Dear Egbe

I am afraid I disagree with you because AHP can’t help the DM in selecting the best alternative due to various reasons

Just as an example, I will analyze one of those reasons, which, as far as I know, has never been mentioned in RG:

It is that AHP considers a pair of criteria and determine its weight based on preferences and considers them constant through the alternatives.

This is incorrect

First, because what AHP determines are trade-offs, and then indicating how much a criterion varies in preferences with respect to others, therefore, the so called ‘weights’ that come from these comparisons and assuming that they measure criteria importance are a fallacy.

Second, because once AHP says for instance that criterion C1 is three times preferred than C2, then he considers that relation constant, and it is probably not

As an example, suppose that you have to select between three restaurants A, B and C for dinner, and you want to compare the alternatives based on the comparison between C1 (quality) and C2 (price), and you established that for you, quality es preferred to price, and assign a quantitative value to that preference (which, by the way, does not have any mathematical support).

In comparing restaurant A with restaurant B, you decided that food in A has a superior quality than food in B, but also a higher price. According to your prior selection you select A, that is, you sacrifice price, or prefer to pay more, but then you have a gain in quality. An this is fine for this pair of alternatives.

Now you compare restaurant A and restaurant C and finds that C has a lightly inferior food quality than A, but prices are considerably lower. You may decide that you will sacrifice a little lesser quality, but you will get a benefit paying less

This second comparison between quality and price is opposite to the first one, therefore, it does not make sense using a constant preference for all alternatives.

In addition, in its first stage AHP don’t even consider alternatives, that is, the criteria are considered by themselves without taking into account the alternatives that they have to evaluate.

Then, how can AHP work with constant comparisons?

You see, there is not high mathematics here, it is only common sense and a little analysis

Consequently, there is no guarantee that AHP will select the best alternative and even the right ranking

And remember that I have examined only one factor.

In AHP, the findings are based on perceptions of 2,4, ..or 7 decision makers, whereas, survey results are the perception of big sample. Also most of the researcher prefer survey over AHP. So how can you use AHP to validate survey results since survey results are more reliable than AHP findings.

My answer is a big NO.

I don't know your area of research but as far as my knowledge, a case study approach may be used to validate survey results.

Dear Mohammad

100 pert cent in agreement with Vinod.

My answer is also NO

You cannot validate data obtained from a survey, where people is consulted about some issue and the synthesis done,with an arbitrary evaluation done by a decision-maker

By the way, this is possibly the most used argument used by scholars criticizing AHP

Regarding validation of the survey I would suggest to perform a hypothesis test

Dear Mohammad,

I agree with Mr. Munier and Mr. Yadav.

AHP is a multicriteria method to process decision makers' judgements about alternatives, acording to a set o criteria, into a ranking.

To validade research findings you must use statistical methods, performing hypothesis tests, as recommended by Mr.Munier.

Dear Dr. Mohammad,

In my understanding, AHP could be very usefull for "preliminary phase" study, when little or even no "best opinions" could conclude the level of importance or significance of a group of criterion. It is mostly contextual. The critical idea of AHP is that opinions should be based on certain expertise, and therefore, AHP is also known as "experts opinions".

Sometimes, AHP is used by researcher to build "shadow hypothesis". The shadow hypothesis are then compared with the hypothesis testing from survey. In other words, we don't utilize AHP to validate results from surveys. Instead, we could use AHP as a tool to compare between experts' opinions and fields opinions. Should there is a gap, it would be the base for further analysis and discussions.....

If we need to validate survey results, I believe case studies are the common practice, as Mr. Vinod Yadav mentioned earlier...

Thank you for your all responses and much appreciated. Much clearer

Dear Oki

I am afraid that I do not agree with what you said regarding AHP being contextual.

The Dictionary defines context as 'the circumstances that form the setting for an event, statement, or idea, and in terms of which it can be fully understood and assessed'.

And that is precisely a condition absent in AHP, since it does not consider the setting of an event or scenario..

For instance, if an scenario implies relationships between criteria, AHP ignores it (not ANP).

If the scenario involves relationships between alternatives, AHP ignores them. ANP considers them but only the existence of relationship but not, the most important, the quantitative influence of one over the other.

If the scenario - practically ALL scenarios - uses resources, both AHP and ANP dismiss them

It is very difficult to find a scenario without quantitative data which possibly is very reliable. However, AHP and ANP override that data and prefer the DM preferences.

In addition, DM preferences are based on him being rational and with abundant data. Maybe he has abundant data, and I am sure he has, when he is dealing with personal or corporate scenarios, but not when he is dealing with many different aspects of the scenario, such as engineering, economics, social, environmental problems, exogenous factors, etc.

Regarding the rationality, how can you be sure that t he DM is rational? Of course I am not considering that the DM maybe intentionally biased, or to say that elegantly 'to have vested interests', but he could ....

Now, what you say about shadow hypothesis is very interesting. However, if to analyze tit you need to perform a survey, which is the correct way, what is the use of the shadow hypothesis? Just to show that the DM was right, or wrong?

Dear Mohammad FakhrulNizam Mohammad, in Research Gate have been raised several questions that involve AHP or ANP, some of those who have responded have participated in several of them, is the case of colleague Nolberto Munier, with whom I agree in many of their approaches.

One of these discussions can be seen in: https://www.researchgate.net/post/How_can_I_combine_AHP_and_TOPSIS_approaches_to_optimize_the_layout_of_a_dynamic_construction_site?_ec=topicPostOverviewFollowedQuestions

Repeating what has been expressed on other occasions, AHP, only serves and very partially, to prioritize, not to make any decision on the results thrown.

My doubts about the use of AHP, are given because when applying this technique, from the beginning, in its way of operating, several mathematical errors are committed. As ANP needs and relies on AHP, it inherits all its faults and I would say that it adds some of its own.

In summary, avoid using AHP or ANP, and for what you are raising as you have answered several colleagues the answer is NO.

I hope you have been of some use and many successes in your research.

Best regards,

José Hernández.

DearJose

I agree with what you said, especially when you say 'Avoid using AHP and ANP', except if the user has a trivial problem, such as personal or corporate scenarios

I agree with the relevant previous responses, as well we could note that as it is claimed by saaty the tolerated ans suited number of criteria that we could use in a decision making problem with AHP is five (up to seven criteria). Given the huge number of survey studies that will be collected and compared, the pair wise comparaison either between criteria or between alternatives become therefore very complex and difficult to be done with AHP. In such situation, however, AHP method could be used in earlier stage of MCDA problems for weighting criteria.

Dear Omar

On top of what you say, it has been mathematically proved that for more than THREE alternatives, the Eigenvalue method used by AHP does not produce reliable 'weights' when compared with the geometrical average.

But for me, one of the most controversial aspects of AHP and ANP --, out of several - is that it is NOT TRUE that it produce weights that represent criteria relative importance. The priorities are in reality trade offs values that indicate how much a criterion changes when another change. It has nothing to do with criteria relative importance

Dear Munier,

On last of what you say prof, i completly agree with you, but i think that a senstivity analysis of criteria importances made by decision makers at the later stage of decision making problems could justify their prioritization and subjectivity, especially when final ranking is still stable.

In the AHP method, the responses from the experts are collected using pairwise comparison between the factors and comparison matrix are created. I think, AHP is used for relative comparisons between the factors. However, survey method is used where we need a large sample size.

My answer is, AHP can not be used for validation.In another way, I think that AHP can be used for drawing inferences from the validated set of data after prioritizing set of sub-factors which were pair-wise compared.

According to my study AHP is useful for decision making in project management.

Dear Omar

I agree that sensitivity analysis (SA) is a very good tool to test a result.

However, if this result is obtained by using preference 'weights' for criteria, then SA is extracting conclusions based on something that could be biased. It is different when SA is performed on a result product grounded on reliable quantitative data and as good as possible qualitative data.

In addition, sensitivity analysis as is performed nowadays is based on analyzing the variation of just one criterion, chosen because it has the highest 'weight; which is not even that, but a trade-off value, and then not suitable to relatively evaluate criteria, let alone to be used for sensitivity analysis.

As everybody knows a different DM may have different preferences and then obtaining different results; what is then the value of making a SA? You are making a SA based on a DM preferences that could be different from another.

Group Decision-Making can greatly improve this issue, as long as you synthesize the different values using the geometric mean and using these values to build the initial decision matrix, not for determination of 'weights' for criteria.

The problem is now to determine which CRITERIA, not a sole CRITERION, to use for SA.

SA can be safely and rightly done using the marginal values of criteria., and then selecting those CRITERIA, not a CRITERION, that makes a solution possible.

This can be done using Linear Programming. This is not my invention; It was created in the 1950s, and it is still used today by 70,000 companies around the world, in large and complicated problems.

Dear Mohammad

I guess that what you call 'factors' are the criteria and the alternatives, and if it is I agree with you.

The AHP method it is assumed that evaluates criteria as per its importance. It is not so.

The so called 'Priorities' generated by A|HP are not such, but trade -off values, and thus, they indicate how much a criterion change with another criterion is varied, but NOT which its importance is.

Dear Muhammad

It could be interesting if you can elaborate and tell us in which area of Project Management the AHP may be useful.

In my personal experience, during my 20 years working in project management, and in several fields, I never saw the need for using AHP, but of course, there is always something to learn

Dear Mohammad,

As other colleagues the answer is of course ,NO.

Dear Munir,

Yes, as you have stated AHP neglect the interrelation between the criteria when it should be neglected. If the there is any relation between the criteria then you have to use ANP “DM decide these relations”.

Dear Ramirez,

Would you please provide us with some mathematical errors that are committed by applying AHP.

Dear Sarbast

First: How do you determine that there is or not relationships between criteria? Some are straight forward, but many not.

Second: What is the yardstick to determine if a certain relationship should be considered or not?

Third. Yes, ANP considers interrelations and probably that is the reason for Saaty to develop it. However, what ANP does not take into account is HOW that relationship of criterion A affects criterion B.

For instance, there is no doubt that a criterion risk in closely related to criterion alcohol content in a driver. Look at the graphic I am attaching. Data is from Wikipedia but computation is mine. You can see that the risk increases exponentially with alcohol con tent.

However, ANP considers that there is a relationship, that it assumes is constant.

Do you think that this is correct?

Dear Sarbast

First: How do you determine that there is or not relationships between criteria? Some are straight forward, but many not.

Second: What is the yardstick to determine if a certain relationship should be considered or not?

Third. Yes, ANP considers interrelations and probably that is the reason for Saaty to develop it. However, what ANP does not take into account is HOW that relationship of criterion A affects criterion B.

For instance, there is no doubt that a criterion risk in closely related to criterion alcohol content in a driver. Look at the following graphic, data are from Wikipedia but computation is mine. You can see that the risk increases exponentially with alcohol con tent. ANP then considers that there is a relationship, that it assumes is constant.

Do you think that this is correct?

Just to have an idea of how common (and convenient for AHP users!) this dismissing reality is, look at papers published on works done using AHP , there are probably thousands, and examine the criteria. Most of the cases you can be sure that relationships exist, however it is ignored. Or as a practitioner told me when I criticized his work on this regard. He said

'I have decided not to consider it' . Of course he did not elaborate on the reasons.....

Dear Sarbast

I don't know Mr. Ramirez answer, but if you allow me I will also answer your question

Drawbacks of AHP:

* Not considering criteria relationships

* Not considering alternatives relationships

* If alternatives are more that 3, the eigenvalue method to find priorities is not recomended

* Limits of up to 9 criteria, even recommended by Saaty

* The preferences system for criteria an alternatives. The DM works hard to find consistency of HIS preferences. This is normally alien to reality that is inconsistent

* Replacing by estimates, reliable and confirm values in quantitative criteria. For instance prices, output, man hours, etc

* The Saaty scale. What happens when transitivity is higher than 9?

* it is against all logic to take decisions on behalf of may be thousands of people and also it violates Arrow theorem

* AHP and ANP add all priorities to 1 in order to normalize. However it assumes that a change in one criterion impacts proportionally in all other. This is absurd, since if one criterion is say 'price' and the other is say'demand' it means that an increase in price LINEALLY affects the demand. This is against logic, and against to what economy principles say, since both variables ARE NOT LINEALLY related, but by a curve function

*AHP determines priorities that it call 'weights' They are not weights but trade-off values, and then they cannot be used to relatively rank criteria by their importance. Even worse, these so called 'weights' cannot be used to evaluate alternatives

There are more, but I believe than these answer your question.

By the way I had the privilege to discuss most of these aspects with Dr. Saaty on February 2017, and really I did not get satisfactory answers. Unfortunately, his passing away in August 2017 interrupted the dialogue.

Dear Sarbast Moslem, thank you very much for your question and although it is personal, I hope not to offend you by answering in public.

The problem with AHP is that it is not mathematically consistent; to put it in simpler words in AHP and ANP 2 + 2 are not necessarily 4.

This is a fundamental problem that has as its starting point the scale used by Saaty, its creator.

Consequence of this mathematical inconsistency, all the problems of AHP and ANP are generated.

In the work that I recommended to read in another answer on AHP, although the article for reasons of reliability is not complete, with the two pages that are presented you can see a couple of consequences of this lack of consistency.

The work is available in:

https://www.researchgate.net/publication/308994814_Shelter_Selection_with_AHP_Making_Use_of_the_Ideal_Alternative

This lack of consistency can be corroborated very easily if you compare two attributes, or two alternatives (A and B), where you, following the Saaty scale, consider that B is slightly better than A and assigns a 2. Since you have used AHP, you can construed the table and get your own conclusions.

However, I apologized at the beginning if I offended you, for answering publicly.

The reason is that the vast majority of AHP users, it focuses on both the peripheral and the accounts and they are not able to see what is happening mathematically.

So I feel a little sorry for others when someone claims that AHP or ANP works well in this or that field.

I hope that if you have some mathematical training, see what is happening to you, what your results are reflecting. (By the way we are engineers and chemists; none of the group is a mathematician of initial training)

In any case if you do not see it, do not feel bad. There are many researchers with whom I have talked and do not notice that 2 + 2 is not being four.

Again, thank you very much for your question and my apologies to you and other AHP users if I offend alls, with my response, but mathematics has a bad habit of being exact and consistent.

Best regards,

José Hernández.

Dear Sarbat,

If you permit me to clarify one point related to criteria axioms or requirements, which DMs have to respect in building criteria :

Completness, Minimum size, non overlaping, non redudancy and mutualy preference independency. This last axiom means that DMs must avoid any relationship, which could exit between criteria and might affect thus the performance rating of alternatives, i.e. scoring of an alternative on one criterion should not depend on its scoring on other criteria. Probably in certain problem, criteria could be correlated, in such situation DMs should propose a new composite criterion or decide to remove them from the selection model. In light of this consideration, i think that is not a question of ANP or AHP. Indeed, We should not accept relationships between criteria in order to use a valid selection model.

Dear Prof. Munier

The max. number of criteria is valid only branch wisely so max. 9x9 matrix is recommended but altogether there might be many more criteria (just as we applied). The reason of this limit is - according to Saaty - the limitation of the human brain to concentrate the transitivity in the case of such a lot factors.

However I absolutely agree with you related to criteria connections. Me neither find ANP satisfactory, that is why we are working on constructing an AHP-ISM model.

Dear Prof. Ramirez

Thank you for your answer.

As far as I know, Saaty invented consistency check in AHP that ensures that all matrices meet the consistency criterion of acceptable inconsistency, and we get high consistent answers when the experts are our evaluator group, for example:

I created questionnaire for public participants and for experts, the consistency value with experts was high. While, the consistency value with the public good and CR was less than 0,1 for both experts and public.

Of course, we are not mathematical scientists but AHP method was mathematically proved by Saaty and it has been used in more than 16700 academic researches for the last four years.

Dear Sarbast

I am not a mathematician either, however I can point out, and I have done it many times in RG , that AHP is flawed, simply using common sense and experience in dealing with MCDM methods.

In addition, there are many RG people that have reached the same conclusion by using mathematical analysis.

Curiously enough, in three or may be four years that I have been writing about AHP and its drawbacks, nobody came to defend it.

In my opinion practitioners are misled by the easiness of AHP, and apparently they don't think that said easiness comes at a price. The problem is that since true results are never known, any result by any method is accepted. Who is going to discuss it?

Dear Prof. Munier

The max. number of criteria is valid only branch wisely so max. 9x9 matrix is recommended but altogether there might be many more criteria (just as we applied). The reason of this limit is - according to Saaty - the limitation of the human brain to concentrate the transitivity in the case of such a lot factors.

However I absolutely agree with you related to criteria connections. Me neither find ANP satisfactory, that is why we are working on constructing an AHP-ISM model.

Dear Sarbast

Yes, of course you can have more than 9 criteria, although it is not recommended

Dr Saaty based his appreciations on a concept found by a psychologist, who established certainly that limit, but remember that it was only a hypothesis, perhaps validated by psychological tests, but not by mathematics.

Regarding you answer to professor Ramirez

And where the acceptable inconsistency come from? Who said and proved that it is correct?

Saaty adopted that 10 % maximum because it comes from a condition in the eigenvalue procedure

But most important, why is it necessary to have transitivity in the DM preferences?

Dear Professor Omar

At the beginning you say that the DM must avoid relationships.

How? Just by ignoring them?

If he does, what is the chance that his result be correct if he works with no representative data?

I am puzzled by your last paragraph, or most probably I did not understand your point of view.

You say that we should not accept relationships between criteria in order to use a valid selection model. Well, what about ANP that works with them?

In all honesty I don't understand. Could you please clarify it?

Agreed, the DM, knowing that there are relationships may decide not to consider them, but on what grounds? It is not a matter or personal decision, but of honouring reality, something for which AHP is not very prone indeed.

If he is using AHP of course the reason is that the method does not accept them, therefore it is a matter of the method, not of the problem. What he should do is look for another method that accepts relationships. Yes, he can switch to ANP, but to no avail, since this method only registers what important is one regarding the other, but not its value.

To clarify perhaps my confusing analysis, please allow me to propose an elemental example.

Assume that a scenario calls for selecting the best road between A and B, amongst several.

The different alternatives are subject to criteria

a) Speed

b) Safety

c) Weather

When comparing speed with weather, regarding the main objective, the DM considers that speed is more important than weather and assigns a value of 2 at this radio. How he gets the value of two in the Saaty scale is a mystery, but it is supposed that he considers aspects such as travel time, business, freight traffic, etc., or maybe he used his intuition, or how he feels that day, as some AHP defenders postulate.

He also assumes that there is a linear relationship between these two criteria and then weather is ½ the importance of speed. One wonders how he knows that there is a linear relationship, but he adopts it anyway, why to bother is making some research?...........

Now, he got curious and decides to inspect dependencies between criteria and for the same problem, and finds that speed is dependent of weather, simply using common sense, since if there are heavy rains, snowfalls, etc., the speed is reasonably contingent or conditional to it. That is, it appears the weather is more important than speed, while the opposite does not exist, since weather is independent of speed. He is even able to get the values of this relationship using the Pearson Correlation Coefficient Rho and finds that it is 0.8. That is, for 1 unit increase of bad weather there is a -0.8 unit decrease in speed, and this value is not invented, it comes from statistics.

Consequently, the second analysis invalidates the DM preferences.

Bye the way, this could be a test to check accuracy of the DM preferences.

Taking into consideration this simple example, is it ‘legal’ to avoid dependencies?

Dear Professor Munier,

With a great pleasure, I appreciate sharing discussion with you about this topic and made my response more clear. Firstly, to explain my point of view, the mutually preferential independency could be defined by asking the following question:

Can each of the criteria be scored on its own, without having to consider any of the other criteria? If not, the criteria may not be preference independent, and the selection model should be restructured or the criteria redefined.

In health sector for instance, frequency and mode of administration of a medicine are two criteria, which DMs could not make a preference on the frequency without knowing the mode of administration. The two criteria can be combined into a single criterion with sub-criteria for example, such as “tablespoon thrice a day” and "injection twice a week".

Another example related to select the best club of aerobics and bodybuilding to make a membership, having no preference for which sport to play, but being assisted by a coach. The following criteria are defined:

C1: club adhesion fees

C2: travel time

The DMs decide that saving 5 minutes in travel time is better than save 5 euro on adhesion fees, i.e. C2 > C1 . But, suddenly they discover that the weight would depend on which sport the adherents chose to practice in club, because the sport aerobics in certain clubs involved traveling twice a week to be assisted by a coach, while bodybuilding involved traveling three times a week. The last criterion C3: Sport_NumberOfTravel breaks the axiom of preferential independency, since the two previous criteria depend on it. The Solution is decomposing C3 by specifying for each sport the tolerated number of travels for any club.

In fact, the additive model describes the DM's preferences only if the attributes are mutually preferentially independent.

Concerning your example to select the best-fit road between A and B, amongst the criteria: Speed, Safety and Weather. Suppose

Speed = {x1=100, x2= 80}

Weather = {y1="rain", y2="nice"}

When DMs make their preferences as follows:

(x1, y1) > (x2, y1)

(x1, y2) > (x2, y2)

That is, The Speed 100 is always preferred to the speed 80, irrespective of the weather in question.

However, if preferences are made such as following:

(x1, y2) > (x1, y1)

(x2, y2) > (x2, y1)

Indicating that the DMs prefer the speed 100 if it is a nice weather, but if it is raining they consider the speed 80 as a better option. This last case, despite being a wise choice in relation to road accidents, the criteria speed and weather are preferentially dependent.

Meanwhile, we should not to be confused with a possible correlation of alternatives scores on certain criteria as you claimed in your response (That is, for 1 unit increase of bad weather there is a -0.8 unit decrease in speed). The key idea is avoid correlation to make preference either between criteria or alternatives on those criteria (using saaty scale or other means).

Otherwise, the multiplicative aggregation model could be used, since it suggests a weaker preferential independency, although it is rarely applied in practice due to the complexity of choosing the synergy factor (k).

NM - Dear Professor Omar

Believe me, the pleasure is mutual. It is very rarely that I have the opportunity to discuss and possibly discover new aspects on MCDM from a learned colleague, especially in AHP which is not my specialty.

OEB- With a great pleasure, I appreciate sharing discussion with you about this topic and made my response more clear. Firstly, to explain my point of view, the mutually preferential independency could be defined by asking the following question:

Can each of the criteria be scored on its own, without having to consider any of the other criteria? If not, the criteria may not be preference independent, and the selection model should be restructured or the criteria redefined.

NM- I believe that you can, using for instance a 1 to 10 scale. You can say that from your point of view you consider price of a large importance and you assign it a value of 8. The same for another criterion such as demand, which even may have the same scoring of 8. From this point of view both are unrelated.

But from the reality point of view the are related since one influences the other.

However. I disagree with your final paragraph because it implies that you change your approach when you should not. The fact that they are related is a fact of life and beyond your intentions you change it, so you have to consider it like or not.

Note your words:’,.. and the selection model should be restructured or the criteria redefined’. It means that you should bring reality to your wishes or needs, when it should be the opposite; You have to adapt to reality.

OEB- In health sector for instance, frequency and mode of administration of a medicine are two criteria, which DMs could not make a preference on the frequency without knowing the mode of administration. The two criteria can be combined into a single criterion with sub-criteria for example, such as “tablespoon thrice a day” and "injection twice a week".

NM- Very good example, the problem for me is that it is only one criterion because the way the medicine is taken is only one. There is no dependency here nor level of importance, since one action implies the other; they are complementary..

In my opinion this is not a criterion but an attribute, that indicates that for medicine A the patient must take two tablespoons each four hour while for medicine B he must take one tablespoon every 2 hours. Both values may then correspond to a criterion ‘posology’ or ‘dosage’

OEB- Another example related to select the best club of aerobics and bodybuilding to make a membership, having no preference for which sport to play, but being assisted by a coach. The following criteria are defined:

C1: club adhesion fees

C2: travel time

The DMs decide that saving 5 minutes in travel time is better than save 5 euro on adhesion fees, i.e. C2 > C1 .

But, suddenly they discover that the weight would depend on which sport the adherents chose to practice in club, because the sport aerobics in certain clubs involved traveling twice a week to be assisted by a coach, while bodybuilding involved traveling three times a week,

NM- In this case you can create a criterion called for instance ‘Type of sports’ and putting the attributes 2 and 3 for number of trips.

OEB= The last criterion C3: Sport Number Of Travel breaks the axiom of preferential independency, since the two previous criteria depend on it. The Solution is decomposing C3 by specifying for each sport the tolerated number of travels for any club.

NM- Agreed

In fact, the additive model describes the DM's preferences only if the attributes are mutually preferentially independent.

NM - Agreed

NM- However, criteria independence very rarely happens in the real world. It is not my opinion, since there are many scholars that think in the same way. In addition, you can see it every day in actual scenarios.

NM - I would like to ask you a question:

If AHP cannot handle criteria relationships, and if these are present in most scenarios, what is the purpose of using it?

OEB - Concerning your example to select the best-fit road between A and B, amongst the criteria: Speed, Safety and Weather. Suppose

Speed = {x1=100, x2= 80}

Weather = {y1="rain", y2="nice"}

NM- You missed my point. I did not define any kind of weather. If road A is a mountain road probably it is subject to heavy snow, while the other road at a much lower altitude is subject to flooding. Consequently, from the point of view of speed x1 is affected by snow and x2 may be affected by flooding. What do you prefer?

If you prefer high speed, chances are that you could be delayed an even stopped during several hours if there is heavy snow. If you choose the lower altitude chances are that you are delayed by heavy flooding

OEB- When DMs make their preferences as follows:

(x1, y1) > (x2, y1)

NM- So, you are saying that high speed with rain, is better or more significant than low speed and nice weather, or that high speed and nice weather is better than low speed and rain. You have the right to think in that way, but in so doing you are voicing your own preferences, however, the world does not function in that way. There are conditionings, norms and protocols that limit your free choice, and those must be included when you make a decision.

OEB- (x1, y2) > (x2, y2)

That is, The Speed 100 is always preferred to the speed 80, irrespective of the weather in question.

NM- See, my friend, it is not a matter of preferences. You need to consider the environment that in your reasoning is absent. And this is from my point of view perhaps the main problem with AHP, where the DM establishes his own preferences, that may be biased as in this case, and not considering reality.

OEB- However, if preferences are made such as following:

(x1, y2) > (x1, y1)

(x2, y2) > (x2, y1)

Indicating that the DMs prefer the speed 100 if it is a nice weather, but if it is raining they consider the speed 80 as a better option. This last case, despite being a wise choice in relation to road accidents, the criteria speed and weather are preferentially dependent.

Meanwhile, we should not to be confused with a possible correlation of alternatives scores on certain criteria as you claimed in your response (That is, for 1 unit increase of bad weather there is a -0.8 unit decrease in speed). The key idea is avoid correlation to make preference either between criteria or alternatives on those criteria (using saaty scale or other means).

NM- I did not claim about correlation on alternatives scores but on correlation between vectors speed and weather, as a function of their attributes. In my example I found the correlation between the two vectors which supposedly was 0.80. For instance, every increase in 1 cm. of snow on the road correlated with a decreasing speed of 100 x 0.80 = 80 km/hr.

Why the key idea is to avoid correlation, when that is something that you do not control?

OEB- Otherwise, the multiplicative aggregation model could be used, since it suggests a weaker preferential independency, although it is rarely applied in practice due to the complexity of choosing the synergy factor (k).

NM- Sorry, you lost me, but what synergy factor are you talking about in using the geometric mean?

Dear professor Munier,

I think we talk about the same thing, the selection models using AHP or other MCDA approches cannot avoid using preferential independent criteria in reality, so that i suggested using the multiplicative aggregation to calculate the utility value (overall performance scores on all criteria obtained by an alternative) instead of the additive aggregation.

U=sum(vi*wi)--> additive model

U=sum((k* vi*wi-1)+1)/k--> multiplicative model (k is the senergy factor).

Meanwhile, if the additive model is the selected model to aggregate performance rating of performance against criteria, we should avoid preferential dependency between criteria.

Dear Professor Omar

Sorry my friend, but I don’t think that we are talking about the same thing, well perhaps we do, because both refer to preferences, but I disagree with the fact that other MCDM cannot avoid using independence criteria. Many do, SIMUS is one of them, as well as ANP.

There is something that apparently many people are not aware of, and it is the fact that the decision-making problem is s systemic approach, as Saaty also recognized when he defined his model as a system.

As such, you cannot consider components elements of the problems separately, which is what AHP does by wise-comparing criteria and alternatives. Everything is interrelated, and most possibly Saaty developed ANP where he works on a network and therefore with all elements directly or indirectly related. In reality AHP is only a case of ANP.

Obviously, I misunderstood you in your last letter. I thought that you were taking about AHP and for that reason I could not understand what you said about the synergy factor.

Now that you are talking about MAUT I can understand your comment. AHP is not MAUT, and at the end of the XXth Century there was a hot debate between Saaty and several scholars who proposed him to use the multiplicative approach instead of the additive to avoid the Rank Reversal problem. Saaty resisted fiercely, but at the end he agreed.

However, whatever method you use it is still based on preferences, unless the utility function is determined by mathematical means. This involves calculating the marginal utility of each criterion, and it is exactly what Linear Programming does when solving the dual problem. Using IOSA (Input-Output Sensitivity Analysis) which is part of SIMUS, based in Linear Programing, you can determine mathematically the utility function, and this is the way that you can inform stakeholders about the robustness of a solution, as well as compute quantitatively the risk generated by exogenous factors. Since risk is the product of a probability of occurrence, that can be computed by statistics, and the impact, which is the difference in utilities, and then this computation is easy, and the result very valuable.

I kindly want to remind you that I asked if you could answer a question of mine. I would very much like to have your answer

Best regards

Nolberto

Nolberto Munier I also agree that AHP is flawed, but other methods as well. It must be noted that: In some situation, AHP, or pairwise comparison in general, is effective. However, multiple aspects that contribute to the "right" application of the method is often not seriously considered. I must say that the core idea behind the method is rather simple and easy to be understood and apply, excessive enough for it to be used even in unfavorable conditions.

Dear Sol

Could you tell me which are methods flawed and why?

MAUT, ELECTRE, PROMETHEE, VIKOR, TOPSIS , and many others are based on solid mathematical principles. You can blame them of using subjectivity in a greater or lesser degree , but not on their grounds.

Quite the opposite in AHP that in many aspects in not well founded.

Even if you recognize that it is flawed, how can you use it with confidence?

In my opinion, regarding pair-wise comparison, and I agree that most methods use it, is not the right way to make comparisons, at least in MCDM, because in so doing you are assuming that criteria are not interconnected, which is not true practically in any case.

I would very much appreciate it you can elaborate your sentence that 'multiple aspects that contribute to the "right" application of the method is often not seriously considered', which are these aspects?

I agree with you in the sense that from my point of view, none method can reproduce a scenario even remotely, and that for me it is due to the structure of such methods.

I also agree that the core idea behind the AHP is easy to understand and apply, and that is the reason for its clear dominance, but it does not mean that you can solve a problem with it.

As I always had said AHP is probably the best method to solve trivial problems, where the receptors of the benefits and consequences of the project fall on their developers such as selecting a restaurant, a car an apartment o selecting people for a company. The reason is that in those cases the DM or DMs know exactly what they wish and they need. You cannot transport that to projects where there are thousands of people affected.

I had the privilege of discussing this same issue with the late Dr. Saaty, and I could not get an answer from him.

What do you mean by 'unfavorable conditions'?

OK, suppose you must build a copper concentration plant in one of three different places, all of them very inaccessible. Could you please tell me how do you manage that problem in AHP? Based on your preferences?

In other method it is fairly simple since you establish a criterion such as 'Access difficulties' and you evaluate them by inspecting each zone, seeing the state of bridges, harbors, etc. That is, you can collect very reliable information.

Can you do that based on preferences?

Dear Dr. Munier,

Thank you for your reply, I have seen that we are agreed with each other in some points.

Regarding the flaws of AHP, what I understand is it is suitable with quick and less important problems. I assume that by "The reason is that in those cases the DM or DMs know exactly what they wish and they need. You cannot transport that to projects where there are thousands of people affected.", you mean the scale and importance of the problem, or the conflicting views of the "best"?

I certainly do not think that the conflicting views of the "best" is a sensible interpretation here because a DM will have to determine his/her criteria before the application or selection of methodology. In other words, the standards of the "best" must be had before the application of MCDM techniques. If what you are regarding to is the scale of the problem, I think what you are implying is the accuracy of AHP in indicating the "best" option, due to its flaws.

By flaws, I meant weaknesses, and in that sense, I think that not any methodology is perfect. It is just that some of them are really, really good for a particular problem, and not for some others. I only considered AHP as having big , big weaknesses in comparison with other methods with solid mathematical principles, and that affect its effective in supporting DMs when the problem is getting bigger or more significant.

By 'multiple aspects that contribute to the "right" application of the method is often not seriously considered' or 'unfavorable conditions', I mean that a problem must be considered before a method could be chosen, like the characters of a bacteria must be known before a medicine could be developed. If the problem and current situation (expert availability and quality, uncertainty or shortage of information, the ability of compensation across criteria, time, costs, etc) could be solved effectively with a method, then it should be selected by the DM. Many researchers or practitioner just put a method in and state that hey I solved this problem by using method X without rigorously examine the suitableness of the method with the conditions of the problem. AHP might be used for small cases or in a limited budget and time situation. The successful applications of AHP is the evidence that it is effective in some specific situation.

About your example problem regarding copper concentration plants. I understand that AHP might be intolerably weak in some cases, but that does not mean that it is totally flawed to the point of useless in all situations. It does have a mathematical ground, although I find it totally nonsense if applying in many cases.

Dear Mr. Nguyen

SN - Thank you for your reply, I have seen that we are agreed with each other in some points.

Regarding the flaws of AHP, what I understand is it is suitable with quick and less important problems.

NM -I agree

SN - I assume that by "The reason is that in those cases the DM or DMs know exactly what they wish and they need. You cannot transport that to projects where there are thousands of people affected.", you mean the scale and importance of the problem, or the conflicting views of the "best"?

NM -I don’t refer to any scale. What I say is that the DM can’t assume the responsibility of interpreting what thousands of people wish or think. He must work with data obtained by surveys and polls and condensed in percentages that inform what people think. In these cases, if the DM thinks that his preferences are more valid that those of thousands of people, he is in addition violating the Arrow Impossibility Theorem, that precisely addresses this subject.

As you can see it is not only common sense, since it is also supported by science. In case that the decision is related to moving may be millions of people (as happened in the Three Gorges Dam in China), or in the Itaipú Dam in Brazil, how could the DM know the consequences of that movement will have on people? When I say that people need to be consulted I am not referring of course to technical or economic decisions, but on how the project will affect them, and there is nobody better suited to answer this question than the people by themselves, not by the DM

SN - I certainly do not think that the conflicting views of the "best" is a sensible interpretation here because a DM will have to determine his/her criteria before the application or selection of methodology.

NM- Of course

SN - In other words, the standards of the "best" must be had before the application of MCDM techniques. If what you are regarding to is the scale of the problem, I think what you are implying is the accuracy of AHP in indicating the "best" option, due to its flaws.

NM- No, again, I am not talking about accuracy, but about using a procedure that is not related with reality

SN- By flaws, I meant weaknesses, and in that sense, I think that not any methodology is perfect. It is just that some of them are really, really good for a particular problem, and not for some others.

NM -I agree, however, AHP and ANP are mathematically flawed, and if you want I can justify what I say.

SN- I only considered AHP as having big , big weaknesses in comparison with other methods with solid mathematical principles, and that affect its effective in supporting DMs when the problem is getting bigger or more significant.

NM - Yes. In my modest opinion AHP is weak in two counts; from the mathematical and from the procedure points of view

SN - By 'multiple aspects that contribute to the "right" application of the method is often not seriously considered' or 'unfavorable conditions', I mean that a problem must be considered before a method could be chosen, like the characters of a bacteria must be known before a medicine could be developed.

NM- I agree, excellent analogy

SN - If the problem and current situation (expert availability and quality, uncertainty or shortage of information, the ability of compensation across criteria, time, costs, etc) could be solved effectively with a method, then it should be selected by the DM.

NM- Exactly, I wonder how the D M may choose AHP to solve a problem where there are relationships between criteria, when he knows that AHP uses compensation and that the latter assumes independence between criteria. I asked this question many times to people that used AHP in problems where interrelations between criteria were evident, and some responded that they preferred to ignore it, because they consider not important……..Extract your on conclusions.

SN- Many researchers or practitioner just put a method in and state that hey I solved this problem by using method X without rigorously examine the suitableness of the method with the conditions of the problem.

NM-I agree in a 100 per cent, and the worst is that after they got a result they affirm that the application was successful

SN - AHP might be used for small cases or in a limited budget and time situation. The successful applications of AHP is the evidence that it is effective in some specific situation.

NM - I wrote the last paragraph when I had not read this paragraph of yours. I ask them on what grounds can you affirm that some applications of AHP were successful? To measure the success of something you need to know which successful mean or is. As of to-day no method, except Linear Programming in mono-objective problems, may affirm that the solution reached was mathematically the best, but it can not affirm that it was successful because the ideal or best solution is unknown.

SN- About your example problem regarding copper concentration plants. I understand that AHP might be intolerably weak in some cases, but that does not mean that it is totally flawed to the point of useless in all situations.

NM - In this case, which by the way, is a real case. I would not say that AHP is weak. I would say that AHP simple cannot solved this problem; it was not designed for that, and one of the reasons is because it does not consider resources and restrictions, for instance relative to environment, maximum supporting loads for bridges, maximum slope in roads as many others. You cannot work with preferences here

If I remember right I said in my first answer to you that I consider AHP probably the best method for some type of problem, where personal decisions are paramount

SN -It does have a mathematical ground, although I find it totally nonsense if applying in many cases.

NM - agree in 100 per cent

Dear Dr. Munier,

I observed that we actually agreed in most parts, and I am grateful that I could learn from discussion like this.

NM -I don’t refer to any scale. What I say is that the DM can’t assume the responsibility of interpreting what thousands of people wish or think. He must work with data obtained by surveys and polls and condensed in percentages that inform what people think. In these cases, if the DM thinks that his preferences are more valid that those of thousands of people, he is in addition violating the Arrow Impossibility Theorem, that precisely addresses this subject.

As you can see it is not only common sense, since it is also supported by science. In case that the decision is related to moving may be millions of people (as happened in the Three Gorges Dam in China), or in the Itaipú Dam in Brazil, how could the DM know the consequences of that movement will have on people? When I say that people need to be consulted I am not referring of course to technical or economic decisions, but on how the project will affect them, and there is nobody better suited to answer this question than the people by themselves, not by the DM.

NM- No, again, I am not talking about accuracy, but about using a procedure that is not related with reality

SN - Thank you for show me this aspect, I also understand the cases you gave as examples. AHP is simply cannot get the job done in these types of cases where societal decisions are concerned or explicit, cardinal data must be gathered for a reliable and rational MCDM procedure.

NM - I agree, however, AHP and ANP are mathematically flawed, and if you want I can justify what I say.

SN - I agree. I must say that I know about their rank reversal problem, arbitrary scale of preference, likely low consistency, and probably poorly grounded theory. It would be great if there are more of them that I do not know.

NM - I wrote the last paragraph when I had not read this paragraph of yours. I ask them on what grounds can you affirm that some applications of AHP were successful? To measure the success of something you need to know which successful mean or is. As of to-day no method, except Linear Programming in mono-objective problems, may affirm that the solution reached was mathematically the best, but it can not affirm that it was successful because the ideal or best solution is unknown.

SN - Actually, I thought about an article that I read when I was writing this paragraph. I have searched and this is the doi number of the article. "10.1002/bs.3830250303" The aim here is correct prediction and the method of validation is reality checking. I know that one instance cannot build a ground of confidence in application, but I do not think that the outcome of the case is coincident.

Dear Mr. Nguyen

NM -I don’t refer to any scale. What I say is that the DM can’t assume the responsibility of interpreting what thousands of people wish or think. He must work with data obtained by surveys and polls and condensed in percentages that inform what people think. In these cases, if the DM thinks that his preferences are more valid that those of thousands of people, he is in addition violating the Arrow Impossibility Theorem, that precisely addresses this subject.

As you can see it is not only common sense, since it is also supported by science. In case that the decision is related to moving may be millions of people (as happened in the Three Gorges Dam in China), or in the Itaipú Dam in Brazil, how could the DM know the consequences of that movement will have on people? When I say that people need to be consulted I am not referring of course to technical or economic decisions, but on how the project will affect them, and there is nobody better suited to answer this question than the people by themselves, not by the DM.

NM- No, again, I am not talking about accuracy, but about using a procedure that is not related with reality

SN - Thank you for show me this aspect, I also understand the cases you gave as examples. AHP is simply cannot get the job done in these types of cases where societal decisions are concerned or explicit, cardinal data must be gathered for a reliable and rational MCDM procedure.

NM - I agree, however, AHP and ANP are mathematically flawed, and if you want I can justify what I say.

SN - I agree. I must say that I know about their rank reversal problem, arbitrary scale of preference, likely low consistency, and probably poorly grounded theory. It would be great if there are more of them that I do not know.

NM - I wrote the last paragraph when I had not read this paragraph of yours. I ask them on what grounds can you affirm that some applications of AHP were successful? To measure the success of something you need to know which successful mean or is. As of to-day no method, except Linear Programming in mono-objective problems, may affirm that the solution reached was mathematically the best, but it can not affirm that it was successful because the ideal or best solution is unknown.

SN - Actually, I thought about an article that I read when I was writing this paragraph. I have searched and this is the doi number of the article. "10.1002/bs.3830250303" The aim here is correct prediction and the method of validation is reality checking. I know that one instance cannot build a ground of confidence in application, but I do not think that the outcome of the case is coincident.

Dear colleagues who have followed the question Can we use Analytical Hierarchy Process (AHP) in validating or collecting survey?, few days agro I uploaded the article:

https://www.researchgate.net/publication/327477737_Entrenamiento_para_afrontar_catastrofes_con_un_Modelo_Multiatributo_La_Seleccion_de_posibles_refugios?_sg=PbrTNgzzH0lQyj4fvkHQsv2fnIlJub5sVAK1MFwEu_EUvmMe_Vph-krNntAzIpPUjgRgpe2Qb90JcDJ3lO2WJ5-af4xJbI3cyML_fGXC.tNy97kqPeJC06VYAGb0daDjr8N9EHKISy3E_1w3wZPjieo5t9JrGgRJRVllOTYgGQ0-rzojI_siByAulcTJa6w

Yesterday I upload, the English version of it:

https://www.researchgate.net/publication/327704849_Training_to_confront_catastrophes_with_a_Multiattribute_Model_Selection_of_possible_shelters?_sg=PbrTNgzzH0lQyj4fvkHQsv2fnIlJub5sVAK1MFwEu_EUvmMe_Vph-krNntAzIpPUjgRgpe2Qb90JcDJ3lO2WJ5-af4xJbI3cyML_fGXC.tNy97kqPeJC06VYAGb0daDjr8N9EHKISy3E_1w3wZPjieo5t9JrGgRJRVllOTYgGQ0-rzojI_siByAulcTJa6w

In this article we use a simple and robust multicriteria technique that can be interesting for all of you.

Best regards,

José Hernández.

Dear Mr. Nguyen

NM. Sorry for my late response. I had not seen your answer to me before.

SN.What I meant there is exactly the same one that you said, the final solution, or at least, supportive information for the decision of him/her.

The view upon the received solution should be objective.

NM. Well, in my opinion all depends on what you interpret by ‘view’. Of course, the result must be objective in the sense that it must fulfill a need, however, I believe that is precisely on this result where the decision-maker (DM) can put his knowledge and expertise to work. For instance, suppose that a MCDM method selected equipment C amongst equipment A, B, and C.

That is, the mathematical model selected C according to the data that is supposed to be reliable for all equipment. However, the DM can say, ‘Yes, I acknowledge that C has been selected but I have a personal experience on it, which is quite negative for so… and so…, and then, I don’t think that it is reliable, and then he decides to select A which is the second best. This is purely subjective and perfectly understandable, and it is part of the explanations that he must give to the stakeholders.

SN. And that's true, in a realist view, there is a objectively existed "right" result.

NM. Yes, I also believe so. As an analogy, for me the existence of the human race is an example that reality exists. Mother Nature, among thousands of possible combinations from the original primitive life, ‘created’ a genetic procedure, meaning that only the stronger organisms and those able to adapt to the environment survive, and then selected the human race as a right result.

By the way, this is the principle followed by present-day genetic algorithms for MCDM, which are the most advanced and allow to solve problems that no other algorithm can.

SN. However, in several cases, the same situation of problem cannot be recreated or excessively difficult to do so. It creates an "unknown": there might be an option that we mistakenly ignored or rejected. Even if we agree in a "true" right decision, does it matter if we cannot find and prove it?

For example, A, B, C is considered, the final result is that B is chosen and applied. How could we know that C is 100% not as good as B, especially when it involves risks and uncertainties (qualitative assessment; intangible or non-quantifiable subjects). If we cannot prove that, in that specific case, our method did give us the "best" solution by facts, I do not think that's an absolute 100% sureness. As a result, if another methodology gives back different result, that is still totally make sense.

NM. I agree in a 100% with you. However, in your last sentence remember that apparently you are assuming that in that another technology you do not forget or ignored something, as you did in the first. I believe that to make comparison, exactly the same data and conditions should be in both methods. In my opinion, a MCDM goodness lies it its capacity to model reality and not depending on subjective preferences, assumptions or ideas. In other words, an algorithm that solves a problem without modifying in any way the scenario. I believe that in that case all new MCDM methods working under this premise, should give the same result. Of course, no method can at present replicate reality in a 100 %, and probably never will, however, goodness among them could be measured as how close modeling reality they are. Observe that when we take personal decisions we look for an alternative among several that best fit our wishes.

SN. Another point is, there is at least one difference I could point out among methodologies, some allow compensation across the criteria, some others do not. That I think, is the different view of "the best" that he/she are looking for.

NM. I also agree with you and as a matter of fact it is a central point in my discussions in MCDM. I maintain that at present none MCDM methods represent reality, and to have compensation or not, is one of them.

In my humble opinion I think it is not a matter of ‘taste’ but a matter of trying to represent a real scenario. For instance, how many methods do you know that consider resources and their limits in their schemes?

How many methods do you know that allow for existing relationships between alternatives, or that consider correlation between criteria?

How many methods do you know that consider that in a portfolio of construction projects, it is NOT a static problem by a dynamic, since not all projects start and finish at the same time?

Do you think that sensitivity analysis as done at present by ALL METHODS is realistic, when they are grounded on the variation of an arbitrary chosen criterion based on weights, which have no mathematical foundation?

Thank you for your comments. Please, continue with them. We are here to learn from others.

Nolberto Munier

Nolberto Munier Thank you for your reply. It is great that I had my chance to discuss MCDM with you. It is still one of my research interests. However, as now I am focusing on a relatively different field and also, my limited knowledge do not allow me to elaborate further on the methodology - specific theme (other than several ones that I mastered). I hope that we will still have chance to meet in this forum as long as we have the same research interests. Again thank you.

Did you apply AHP??

Distinguished Muhammad Azeem Akbar, I would add why?

Best regards,

José Hernández

Dear Muhammad

I replicate Jose Gilberto question:

Why are you using AHP?

As a matrter of fact, the question is exactly the opposite. It should be . Can I use the survey to validate AHP?

Consider that a well conducted survey can produce highly reliable results. Compare with AHP that only provides fiction

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

Mohammad,

AHP can only help you select the best alternative for your project. It does not help you validate your research results except you've different alternatives in your research results and you do not know which is the best one to select. Take note AHP has some flaws and I'll recommend using Logical Decision Software for Windows.

Dear Egbe

I am afraid I disagree with you because AHP can’t help the DM in selecting the best alternative due to various reasons

Just as an example, I will analyze one of those reasons, which, as far as I know, has never been mentioned in RG:

It is that AHP considers a pair of criteria and determine its weight based on preferences and considers them constant through the alternatives.

This is incorrect

First, because what AHP determines are trade-offs, and then indicating how much a criterion varies in preferences with respect to others, therefore, the so called ‘weights’ that come from these comparisons and assuming that they measure criteria importance are a fallacy.

Second, because once AHP says for instance that criterion C1 is three times preferred than C2, then he considers that relation constant, and it is probably not

As an example, suppose that you have to select between three restaurants A, B and C for dinner, and you want to compare the alternatives based on the comparison between C1 (quality) and C2 (price), and you established that for you, quality es preferred to price, and assign a quantitative value to that preference (which, by the way, does not have any mathematical support).

In comparing restaurant A with restaurant B, you decided that food in A has a superior quality than food in B, but also a higher price. According to your prior selection you select A, that is, you sacrifice price, or prefer to pay more, but then you have a gain in quality. An this is fine for this pair of alternatives.

Now you compare restaurant A and restaurant C and finds that C has a lightly inferior food quality than A, but prices are considerably lower. You may decide that you will sacrifice a little lesser quality, but you will get a benefit paying less

This second comparison between quality and price is opposite to the first one, therefore, it does not make sense using a constant preference for all alternatives.

In addition, in its first stage AHP don’t even consider alternatives, that is, the criteria are considered by themselves without taking into account the alternatives that they have to evaluate.

Then, how can AHP work with constant comparisons?

You see, there is not high mathematics here, it is only common sense and a little analysis

Consequently, there is no guarantee that AHP will select the best alternative and even the right ranking

And remember that I have examined only one factor.

Nolberto Munier I understand your logic. I think what I was meant to say is that AHP helps you rank the alternatives for selection. I was answering Mohammad's question on whether AHP can help you validate a projects results which from my experience I would say No except you've different alternatives as a result.

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 Hernández.

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

Dear Krishnendu

What relevant journal are you referring to? You don’t mention any.

Regarding validation, I am afraid that I don’t agree with you. As far as I know, no MCDM method can validate data, and certainly not AHP that works with preferences.

As a matter of fact, all methods must me imputed with validated data, and then, process it.

It does not matter if in AHP it is a sole DM or a group; in this method all of them try just to artificially achieve a transitivity, that most probably does not exist in the real scenario that they are analyzing. Perhaps there are ways to validate the data they produce, but it will be always referred to their individual perception of reality.

What is it useful for? Only for their egos.

Look at how Wikipedia defines data validation:

‘In computer science, data validation is the process of ensuring data have undergone data cleansing to ensure they have data quality, that is, that they are both correct and useful. It uses routines, often called "validation rules" "validation constraints" or "check routines", that check for correctness, meaningfulness, and security of data that are input to the system’.

Dear Krishnendu

Thank you for your information.

I don't know R-Packages, so it is difficult for me to follow your reasoning.

However, I think that no MCDM can validate anything

Dear Krishnendu

After having a glance at the very interesting paper that you mention, I stay on my initial comments.

It is not the MCDM the one which does the validation but the different methods used for cluster analysis.

That is, using several cluster validation methods subject to a series of criteria, Promethee, like other MCDM methods, finds the ‘best’ method, but it does not mean that that Promethee does the validation.

To validate something, you need to have a value for reference, as you do when you perform external cluster validation, because you can compare the goodness of a clustering structure to an external known factor, such as a label with which you can make comparisons.

Feng paper clearly states that it has the purpose of:

1)evaluation of clustering algorithms and

2) estimation of the optimal cluster number for a given data set.

It also states that:

‘This section introduces the selected MCDM method, PROMETHEE II and explains how it is used to rank clustering algorithms and estimate the optimal number of clusters for a given data set’.

I could no find where it says that Promethee is used for validation.

Dear Krishnendu

I am sorry if you find that some of my comments are caustic. Believe me that it was not my intention. Perhaps I am quite direct in my appreciations, but re reading my answer to you I fail to find a caustic comment.

You are asking me something that I don't understand: References to other papers, but about what?

Naturally, MCDM methods are very well known, but which is their relation with validation, that according to your remarks do exist?

Dear Krishnendu

I never said or suggested that you were escaping, those are your words, however I would like for you to explain why do you think that you are doing a work for all of us. This is the first notice I had. What typo of work? Be precise please.

No, I don’t know what Targeted Individuals is, and how it relates with our conversation here.

I don’t understand either why you bring this issue to this forum.

As far as I know nobody has challenged your understanding of what validation is. In my case I simple refuted what you said about that MCDM may be used for validation.

I have the firm conclusion that no MCDM method is fit for validation, when they can’t even validate themselves.

Now, if you can demonstrate that what you said is correct, I will be the first to apologize for a wrong appreciation.

But please. Do that with your own reasons, don’t indicate people to read other scientists’ papers. People usually don’t have the time to read them. As for now, in the subject that you brought, we have only seen no more than words.

You not even challenged what I said in my last letter to you.

RG is a magnificent forum for technical discussions We should take advantage of it. However, if you want to make this private, this is my email: [email protected]

As per your suggestion I tried to read Ms. Ghosh paper. Its link allows to read only the introduction, consequently, I can’t have an opinion on that.

Dear Krishnendu

My answer to your fist letter.

KM. . gr8. Such issues related to MCDA is quite old.

NM. Which issues? Please be specific

KM. It happened during Late Prof.T.L.Saaty. People were not ready to accept it. People considered it as arbitrary. I would request you to read online case studies of AHP and ANP.

NM. Accept what?

I believe me that I have read much more that my share of case studies of AHP and ANP, and that in addition, I have worked with both methods, and also in one of my books explained and developed examples for both. I am not an expert in both methods, far from it, but I know what I am talking about.

KM. 2. Please refer United Nations Institute for Disarmament Research GENEVA. Ask them about Psychotronics Mind Control. Prof. it is up to you to accept or reject the tech.

NM. It is difficult, at least for me, to follow the thread of your writing. In all honesty I don’t have the faintest idea of what Psychotronic Mind Control is. I am an engineer not a psychologist, and really, I am not interested in paranormal and psychic phenomena, but mainly, I fail to see what relation has that discipline with MCDA. Please do not refer me to read something, I beg you to explain with your own words, and you should have begun to explaining us what Psychotronic is.

You can’t start throwing strange words, which possible more than 98 % in this forum do not know what they mean. This is just a friendly advice, if some day to want to start publishing..

KM. 3. Department of Justice through Federal Bureau of Investigation (FBI) is seeking global petition from Targeted Individuals. Again, I would request you to verify it.

NM. Again, What Targeted Individual are? Don’t pretend that we have to go to Google to find out its meaning. And which is the relationship of this thing with a MCDA forum?

KM. 4. Even in Europe use of Psychotronics Mind Control has been banned. People globally celebrated 29th August 2018 as The First Targeted Individual Day. Prof. kindly verify it.

NM. My friend, are you sure you are in the right forum?

KM. 5. I never said Researchgate is not a magnificent forum. Prof. it is your addition. But above tech includes hacking and other form of misuse of webpages.

NM. I never said that you said that. Why this sentence of yours?

KM. 6. I never asked you to read other scientific paper. I just requested you to check the name of the co-author.

NM. Not really, you said first: “ Please refer the research paper " Multicriteria Decision Making Approach for Cluster Validation” and second “Check the attached image”

KM. 7. A group of private investigators in India are doing something wrong. They are hacker and their misdeed has been confirmed by Cyber security specialist.

NM.??????? Could you please be coherent? ‘Something wrong’ is very vague. We are not mind-readers!

KM. 8. We (means several lawyers, police, media people etc) are documented that repeatedly money,career benefits, research publications, promotion etc were shared among people with whom I communicated to suppress aforesaid matter stated above in Sl.No2,3, and 4. Docs submitted in Criminal Court in India and even bailable warrants also issued. I will also share photograph of other perpetrators and their connections with researchgate. That's why said I am doing something for all of you.

NM. I am sorry Krishnendu, I don’t follow you, and besides and I don’t see how you are doing something for us.

KM. 9. Let us come to your point. It is true that you have extensive knowledge in MCDA. I hope you will agree that MCDA tool has strong mathematical base.

NM. MCDA is a process, a methodology, not a tool. It uses a group of different methods that you can call ‘tools’, usually based on mathematics. You can’t use the singular for MCDA, when there are perhaps more than 25 different methods, and not all of them have a strong mathematical base. Two of these are AHP and ANP, the only mathematical component they have is the use of the eigenvectors, and in addition, wrongly, especially for more than three alternatives.

KM. Your statement " when MCDA can’t even validate themselves" is not accepted to me. I would request you to check statistical validation of MCDA.

NM. You have the right of not accepting what I said, and, as I posted many times, I can be mistaken. Then, I accept very gladly to have a discussion with you or with any person to clarify my position, as long of course, that you clarify yours.

What I would appreciate from you is, if you are willing, is just don’t refer me to publications, this is a discussion forum. I would like to hear your reasoning or opinions, not to act as a Librarian

KM. 10. I would request you to share your dataset..

NM. Which data set? I am willing to share everything. Just ask.

KM. Brief your prob statement. Let us try to solve ..

NM. I am sorry Krishnendru, you lost me. I read several times this paragraph, and I still don’t understand what you want. Please, state it more clearly, and I will be happy to comply, if I can.

What do I have let to solve?

Nolberto

Dear Krishnenda

I am responding to your second message:

As you suggested, I read not only read Secc. 6.1 but the whole paper.

My comments are:

1. As most AHP papers, this example shows simplified applications or even simple problems and pretending to be complex, and thus ignoring crucial facts.

Just by reading it, as I have done with many AHP papers, you realize that it is badly incomplete. Do you think that a project of this importance can rely only in three criteria, such as accessibility, topography and land cover, never mind that they have sub-criteria?

What about?

· People leaving in the area

· Wild life in the area

· Rainfall and consequences especially in a tropical area as Malaysia

· Risk due to landslides

· Risk about to pests

· Economic effects

· Cost of the undertaking

· Available water for irrigation

· Adequate weather

· Type of soil

· Cost of seeds

· Production level

· Type of crops

· Distances to markets

· Land ownership, etc.

I am enumerating these even when I don’t k now the area, although I know the country.

Don’t you think that the approach by these authors is very naïve?

2. There is also a bad use of a method such as AHP, that works with independent criteria.

On what grounds was evaluated the accessibility? Only because the expert’s preferences?

I wonder is they realized, and you don’t need to be an expert for that - applying common sense is enough - that in this assessment they need to consider both, the topography and the land cover, and if they did, noticing that they are interrelated, why did they use AHP, which is not designed to work with related criteria?

3. I think however, that they did a good job when validating data from the experts by using two very well-known techniques.

I repeat, they say very clearly that they are validating data, and for me it is correct, but it does not mean that they are validating a method.

As I said in another letter to you, no MCDA method can be validated, because we don’t know the actual or best result of the problem. Therefore there is nothing to compare to.

Lets’ us analyze what validation mean, at least in the decision-making environment

Wikipedia:

Data validation, in computer science, ensuring that data inserted into an application satisfies defined formats and other input criteria

Business Dictionary

1. Assessment of an action, decision, plan, or transaction to establish that it is (1) correct, (2) complete, (3) being implemented (and/or recorded) as intended, and (4) delivering the intended outcome.

2. Assessing the degree to which (1) an instrument accurately measures what it purports to measure, or (2) a statistical technique or test accurately predicts a value. See also validity.

That is, in my opinion, validation means to make sure that a response is similar to an expected result

If it applies to data, it means that they comply with statistical demands, such in the example of Malaysia

If it is related to something material, such the aerodynamics of a car, done on a model in the wind tunnel, they compare performance of the model with expected values, and the same is for a pastry, a movie or o drone.

Observe that in these two cases, you compare results with something that should be probabilistic or to values already established.

In MCDA, you can’t validate a method because there is nothing to compare its results to, since there are not known values.

Regarding this paper I believe that its title should be:

Validation of DATA for Multi-Criteria Decision Analysis Model of Land

Suitability Analysis for Sustainable Hillside Development

Anyway, this is my reasoning.

Dear Krishnenda

KM- Share a test dataset that you want to use for validation. What exactly you are looking for? I mean the problem definition. Put it on discussion. Ask solution.

NM. I imagine that the precedent paragraph is what a DM should do. If that is the case, I agree with you

KM. I worked earlier with Prof.T.L.Saaty. There was issues related to fuzzy AHP/fuzzy ANP, rank reversal, acceptance of hierarchy logic etc. Kindly don't ask me to explain further. You mentioned that validation of MCDA Model is not possible. I upload a paper. Kindly refer.

NM. Why you don’t explain further? It is something secret or is that you don’t have arguments?

It is just a coincidence that every time I ask AHP defenders to explain something, they come with only words like your statement. What kind of technical discussion is this?

Again, you asked me to refer to a paper! If you worked with Tomas Saaty, you should have the answers, don’t you think so? I also had on early 2017 the privilege to correspond with Tomas, and got similar answers

KM. Regarding Tec.h related to TI and sharing of career benefits/provocations etc behind TIs is still the trend in India.Local TV Channels in India are discussing it on regular basis. Please check the attached docs. Don't trust my word. Use your logic, verify it, reverify it.

NM. What is TI? Technical Information? or you wanted to say IT? that is Information Technology?

If it is the first, now you jump to electromagnetic waves?

KM. The attached doc is the main concern in India as no rule/Act has been established so far to support people of India.

NM. Well, it may be important for you, but certainly not for us, at least in this forum

And Krishnenda, I asked you specifically to explain what is the relation of this subject which is obviously important for you, with multi criteria decision making

I AM STILL WAITING FOR YOUR ANSWER.

KM.Let us come to the problem and solution. Prof. remember tech has changed. If you get time please refer "AlterEgo" a device developed by MIT Media Lab. You will get answer of mind reading.

NM. I know what the neural interface Alter Ego from MIT is, but again, why do you bring that subject here?

PLEASE ANSWER MY QUESTIONS AS I AM ANSWERING YOURS

KM.laws_against_criminal_uses_of_electromagnetic_energy_weapons_3.pdf179.88 KB

NM. You are really amazing! Now you bring a new subject. Which will be next? What is its connection with validity?

Dear Krishnendra

Thank you for pointing out my ignorance; only remember that every human being is ignorant of something.

Please don’t be persistent on something such as Targeted Individual, since I am completely indifferent to it.

If you are so keen about this social issue, well, it is your wish and I respect it; I am not judging you for that or for giving unsolicited advice.

If you knew that I would raise these questions, why did you not prepare the answers?

Very simple, because you don’t have responses for them. It is not ignorance; as you said, you knew the problems that I raise, however, you chose to say nothing. Fine, it is up to you if you don’t want to reason.

Can you tell me what ‘reco’ means? When I told you that we are not mind readers it simple mean that we can't guess what is in your mind.

Regarding about ‘rising questions about credibility and knowledge’, I appreciate your concern, but that is something that I dare risk. If I were not convinced about what I say, I would be accepting things as they are, at it appears is the case with so many AHP supporters. Does it suit you better that ‘defenders’?

I am curious. Why are you ‘instructing’ me to drop my research and complaints on Dr. Saaty method?

I would think that it is not a very professional attitude against a colleague. If you are convinced that the AHP method is good, and that I am mistaken, why don’t you demonstrate it?

I have a great respect and admiration for scientists of your country; I have friends there and also published a technical book with one of them. If, I believe, you belong to that sector, why don’t you proceed as a scientist?

Or it is better not to answer and avoid a technical discussion?

As a response to your questions about ‘I hope you may have faced earlier some harsh situation from AHP Defenders’, as a matter of fact, no, I have received no answers, the same as from you. This apparent common denominator suggests that the AHP supporters don’t have enough arguments. What do you think?

I agree with you that selection of criteria and sub-criteria maybe a daunting task, not however, if you know what you are doing. I agree that the paper can give an idea about how to conduct an online questionnaire, and this is valuable.

I also agree that data validation is crucial to everybody, not only to a data scientist.

Regarding criticizing a paper, well, you invited me to read it. If it is published, does it mean that we have to blindly accept what it says? A paper is published to communicate new ideas, new methods or the opinion of the writer on something. Does it mean that we have to accept it as a holy word?

Why do you think is the reason by which most papers indicate the correspondent author?

I have published many books and papers; however, I don’t pretend that everybody has to abide to my ideas.