gracias amigo por tu mensaje.
Dear Nolberto,
I really like your critical thinking and arguments.
Just one note about the limitation of criteria in AHP. In fact hundreds of criteria can be handled in AHP. It depends on the decision structure. Saaty stated that when it comes to a pairwise comparison matrix (PCM), the maximum size (due to the assumed consistency) is 9x9. However, the PCM-s are created by the decision structure, you put only those criteria in a certain PCM which are positioned in the same branch of the decision tree. Consequently, if you have multiple levels with several branches but the branches contain only few (less than 9) criteria, AHP is suitable for the application.
It is another question that the evaluation process is very long and demanding in this case. I agree that AHP in the conventional form is not suitable for any MCDM problem solving.
Dear Szabolcs
Thank you for your initial comment, which and I fully reciprocate, because I enjoy and learn from your publications.
I am glad that with your expertise, you acknowledge that AHP is not suitable for solving any MCDM problem. That is not an AHP attribute only, because none MCDM methods can solve any kind of problems.
Unfortunately what you say, which is absolutely true, is not reflected in the thousands of publications on AHP that have been published, where it appears that any problem is suitable to be solved by AHP.
However, you say 'in its conventional form'. Is there any other form of AHP, from the structural point of view, that can be applied to more complex scenarios?
I guess you are not referring to ANP which is by far a more rational procedure, with a completely different structure, which, in my opinion, was created by Saaty when he became aware of the AHP structural drawbacks.
Regarding you comments about the number of criteria, please kindly read the attached file, which has a drawing than can't be reproduced here.
In there, I express my point of view regarding that issue. I will very much appreciate it in having your opinion.
Best regards
Nolberto
Querido Nolberto
Que si, que estoy de acuerdo contigo, pero me pareciste muy enfadado con AHP cuando interviniste por primera vez.
te saluda desde sevilla, menos confinada ya, tu amiga, María José ([email protected])
Dear Nolberto,
thank you for the response and the example. I defintely agree with you that the attributes of a complex decision should be considered as a system and not as a strict hierarchy (and you also know that I am not satisfied with ANP as a methdological solution). In my opinion, structuring of the attributes is rather a clusterization process. In clusterization, we are searching for strong correlations among some attributes and create clusters by the degree of correlations, while ignoring the weaker correlations (and may accept the existence of the weaker ones but these do not reach the cluster threshold). If we had part with structuring (clustering) the criterion, the problem would be so complex that we could not involve evaluators.
Dear Szabolcs
Thank you for your answer and support, which, coming from an experienced researcher, is very important.
I have said many times here in RG, that I don't understand why practitioners continue using AHP when I have never seen a rational support to this method, not a documented answer, not a single example that proved that what I said was wrong, or that my criticism does not have grounds.
You are the exception, because you have always recognized the drawbacks of the method, and because of that, you are researching, I understand with a colleague, about how to eliminate the drawbacks. In my opinion this is the way to go, although to be honest, I don’t think that there is solution to improve AHP because it is based on a principle such as pair-wise comparison, that is good in some a few specific areas, but not in making decisions in most real-world scenarios, because, out of this, it uses a hierarchical structure, rarely present in them.
I understand that in your last paragraph you are referring to ANP. You speak of clustering and in principle I think you are right. I applied clustering many years ago in urban MCDM scenarios for both, alternatives and criteria, using Linear Programming, and it worked. I was able to get values for each sub alternative and for the respective clusters, meaning sometimes, that not all of the component criteria of a cluster where complied in a a100 %, and the same for alternatives.
It was not a drawback of the LP method, but due to not enough resources, such as funds, manpower, equipment. This is another drawback of AHP and ANP, as well as for most MCDM methods, because I don’t conceive that you can make selections of projects, if you don’t consider what resources and in which amount are they available.
I understand that you are referring to ANP in your last paragraph. You speak of clustering and in principle I think that you are right. I applied clustering many years ago in urban MCDM scenarios for both, alternatives and criteria, using Linear Programming, and it worked. I was able to get values for each sub alternative and for the respective clusters. You say that you are looking for strong correlation between criteria, I did exactly the same, only that not using mathematical correlation, but grouping them according to the department they belonged to.
You also state that this method could be so complex that it could not involve evaluators.
Probably you are right, but I don’t know, because I have no expertise in doing that in ANP. However, think about why you need evaluators. Because you have to use pair-wise comparisons, well, don’t use them, or at least don’t do pair-wise comparisons.
Of course, this process is against the core of ANP that demands pair-wise comparisons, a process that for me is the root of all the problems in MCDM methods, and that also provokes rank reversal.
Time ago I participated in a large project that consisted in determining, out of about 150 environmental indicators for a country, only a manageable number, about 20 or 25. I worked with 4 experts, from an environmental government federal office, and I asked them to evaluate each indicator, using a 1-10 scale, subject to compliance of a set of criteria, naturally, common from them all. The evaluation could be positive when there was a direct relationship, or negative, when this was inverse, or zero, when there was no relationship
Very simple as you see, and where no comparison where made; that function was left to the LP model, and it worked well.
Not only we got the 25 indicators final set but in addition we used entropy in order to capture the maximum information possible from the initial 150 indicators. This entropy determined the objective weight for each criterion. In addition, we could, simply by changing a value, change the number of final indicators and see how the selection changed.
In another assignment a similar procedure was followed for a city in a smaller scale, with only 16 indicators and 25 criteria, in four clusters as: Sustainable targets (8 criteria), General selection (7 criteria) criteria, Areas (7 criteria), and OECD framework (3 criteria).
This was published in Ecological Indicators 11 (2011) 1020–1026, under the title: ‘Methodology to select a set of urban sustainability indicators to measure the state of the city, and performance assessment’
I mentioned this example, only in the hope that it can help you.
One more time, thanks for your answer and contribution.
Dear Nolberto,
I really appreciate all your comments. It would be a privilage for me and for my lab to have the opportunity to work with you once in a transport development decision problem.
If a set of weights is really all you need, AHP is strictly not necessary. The decision-maker can choose weights himself and/or test a couple of sets and see how results react to them.
Dear Nuno
I agree with you. However, in that case, we are always doing the same thing, that is applying weights to criteria without any reasoning. That is the same as playing to the lottery.
The only way is either to GET RID OF WEIGHTS or use objective weights
You put it nicely when you say: 'IF...……."
Dear Szabolcs
Thank you for your offer, I would be delighted in working with so qualified colleagues.
Dear Mubashar
Muhammad proposed the question about if there is an alternative for AHP.
For trivial problems such as selecting a car, a restaurant, a movie or for corporate decisions related hiring personal, AHP is good, although even in these cases, it is not reliable for many reasons that I have exposed here many times, and even wrote a book about that published by Springer
Regarding real-world, complex projects, AHP is useless, and most of the 100 existing MCDM methods, are better. Too bad that many reputable methods such as Promethee, Electre and Topsis use AHP derived weights.
The BW method starts b y arbitrary selecting which is the best and the worst criteria. Based on what? By intuition?
I have put here in RG this same question several times, perhaps you can clarify this issue, since nobody answered. I sincerely hope so
By the way could you explain why BW it uses AHP weights? Why not to use objective weights?
Dear Nolberto,
I have the same thoughts related to BWM. It starts with selecting the best and the worst alternative/criterion. This is where other MCDM techniques end. With my phd student we recently conducted BWM on a problem and will publish the results but the first phase is very peculiar. Form that point the method is nice, simple and consistent. But I am reluctant to apply it again because of the initial step of selecting the best and the worst attribute (stated preferences can be used for this phase and simple arithmetic mean).
Dear Szabolcs
I agree 100 % with you, and in addition it uses AHP arbitrary trade-offs
Hola Nolberto, entonces cuando hablamos de fuzzy AHP tú ya simplemente te desmayas, no???
Has visto la pregunta que hace Ramon Araneta??:" Can I get scores based from 1-10 using weights derived from fuzzy AHP.?",
qué le dirias?
besos, pepi
Dear Pepi
No, simplemente me da pena que la gente no comprenda que ese metodo no es adecuado a sus problemas y que lo sigan usando porque tiene fama, o porque tienen el software o porque alguien resolvio con el un problema similar.
Analisis....., razonamiento....., para que? Es mas facil comprar un software y apretar teclas.
Con respecto al fuzzy AHP, cuando el mismo Saaty no lo aprobaba porque decia que AHP es ya fuzzy, para que seguir hablando?
Oye, que paso con el planteo que te mande sobre las aceitunas?
Nolberto
Using the Fuzzy Cognitive Maps(FCMs) approach is a good suggestion for you. This method is a fuzzy-graph structure for representing causal reasoning. Their fuzziness allows hazy degrees of causality between hazy causal objects (concepts). I recommend that you research it.
In my opinion the best alternative to AHP is multi-objective decision analysis (MODAO. In this regard I prefer to use value measures (as opposed to utility measures) for both consistency and ease of calculation.
Dear Nicholas
In my opinion, the best alternative to AHP is not to use it, AT LEAST in real-world problems.
It is unable to model scenarios even lightly complex. Why?
Because its hierarchical structure, among many other things.
There are myriad of MCDM methods that ARE efficient and fundamentally rational, and that can use objective criteria weights if the need them
You don't need to work with invented weights which depend on the DM
I am glad to hear that it is not just me who recommends not using AHP and its shunts. This I have been repeating for more than ten years.
José Hernández
No, dear Norberto, it is I who is obliged to welcome you.
But I comment that since 2009, when we published one of our first articles showing the basic faults of AHP, we began to gain many detractors. For this reason, since 2010, with the article, in which we made the presentation of the Ideal Alternative, to try to partially solve the serious problems that AHP presents, we got used to fighting against the acolytes of AHP and ANP alone.
So I still prefer not to talk about the club.
But thank you very much anyway, if you want to join our quiet fight for a more respectful investigation of basic mathematical principles.
A hug.
José Hernández.
Dear Jose
You are right, you were in this before my time. Probably I started in RG about 7 or 8 years ago and my first question was to ask about a characteristic of AHP
From then on I wrote hundreds of pages in RG against this method
At least you got many detractors. I was not so lucky since nobody responded to my criticisms and repeated claims for answers and rebuttals, while many people supported me
For me the reason is simple. You can't answer a question if you don't have arguments to support what you say.
Of course I want to joint your fight but being quite is no my style
I don't incur in the mathematics of the method. I am more concerned about its absurdity and lack of common sense
I even have written to MCDM society claiming to establish a quality control of papers published, to no avail
Norberto,
I also do not recommend AHP because it is fatally flawed and does not follow the rules of Axiomatic decision analysis. That is why I recommend MODA, and specifically value focused MODA, which uses objective criteria weights, which I why I recommended it to author of this question. Ultimately if you want people to stop using AHP, which I do, you need to recommend a sound alternative.
Dear Norberto, although we do not are agree on styles, or on approach, if we do it in the essentials. We have both cared to warn people to try to do a little more research on the tools they use. I think that it is not a crime to use an inappropriate tool, but that we are, as researchers, obliged to point it out. By definition, as researchers we must be critical.
Surely in the near future, we will take advantage of the coincidences and undoubtedly we will be able to present some work together.
Best regards,
José Hernández.
Dear Jose
I like your sentence that we both care to warn people, because it was and it is my intention
Of course is not a crime to use an inappropriate tool, but which is debatable and damaging is to try to convince and deceive people, when showing problems' 'solved' by AHP, when just by examining the scenario you find aspects that in no way can be modelled by AHP, let alone solved. It is sad to see these publications that have been approved by reviewers when you can appreciate at first sight that it is not true.
I would be delighted inworking with you
Dear Norberto, at the beginning of the pandemic, we finished an article, where we presented some new suggestions, to improve the possible use of AHP.
Then I have gotten into a couple of projects that are absorbing me for a long time. More than I expected. I guess soon, that I will be able to put my affairs in order. As soon as I do, I contact you in private, so that we can start thinking about what we can work on. The idea is to follow the same line, to raise awareness of the errors that are hidden under AHP and that one should start to have a little more shame when publishing results, with this technique and its derivatives, which cannot be supported.
A hug and we are in touch.
Best regards,
José Hernández.
Dear Jose
In my opinion AHP can't be improved, it is genetically flawed, by not only in one but at least in 30 features that I detail, exemplify and comment in my next book , that will hit the shelves probably in a month. It is published by Springer and Its title is:
'The Analytical Hierarchy Process Method: Where Can It Be Used and Its Structural Limitations for Solving Complex Problems
A Non-Mathematical and Rational Analysis Paired to Views from Experts'
Each feature is analyzed, and commented, and supported by recognized researchers, identified with name and surname and with their publications
As I said many times AHP is good for trivial problems and for scenarios that can be modelled in a hierarchy, as in the military, from where it originated, but for no more than that.
Of course, all MCDM methods, including mine, SIMUS, have drawbacks, but I believe that all of then can be ameliorated
I very much like you last sentence and I am able and willing to collaborate with you and other people, to make people aware of their limitations
My warmest regards
Nolberto
Dear Nicholas
You are right, criticizing is not enough and it is then necessary to recommend better alternatives.
There are excellent options such as PROMETHEE, ELECTRE, TOPSIS, VIKOR, etc., that are rational and can provide good results. The problem is, in my opinion, that most are not capable to model even a slightly complex scenario. From this point of view I would recommend PROMETHEE and SIMUS
Dear Sema
A friendly comment to your message.
The contribution of each RG member is very important since everyone provides experience, knowledge and innovative applications of MCDM methods.
However, it is not enough to assert that a method or methods are the best, as in you case, if you don't explain the reasons of your assertion. Remember that you are influencing other people who are not obliged to believe what you say, if you don't give your reasons.
I am not saying that you are wrong or denying what you say, far from it; I am only asking that you illustrate us about your predilection. Otherwise any healthy discussion is impossible.
@munier Sema Kayapinar Kaya
Ahp is a very nice and useful method. I used both its crisp form and its fuzzy extensions in many of my works. But it is clear that nothing is best forever. More skilled methods are developed than it. We want to emphasize this here and talk about new weight determination methods.
Dear Faith
AHP may be as you say a nice method and useful, but when applied properly, and this is for elemental and trivial problems, and even then, with some harsh restrictions.
It is useless for complex and real-life problems for many reasons, one of them, its hierarchy structure, which nowadays normally does not exist in most projects scenarios.
It was used extensively because in the middle 50s, when Saaty developed it, following a military structure, many companies had adopted the hierarchy structure. But all of then changed long time ago
I don't believe, as you say, that more skilled methods were developed. They were developed because a rational approach to a project was needed; DMs need to investigate and know the nature and characteristics of the scenario, someting that happily AHP ignores. It is unreasonable to apply your personal points of view to complex problems. They are good for selecting a movie or going to a restaurant, but not for selecting between building a bridge or a tunnel across a river
I don't know in the kind of business you are, but I assure you, and I can prove it, that AHP is not the right tool to use in real-world scenarios
Regarding new weighting methods you don't need to look for new developments; you can use objective weights which are mathematically justified, not invented weights.
Preferences are OK for personal and some corporate problems, as well as for the military, but it is absurd to pretend for instance that you can decide by intuition that a criterion or an alternative are better than another, and in addition put a value to that preference.
For instance, in an health care scenario can you say that ambulance services are 3 times more important than number of doctors?
Dear Sema
Probably, but both methods rely in subjective selection, and that, in my opinion, put both methods at the same level of inaccuracy than AHP
Dear Sema
Your statement about that all possible methods are subjective is incorrect
Some methods such as CRITIC and SIMUS are completely objective.
Your opinion on the easiness of some methods is admissible, however, the DM has to select a method that may solve his problem, not a method adapted to his convenience, or ignore, also for convenience, the limitations of a method.
An example is using AHP when criteria are not independent. I am sure that you with your experience can bear witness of this, or just review most methods 'solved' by AHP and published in journals, and just check the criteria, don't do more than that, and you will probably see that this condition in AHP is happily ignored most of the time.
Saaty was very clear to this respect, then, one can't blame the method, but the user
Sorry, but your opinion about AHP being the father and foundation of all methods, is wrong in two counts.
The first method was Linear Programming, created bi L. Kantorovich, and published in his book 'Mathematical Methods in the Organization and Planning of Production', in 1939.
In 1952 he and Koopmans were awarded de Nobel Prize in Economics for it. Later, in 1948 Dantzig developed the Simplex algorithm to solve Linear Programming, the same that you have in your computer as an Excel add-in. By the way, the Simplex was nominated as one of the most important algorithms of the XXth Century.
Roy developed ELECTRE in 1960. Saaty developed AHP in 1970
In addition, I am afraid that AHP is not the foundation of all methods. In reality, all other methods are based on different concepts and structure. Some methods use the criteria 'weights' (which are not such, but trade-offs), generated by AHP in the first stage of its process
I think that an additional source of evolution MCDM will be using Artificial Intelligence with expert functions. You can take part in this regard in the discussion:
https://www.researchgate.net/post/AI_as_expert_for_Analytic_hierarchy_process
Dear Vadym
I believe that yesterday we addressed the issue of AI and AHP and George Hazelrigg and I formulated some questions which you did not answer.
The reference you made has been treated by various researchers and as far as I understand none of them gave a positive mark to what you propose. Of course, you have the right to disagree, but you just posed a possible association without no explanation of how it could be implemented. It does not mean that it is not possible, but we would need to know how can be implemented, since as I understand, right now, it is only an idea
Dear Nolberto Munier , yes, now it is only on the idea level. For testing the power of this idea was started questionnaire: https://www.researchgate.net/post/AI_as_expert_for_Analytic_hierarchy_process
Dear Vadym
I agree that it is only at an idea level, but that level must be possible or reasonable. Sorry I could not see the questionnaire
An expert is somebody with knowledge and experience on something.
In AHP and ANP, pair-wise comparisons can be made on completely different criteria on the base of a common goal, say investment.
If the problem requests to compare two different criteria, such as people housing needs and NOx contamination , an expert on social issues would be summoned to manage the first criterion, and an environmentalist for the second. Then do we need two experts?
If we use only one expert, say the social worker, most probably he/she is very knowledgeable in this aspect, but that knows nothing about the environment. How one expert can make a rational selection if he/she is and expert in one of them and ignorant on the other?
Do you see the irrationality of the method?
In addition, in a scenario with 70 criteria pertaining to say 20 different fields, do we need 20 experts?
colliding among them?
Where is the logic of this scheme?
I don't think that intuition play a role in experts, because then they are using a way without any technical support or rationality, and really they did not study for that. If somebody believes that problems that need to be studied, analyzed, thoroughly examined, can be replaced by intuition, then we better close universities and technical centers.
In addition, to make personal decisions that can affect thousands of people, is immoral from the ethical point of view, and mathematically wrong according to Arrow Impossibility theorem.
Dear Fatih Ecer ,
I have developed two methods called the simple hierarchy ranking analyis multi-criteria decision-making method (SHARA) in the three forms instead of AHP, and also the comlex network ranking anaysis (CNRA) instead of ANP. the both outputs are more reliable than AHP in my opinion.
Dear Shervin Zakeri , thank you for your information. Could you write links to your publications concerning these methods?
Dear Shervin
Good for you in developing your two methods, and you say that they are more reliable than AHP and ANP.
How can you prove that?
Dear Vadym Slyusar , Thank you for your interest. We will submit both methods as one paper likely before the end of January.
Dear Nolberto Munier ,
AHP is already wrestling with a lot of shortages which makes it not suitable but a standby method. Prof. Naoufel Cheikhrouhou , Prof. Fatih Ecer, Prof. Dimitri Konstantas and I have developed an interesting method called VIMM which covers the lacks of AHP and BWM. The paper is submitted at Omega and it is currently under review.
Dear Shervin
AHP has been in standby since after maybe 10 years it was conceived, about the 60s
At the very beginning it had a warm reception because companies were organized since the 1900 according to the hierarchical structure, but when they realized that it could not be used due to new organizational concepts and especially due to the new demands of society and environmental groups, it lost interest. Now wonder that Dr. Saaty developed years later the ANP which is based in a more reasonable concept, as the network is.
However, the same drawbacks (to be polite...) of the method, namely pair-wise comparison and their arbitrary quantification, and relying in what a formula commands, made it clearly unsuitable. That is possibly the reason by which methods such as PROMETHEE, ELECTRE, TOPSIS and many others, which are based on rationality , on knowledge, on experience, on statistics and not in psychological considerations, are used for complex projects.
There is not doubt that stakeholders don't care about what the DM thinks; they work with facts not with intuitions.
It would be interesting to know how many of the thousands projects developed in AHP could pass the stakeholders scrutiny.
Unfortunatelly, many practitioners are not aware of the limitations of AHP and continue using it, and which is worse, their papers happily accepted by journal reviewers.
Congratulations on your VIMM method and we hope that it will be a landmark in MCDM
Dear Kamran,
You can try BWM (Best Worst Method) as an alternative to AHP. The method was found by Rezai. and, you can achieve the website which included the method information.
Dear Omer
As far as I know the BWM has similar disadvantages as AHP, since you have to select both ends of criteria or the alternatives. On what grounds do you do that? On intuition?
And, in addition, you must apply pair-wise comparison that produces another set of invented values
I would appreciate it if you can give a RATIONAL explanation to this.
I have posed he same question several times, here in RG, and suspiciously never got an answer
Dear Nolberto Munier
Yes, BWM is like AHP in terms of methodology, and the difference between these methods is scale.
Dear Omer
I appreciate your answer, but really, you are not very explicit
It appears to me that it is another method to convince people that serious problems can be solved by intuition
What is the advantage of a method that follows the same absurd procedure of a method created 50 years ago?
Dear Manjunah
You are right, the CRITIC method (Criteria Importance Through Intercriteria Correlation), is an efficient procedure to obtain objective weights and it is useful in diverse applications. However, I don't think that it is suitable for MCDM problems, since those weights do not have the ability to evaluate criteria.
The reason is that weights, at least in MCDM, need to contain a certain amount of information and these weights don't have it.
Different is the case of weights derived from entropy, because they do have a certain information content, which not only can be used to quantify criteria but also to evaluate alternatives
Regarding PCA I guess that you refer to the Principal Component Analysis. I don't see how CRITIC and PCA work together her. Care to explain?
You can use the Analytic Network Process (ANP), which is an improvement over AHP. You can use TOPSIS, PROMETHEE, PAPRIKA, ELECTREE, etc. It is not clear what you need to do with respect to GIS systems using weights. If you clarify the question, it will be easier to answer.
Dear Cenk
You are right, ANP is the alternative of AHP when the criteria are not independent.
However, ANP is as biased as AHP, since it uses pair-wise comparisons that produces artificial weights, and that have no relation with the real scenario..
There are many methods that can be an alternative to AHP and ANP such as PRO METHEE and SIMUS, using entropy or objective weights in the first, and no weights in the second, which are by far more realistic than AHP, with its lineal hierarchy, that only may exist in the mind of the DM.
I understand that what Muhammad is asking, is about how to determine weights to find the significance of levels when using the Geographical Information System (GIS). The answer is: Use entropic weights based on your findings from GIS.
From there you can haver distances, populations, buffers, number of roads crossings, etc., and from them, objective weights.
Dear Nolberto Munier , thank you for your explanation, I understand it better now.
Hey all,
Attached you will find my list of the most useful MCDM approaches to have a solid criteria weighting (beside the classic weighting methods of "direct rating", "pairwise comparison", "ratio method", "ranking method", "ideal point method", "SWING method", "delphi method", ...)
- AHP - Analytic Hierarchy Process (Saaty, T. L.: The analytic hierarchy process: Planning, priority setting, resource allocation. New York: McGraw-Hill, 1980. ISBN: 978-0-070-54371-3)
- FAHP - Fuzzy Analytic Hierarchy Process (van Laarhoven, P. J. M.; Pedrycz, W.: A fuzzy extension of Saaty's priority theory. Fuzzy Sets and Systems, Volume 11, Issue 1-3, 1983. pp. 229-241. DOI: 10.1016/S0165-0114(83)80082-7)
- Entropy (Shannon, C. E.: A mathematical theory of communication. The Bell System Technical Journal, Volume 27, Issue 3, 1948. pp. 379-423. DOI: 10.1002/j.1538-7305.1948.tb01338.x)
- DEMATEL - DEcision-MAking Trial and Evaluation Laboratory (Gabus, A.; Fontela, E.: World problems: An invitation to further thought within the framework of DEMATEL. Genf: Battelle Geneva Research Centre, 1972.)
- CRITIC - CRiteria Importance Through Intercriteria Correlation (Diakoulaki, D.; Mavrotas, G.; Papayannakis, L.: Determining objective weights in multiple criteria problems: The CRITIC method. Computers & Operations Research, Volume 22, Issue 7, 1995. pp. 763-770. DOI: 10.1016/0305-0548(94)00059-H)
- SWARA - Step-wise Weight Assessment Ratio Analysis (Keršuliene, V.; Zavadskas, E. K. & Turskis, Z.: Selection of rational dispute resolution method by applying new step‐wise weight assessment ratio analysis (SWARA). Journal of Business Economics and Management, Volume 11, Issue 2, 2010. pp. 243-258. DOI: 10.3846/jbem.2010.12)
- IDOCRIW - Integrated Determination of Objective CRIteria Weights (Zavadskas, E. K.; Podvezko, V.: Integrated determination of objective criteria weights in MCDM. International Journal of Information Technology & Decision Making, Volume 15, No. 02, 2016. pp. 267-283. DOI: 10.1142/S0219622016500036)
- BWM - Best-Worst Method (Rezaei, J.: Best-worst multi-criteria decision-making method. Omega, Volume 53, 2015. pp. 49-57. DOI: 10.1016/j.omega.2014.11.009)
- Pearson correlation coefficient (Pearson, K.: Note on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, Volume 58, Issue 1, pp. 240-242. DOI: 10.1098/rspl.1895.0041)
All the best, making good decisions and #stayhealthy,
Jerome
Dear Jerome
Thank you for your effort in making us know the different methods for ranking criteria
Out of the 9 methods that you show, in my opinion, there are only three that are useful, Entropy, CRITIC, and IDOCRIW, because are the only ones that are objective. All the others rely on subjective appreciations that have no correlation with the alternatives the criteria must evaluate.
DEMATEL, is for instance a good method but it is a cause-effect relationship, more akin with Pearson correlation, although the later does not necessarily indicates a cause-effect relationship
Hi Muhammad,
The FUCOM provides the same results as the AHP with less comparison, which may imply that the FUCOM is better than the AHP. Now，methods better than the FUCOM its derivatives, such as the fuzzy-FUCOM and the grey-FUCOM.
Articles citing the FUCOM would help you to know the latest trends using it.
Please, the attached file.
Dear Nolberto,
you are absolutely right, the only objective methods are the named one. However, sometimes it would also be useful to use the subjective methods, if you have already some knowledge gained from last projects or from your experience in general within the given topic. Thus, the full list of methods listed above.
Have a great day and as always making good decisions,
Jerome
Dear Jerome
Yes, in personal and in some corporate projects subjectivity is possibly the most important feature.
In my opinion is that circumstance only you know what you want and your possibilities, something that does not happen ir the real-world projects. And what is important, your decision will ONLY affect you or the company, and not to thousands of people that have nothing to do when you apply subjectivity on a big project. In other words, you can decide on your own projects, but you can't decide for other persons involved in a large project.
Not everything is always white or black, and then, we can't discard subjectivity in large projects either.
Only, that subjectivity must be applied, and supported by know-how and expertise to improve a result that was obtained objectively, and then working on solid bases.
What you can't do is modify initial data with your subjectivity, but once you got an objective result you have a solid base to modify or even reject it.
For instance, assume that in selecting between three equipment A, B and C for the same task, say three lathes; the objective result says that the best is B. However, you, as a decision maker knows someting against that equipment that was not considered, for instance, that it is not the preferred among the users, something that should have been considered in the initial decision matrix.
Then, the DM can reformulate that matrix considering a new criterion that contemplates the opinion of users regarding each equipment, and then running again the software.
Perhaps he can get the same result or not, but the fact is that this second result is based on something that was consequence of his expertise and know how
Dear Muhammad
I would not dare to say that FUCOM is better because it makes less comparisons; it is certainly better from the workload point of view, but it does not mean that its is better.
I don't know your method, but it appears to have the many drawbacks of AHP, which in addition, is flawed
One of the most common methods of expert assessment of the causality of relationships are methods that allow you to evaluate various coefficients of causal relationships between factors of socio-economic processes: DEMATEL, MICMAC, as well as a method for detecting and assessing the impact of implicit factors.
The DEMATEL (Decision Making Trial and Evaluation Laboratory) method is one of many multicriteria methods decision making and implies the effective identification of the causal links of a complex system based on the aggregation of expert assessments. This method aggregates collective expert opinion in order to exclude random relationships between indicators and criteria, and on the basis of causal links to identify the most important indicators that determine some integral characteristic. The method allows you to determine direct, reverse and indirect relationships, as well as the direction of the interdependence between the criteria and indicators. The MICMAC method stands for "Matrix d'Impacts Croises Multiplication Appliqu un Classement "
Dear Dmitry
Muhammad Kamran is asking for an alternative to AHP, a very well-known MCDM method, and as far as I know, DEMATEL is not a MCDM method.
In addition, it is based on casual or cause-effect relationships, and that is not on what AHP is grounded, quite the opposite, since in this method criteria must be independent
Are there any techniques that allow for pairwise comparison of alternatives (similar to AHP) without the need for criteria?
Dear Lawrence
All MCDM methods, in one way or another, make pair-wise comparisons, that is the essence of them.
Criteria are fundamental in MCDM, because they are which allow for comparison between alternatives, if not, on what base are alternatives compared?
However, a method, Linear Programming, is different from all other methods, since it compares and determines alternatives between them, using the cost of opportunity principle of Economics, but to do that, it also needs criteria, since they define the dimensional space where all the feasible solutions are, and the importance of alternatives in linked with this space.
Best Worst Method (BWM) is a useful MCDM method with many advantages.
Dear Muhammad,
Using MADM techniques depends on the size and types of problems. Many researchers have applied AHP, FUCOM, BWM, and LBWA. However each of these techniques has its advantages and disadvantages.
All of these methods need pairwise comparisons for working. However, the number of pairwise comparisons required for running these methods are different. If the number of criteria is n, FUCOM, BWM, LBWA, and AHP need (n-1), (2n−3), (n−1), (n(n−1)/2) number of pairwise comparisons respectively. Hence, AHP requires more pairwise comparisons compared to FUCOM, BWM, and LWBA, especially when the number of criteria is high. Furthermore, a study conducted by (Pamučar et al., 2018) revealed that the results from FUCOM and BWM may lead to a better consistency ratio over AHP when the number of criteria is high. But if the size of the problem is small probably AHP is a better technique. In addition, solving such techniques like BWM has more complexity regarding mathematical modelling.
As I said, it all depends the characteristics of the problem.
You may read step 3, section 3 of our article given below:
Amir Hossein Azadnia, Mohsen Geransayeh, George Onofrei, Pezhman Ghadimi,
A weighted fuzzy approach for green marketing risk assessment: Empirical evidence from dairy industry,
Journal of Cleaner Production
It's also been discussed there.
Hope that helps.
Hello, please take a look at this research. These statistical coefficients are used for determining the conformity or reliability of experts' evaluations, and the Kendall coefficient with a value greater than or equal to 0.7 was considered as the stopping index for the procedure of the Delphi method.
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