Dear Emamat

For preparing the pairwise comparison matrix in AHP, Saaty’s 1-9 scales are generally used  for qualitative data and not for quantitative data. For quantitative data like yours, researchers have used their normalised amounts as their ratings in the pairwise comparison matrix. 

For an example, the values for alternative i and j are, respectively, wi and wj, then the preference of alternative i to j is equal to wi/wj . Therefore, the pairwise comparison matrix can be formulated as :

W1/W1   W1/W2   ...  W1/Wn

W2/W1   W2/W2 ...    W2/Wn,

   ....................................

Wn/W1   Wn/W2 ...   Wn/Wn,,

So, in mentioned example pairwise comparison matrix is:

(the attribute is price as a cost attribute)

(Price)   A1     A2     A3

A1          1       5      50

A2                   1      10

A3                            1

and we should normalize it in next step.

Is that correct?

Dear Seyed M. Mohsen E., to AHP work with more or less sense, there should be a previous characterization, this should be done independent which use qualitative or quantitative variables. In the work “Shelter selection with AHP, making use of the Ideal alternative”, we present a table with the characterization of the alternatives. In the version of this article that is available in Research Gate, for reasons of confidentiality agreement which we signed with the publishers, are not these tables. But if through your institution you can have access to the full article, you can see it. In any case our recommendation is to use technique multicriteria more robust, whether Matrixes Of Weighing with Multiplicative factors (MOWwMf) or Multiattribute Model with Multiplicative factors (MMwMf).

Hoping that our response, will be of any utility was carefully. Best regards,

José Hernández

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.

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

I agree with the great quantitative weaknesses of AHP.

    José Hernández

I agree in one hundred per cent with Neal Hulkower.

I have also written in RG that the main drawback, although not the unique, is that AHP overrides quantitative or even qualitative information and replaces it with subjective appreciations from the DM. For instance, if we have information in percentages from a survey performed on say 1000 people, how can we believe that the opinion of the DM may prevail over that of 1000 people?

In addition, if we have say 10 criteria addressing economy, environment, social, crime,  engineering, safety, risk, etc., is it assumed that the DM is an expert in all of them and thus qualified  to  judge?

I recognize that AHP is a great model, probably the best,  when there are at play personal preferences and when the DM is also the receiver of the benefits, such as selecting a car for him or choosing a movie, but I fail to understand how AHP can be applied to serious problems such as industrial locations.

It could very well be that I am mistaken,  so I would very much appreciate it if somebody can answer these and other questions. Some weeks ago a made a public request on RG about these an another weakness on AHP to open for a public debate, but unfortunately only three or four people answered. However, those who did agreed with my concern.

I believe that RG is a magnificent forum to discuss these issues technically, and then I believe that we should use it, for expressing our ideas and for learning from others.

Dear Sayed,

To answer your question, first you have to define if  the final priorities will just represent the numbers as they are, or there are relevant information from the DM (sensations and perceptions) that has to be considered.

For instance, if they are just numbers then Alt.1 is 5 times better than Alt.2 and 50 times better than Alt.3 (built from its own ratios and supposing that cheaper is better). Thus, the priority vector would be aprox: {0.820, 0.164, 0.016}, keeping the ratios unaltered.  But, if there is an influence (interpretation) of the intensity of preference from the DM, then this information should be take into account when conforming  the final priority vector.

The explanation of this is very simple, that is because the numbers (its meaning) is not the same for a poor person that for a rich one. By the way, that is why different people can make different decisions in front of the same data set.

I think there are people that do not understand well what is behind AHP/ANP (the concepts of measurement, scales, composition). For instance, sometime they mix ordinal and cardinal scales like it was the same thing. Other times, they make comparisons of different methods and theorems based in different kind of numbers (different scales), which of course drive them to wrong conclusions.

My suggestion is, try to understand what you are doing, what is behind any method you are going to apply, what are its axioms, what kind of numbers are you dealing with.

Dear Claudio

NM Thank you for your clarification about AHP.

CG. To answer your question, first you have to define if the final priorities will just represent the numbers as they are, or there are relevant information from the DM (sensations and perceptions) that has to be considered.

NM I think that this is basic, however I have never seen it expressed as you do. I think that is a very good point that unfortunately not many practitioners consider and then very valuable.

Related to it, I would like to add that in my opinion the first thing to do, whatever the nature of the criteria, is to determine if they are independent or related. In the first case AHP should be used, and ANP in the second. Nevertheless, I consider that some practitioners are using AHP without even analyzing if there are relationships, which can easily be seen by observing the criteria. In my opinion, in so doing, they are ignoring reality. For instance in the classic example of deciding for a car that is posted in several AHP explanations, criteria like Price, Miles per gallon, Comfort and Accessories, are considered independent,  and clearly, they are not, however, AHP is used and which is worse, published and accepted by journals.

CG For instance, if they are just numbers then Alt.1 is 5 times better than Alt.2 and 50 times better than Alt.3 (built from its own ratios and supposing that cheaper is better). Thus, the priority vector would be aprox: {0.820, 0.164, 0.016}, keeping the ratios unaltered.  

NM I guess that you are referring to the second part of AHP, and then I assume that you have first determined criteria weights based on the DM preferences on criteria. Shouldn’t these ratio values by multiplied by the corresponding criterion weight?

But, if there is an influence (interpretation) of the intensity of preference from the DM, then this information should be take into account when conforming  the final priority vector.

Are you suggesting that even with these real values, the DM influence of sensations and perceptions should prevail and then overriding actual data?

CG The explanation of this is very simple, that is because the numbers (its meaning) is not the same for a poor person that for a rich one. By the way, that is why different people can make different decisions in front of the same data set.

NM Of course, I agree with you on this, but for me it reveals the main weakness of AHP, because important decisions such as to consider for instance than transport is more important than say water availability in a scenario for deciding a plant location, and that said decision is taken either by a person or by a group, is dangerous for its potential effects. A decision like that should be based on solid grounds, not on perceptions.

Now, as I understand it, there could be different cases from the priority characterization

1. All criteria are qualitative. In this case the normal AHP procedure applies, assuming that criteria as well as alternatives are independent.

2. All criteria are quantitative. In my opinion there are two options:

  a) Either you consider all of them ratio relationships, and the influence of the DM is limited to compute the criteria weights or   

 b) you can find the numerical differences between the quantitative values.

What I mean is that the DM can compute the differences between quantitative data. Say for instance that the  

Difference between A and B is 187,

Difference between A and C is 98,

Difference between B and C is 209.

The problem, as you state, is that these differences may have different significance, and according to who makes the analysis (it is like your analogy, which by the way is very illustrative, of the poor and rich person, 50 Euros may be a lot of money for the first and insignificant for the second).

Same may happens here in this example when the DM can say ‘I consider that the difference between A and B is large and then A is 7 and B 1/7, and the difference between A and C is not too much, and I value C with 6 and A with 1/6. The difference between B and C is very large and for me I value C 9 and A with 1/9.’ Of course this can be done, but in so doing in this case the DM is overriding reliable original data and establishing by personal or even by group preferences an order that can be different from the original. Is this reasonable? And if it is, on what grounds, because a person has been hired as DM? What about another DM perceptions and opinions?

3. What happens if we have 10 criteria where 6 of them are quantitative and 4 qualitative? You know that this is the most frequent problem, that is, to have a mix of quantitative and qualitative criteria. How do you proceed in this case?

I don’t think that you are entitled to use the DM sensations and perceptions and determine the weights for qualitative criteria, while on the other hand you are using ratios for quantitative criteria.

Of course, both are ratios, but the first is based on a conventional 1 to 9 scale while the others are based on true values

I think there are people that do not understand well what is behind AHP/ANP (the concepts of measurement, scales, composition). For instance, sometime they mix ordinal and cardinal scales like it was the same thing.

That is why I don’t think that case in point 3) above is allowed. Therefore, which is the procedure in case of mixed criteria?

CG Other times, they make comparisons of different methods and theorems based in different kind of numbers (different scales), which of course drive them to wrong conclusions.

NM Is it not the same as you said above? In addition you say that it could drive to wrong conclusion, however, how do they know (or how anybody can judge), which is the right conclusion if they do not know which the true result is? That is the problem with all MCDM methods; every results is valid because there is no way to prove it.

I will very much appreciate your response to my questions, than I think may help a lot to people like Seyed Mohsen Emama that proposed a very important question, as well as many others.

Thank you

Nolberto

Dear Nolberto and Sayed,

Due to the long of the message  (5 pages long), I preferred to send it as an attached .doc file, under the name of "Nolberto answer".

Best regards,

Claudio

Dear Claudio

Please find my answer attached

Nolberto

Dear Nolberto, my answer attached.

Dear Claudio

My answer attached

Even if I have said that I will not follow this discussion, I do want to correct a sentence that I found very dangerous, especially for young people and beginners.

Any person that want to use a method (any), it has to understand well (very well) its scope, how it works what are its axioms and theorems, what kind of numbers is using how  those numbers are mixing: data (ordinal, interval, ratio, absolute...), information (which is not the same thing than data), people perceptions and desires (their systems values) and how all those pieces come togheter and fix in a structured way, modelling the problem in a representative decision making model. Because, one day this person might be in the position of making important decision or helping to make it like a facilitator (not a dictator), and if he doesnt understand well what he is doing when applying the method, then he can make a very huge mistake, making loose a lot of money to a Company or worse get suffering the people reached by that decision.

On my opinion, this process is not like a driving a car in a beach week-end, in which the driver doesnt need to understand how the engine work. But, (following the same analogy), this person is more like to a pilot of a jumbo jet or an astronaut. I expect from them know well how their engines work. A lot of people and money may depend of their knowledge, and their hability to gather different data and interprete that data to obtain valuable synthetical information. Or perhaps, like a medical doctor when gathering data from his patient (We all hope the doctor knows what he's doing when transforming all the gathered data into information and make his final diagnosis and prognosis).   It would be very dangerous if those people would not know well what is in the bases of the tools they are using.

In conclusion, for being serious and professional in our work (as assistant in decision making for instance), we MUST know and understand well the tools we are using. In this case, the axioms, hipothesis, theorems of any method (or combination of methods) that we could going to use.  By the way, if there is a method which dont have these elements in a clear and explicit form then discard that method inmediately. (Bertrand Russell).

Dear Claudio

CG. Any person that want to use a method (any), it has to understand well (very well) its scope, how it works what are its axioms and theorems, what kind of numbers is using how  those numbers are mixing: data (ordinal, interval, ratio, absolute...), information (which is not the same thing than data), people perceptions and desires (their systems values) and how all those pieces come togheter and fix in a structured way, modelling the problem in a representative decision making model.

NM If you say so, explain me why a very large number of practitioners have been and at present are using  AHP when they know that their criteria are not independent,  considering that this fact can’t be ignored since Dr. Saaty himself clearly states that,  or when the model grants up to a10 % ‘permission’ (based on unknown and unexplained grounds), when their preferences don’t comply with the transitivity axiom? Don't yoy say that the practitioner must know all the axioms, therefore, knowing them why he ignores their compliance?

You pls. tell me, and if you don’t want, please explain that to our readers in RG.

CG Because, one day this person might be in the position of making important decision or helping to make it like a facilitator (not a dictator), and if he doesnt understand well what he is doing when applying the method, then he can make a very huge mistake, making loose a lot of money to a Company or worse get suffering the people reached by that decision.

NM One thing is to understand what he is doing, and I plenty concur with you in this aspect, and another is to know the intricacies of theorems and axioms on which the MCDM system is based.

In my opinion, worse and more dangerous than that is using a model which is not adequate to his purposes for whatever reasons, and most especially in deciding by personal preferences the selection of a project.

CG On my opinion, this process is not like a driving a car in a beach week-end, in which the driver doesnt need to understand how the engine work. But, (following the same analogy), this person is more like to a pilot of a jumbo jet or an astronaut. I expect from them know well how their engines work.

NM Of course they must know how the jet engine work, because he needs sometimes to adjust some parameters such as fuel injection, but again not at the extreme to understand the thermodynamics of the engine as you suggest. In addition, you forget that a driver can park his car when he wants while the pilot or the astronauts obviously can’t..........Not a large difference. Isn't it?

Apparently, you fail to remember that until the 80s, airplanes flew with a flight engineer in charge of all the airplanes systems. If, as you say, the pilot must dominate them all and on top of that fly, why regulation forced to put a flight engineer? Now he is no longer necessary, because integrated circuits and computer advances perform his functions, and that leaving free the pilot for flying.

CG A lot of people and money may depend of their knowledge, and their hability to gather different data and interprete that data to obtain valuable synthetical information.

NM Interpretation is precisely the danger because not two persons may interpret the same thing. Why don’t you to design a high-rise based on preferences and interpretations instead of on sound data and engineering principles?

CG Or perhaps, like a medical doctor when gathering data from his patient (We all hope the doctor knows what he's doing when transforming all the gathered data into information and make his final diagnosis and prognosis).   It would be very dangerous if those people would not know well what is in the bases of the tools they are using.

NM Fine, then, according to you a family doctor, should have a deep knowledge of X-rays physical principles such as their most adequate wave length, as well as all biochemical procedures for doing a blood analysis , or the fabrication of each prescription that he recommends, and even how is fabricated the soap he recommends for dry skin. By the way, they are not tools, they are procedures, performed by technicians.

CG In conclusion, for being serious and professional in our work (as assistant in decision making for instance), we MUST know and understand well the tools we are using. In this case, the axioms, hipothesis, theorems of any method (or combination of methods) that we could going to use. 

NM Yes, I agree with you, but one thing is to know them, their applications, their limits and their capabilities, and other very different is to dominate the algebra, theorems and axioms that make them work, and on what they are based. How many DM do you think are that have heard about eigen value analysis, as used in AHP and ANP, or the Lagrange multiplier used in Linear Programming, or the utility function used in SAW?

CG By the way, if there is a method which dont have these elements in a clear and explicit form then discard that method inmediately. (Bertrand Russell).

NM I agree but now you are mixing ideas. Of course the methods or models have to have those elements but it does not mean that the user have to share that knowledge

I would like to thank you all for your active participation.

You are welcome Seyed, I just hope you have found the answer that you were looking for. Regards.

It was a pleasure Seyed. You posed a very good question.

I hope that our answers will clarify your doubts

Nolberto

Dear colleagues, followers of this question. A few days ago I uploaded the Spanish version and the English version of the work: Effect of the use of an ideal alternative in Hierarchical Analytic Processes [English new version], what I hope will be of interest to you all.

I apologize to those who receive this information multiple times, since I am sending it to several questions related to this topic.

Thanks for your attention.

Best regards,

José Herández.

https://www.researchgate.net/publication/329428672_Effect_of_the_use_of_an_ideal_alternative_in_Hierarchical_Analytic_Processes_English_new_version?_sg=-pfclX-93JX-AHJNMyHrRCDktHEGoh_w3U-a4drrOnfO0Htr3hgHXSSShTJV9-5OMupemcCPeEr4D-ptV0WiiycquFFZ_w6hdPvReE36.yW6n8V_drCDY7WAQbATBfY_2kpzrGoi9Of9WOQk3XHnboix_Ee-UDgmxgyQW-nScTij7mbRJ1N2n4G1qHweUNA

https://www.researchgate.net/publication/329045259_EfectoUsoAlternativaIdealAHP181114RG?_sg=-pfclX-93JX-AHJNMyHrRCDktHEGoh_w3U-a4drrOnfO0Htr3hgHXSSShTJV9-5OMupemcCPeEr4D-ptV0WiiycquFFZ_w6hdPvReE36.yW6n8V_drCDY7WAQbATBfY_2kpzrGoi9Of9WOQk3XHnboix_Ee-UDgmxgyQW-nScTij7mbRJ1N2n4G1qHweUNA

It is better to use best worst method rather than AHP method because this method has highest consistency as compared to AHP method

Dear Saif,

In BWM less comparisons are required, so consistency will be high. I have applied this method in my thesis and several papers. I suggest you to apply this method.

Dear Saif

With due respect I believe that your assertion may be not true.

Until today researchers have agreed that in MCDM there is not a method better than another.

From my modest point of view and examining the fundamentals for the better-worse method developed by Dr. Rezaei, in his paper ‘Best-worst multi-criteria decision-making method’, it relays on pair-wise comparison between the best and the worth criterion.

The pair-wise comparison is a good tool for expressing individual preferences in trivial problems but not for serious ones. In the first, the DM preferences may lead to a result that affects him or his company, and its use makes sense because it is supposed that he knows very well what he or his company want. Therefore, the consequence of his actions fell on himself or the company that he represents.

In serious problems like determining plant location, this application is not convenient for the simple reason that a DM may not take decisions on crucial criteria that involve many people, such as advantages or disadvantages that each plant may bring, and how they can affect their lives. The DM will never be able to match the information that can provide people that will be affected by the different alternatives. Unfortunately, methods like AHP and ANP, where pair-wise comparison is extensively used, don’t consider that simple fact and believe that a DM own preference is enough.

In addition, even for trivial problems the pair-wise comparison may be no realistic, even when the consequences of the decisions fall on the DM or in his company

Why? First, because when analyzing the relationship between two criteria, the method assumes that it is measuring their relative importance, and this is not so, since what it is measuring are trade-offs, and for that he gives a number of that superiority using a conventional scale that does not have any mathematical support.

In addition, it assumes that the preference between two criteria is constant, and then it applies it tu qualify alternatives.

However, many times, in a trade-off saying for instance that criterion C1 is four times better than criterion C3, he assumes that this superiority holds for all pair of alternatives, which may be not true.

If he uses this value to rank for instance between alternative A1 and A3, it is fine. However, when he analyzed the pair A1 and A4, it is possible that it does not hold, because there is a different trade-off.

Why is this produced?

Because, trade-offs are considered independent of the alternatives, which does not have too much sense. When you compare two criteria, say quality and price and you decide that quality is three times better than price, on what basis do you perform that comparison? That is, if C5 is three times better thanC7, my question is, WHAT FOR?

OK, you can say because the comparison is done regarding a main objective. However, to reach that objective you forcefully need the alternatives, therefore my question is: Where the alternatives enter in this equation?

You can say, that in a second stage, therefore, you are using to qualify alternatives a quantitative preference to a factor that did not take into account the alternatives.

As a bottom line it does not appear that Best-worse method is the most appropriate to select weight. For than you can use a method such as SWARA or still better, use objective weights from statistics, MonteCarlo or entropy

Regarding the PIV method, authors Mufazzal and Muzakkir , don’t say that PIV solves RR problems as you state; they said that in can minimize it, which is not precisely the same.

Again, greetings to all the esteemed colleagues who are followers of this question. Last week I submit to the Research Gate platform, the Spanish version and the English version of the work: Multicriteria models to evaluate social development projects [New version], what we assume may be in the interest of all of you.

I apologize to those who receive this information multiple times, since I am sending it to several questions related to the subject.

Thank you for your attention and I hope you find the information useful.

Best regards,

José Herández.

https://www.researchgate.net/publication/330205251_Modelos_multicriterio_para_evaluar_proyectos_de_desarrollo_social_Nueva_version?_sg=-kvK9X0bzxMahqSlW07QkmzFnhDBAoWH5RgS2uwZvCOL_CMOE2P-9-0hA85EG7X4l-4GTMNWR2uMTJ5B8Ks5hxVMxEy9iULap7QfAfUz.SDl1CjD-_Gc_FAvKYD1YlNXOXTMLbA4_iR5GwJ4xApIdL-NR_6HdVD_kinFOZ7hC4_bsbjKiYmbltNswb_XAvg

https://www.researchgate.net/publication/330354600_Multicriteria_models_to_evaluate_social_development_projects_New_version_Modelos_multicriterio_para_evaluar_proyectos_de_desarrollo_social?_sg=-kvK9X0bzxMahqSlW07QkmzFnhDBAoWH5RgS2uwZvCOL_CMOE2P-9-0hA85EG7X4l-4GTMNWR2uMTJ5B8Ks5hxVMxEy9iULap7QfAfUz.SDl1CjD-_Gc_FAvKYD1YlNXOXTMLbA4_iR5GwJ4xApIdL-NR_6HdVD_kinFOZ7hC4_bsbjKiYmbltNswb_XAvg

Hello In paired comparisons, we need to be based on the verbal spectrum. It is not interesting to associate real numbers with paired comparisons.

سلام

در مقایسات زوجی کلا باید بر اساس طیف کلامی (کیفی) پاسخ بدهیم دخیل کردن اعداد واقعی در مقایسات زوجی جالب نیست

Dear Soliman

It may be as you say, but in MCDM we must work with numbers not with feelings.

Imagine if an engineer makes a comparison for building a high-rise on two criteria that respectively refer to using steel, concrete or wood.

Would he dare to say 'I prefer wood, and for me it is 3.5 times better than concrete. What do you think?

Now, it you have to select among several restaurants for dinner, and you must select therm comparing say quality and price, yes, I believe that here it is worth using pair-wise comparisons, but not in serious projects.

Dear Jose

Thank you for sharing your work

I am interested in learning how you compare the two methods that you mention, and which I don't know, with AHP.

That is, I don't understand which is the purpose of the comparison

Can I assume that your two methods use weights generated by AHP?

Excellent answers