TOPSIS; the method's computation is very easy. I used some methods to evaluate a problem. The TOPSIS method showed the same result. I think because of the method considers both PIS and NIS it is preferable.

this method (TOPSIS) can used in price strategy?

@Wani Wan: I think TOPSIS method is useful when you determine the ideal positive and ideal negative measures of your problem.. Could you please tell more about price strategy?

To Wani Wan:

I think, you can use TOPSIS in price strategy. The TOPSIS method is usefull technique to monotonic and nonmonotonic crtiteria. The biggest problem can be determine weighting of the criteria.

To Milad Shaddelan:

Could you give an example that PIS (positive ideal solution) or NIS (negative ideal solution) cannot determine? It seems to me that if the character of the criteria is known (monotonic or nonmonotonic) we always can determine PIS and NIS.

have a nice day WS.

@Wojciech : :D there is a possibility for prices to increase unlimited and I considered this matter :D

Yes, but in TOPSIS procedure you must find NIS and PIS for all sets considered alternatives. I don't understand, why unlimited increase of price is the problem for you?

this, my research related to how to determine the price of retail products which will benefit customers through a membership card? what criteria can I study to determine the retail price of this product? conclusion I get from this study is that despite retail price expensive or cheap products, it may be beneficial to the customer / user. I study in the field of econometrics.

whether the pricing factors as may be determined by TOPSIS? I study using survey data.

It seems to me that you don't understand the idea of MCDM methods. These methods are usefull to determine preferences of the decision maker. The preferences are measured in the range from 0 to 1. In my opinion, MCDM methods are unhelpful in this problem. The price can be very often one of the criteria. You can measure satisfaction in respect of price and profits from a membership cards, but not vice versa.

Unless, I misunderstood something.

The choice of MCDM technique depends upon nature of problem. 

If you have a lot of variants - for example UTA method or Electre III (multicriteria ranking problems)

I prefer to use AHP for decision making or setting priorities.  Following paper may help available at researchgate.

Analytical Hierarchy Process Applied to Vendor Selection Problem: Small Scale, Medium Scale and Large Scale Industries

http://sourceforge.net/projects/concluder/?source=directory

tutorial for it:

https://www.youtube.com/watch?v=tzQ4XYNTaig

and publications related to it:

https://www.researchgate.net/publication/289378862_My_selected_publications_2016-01-05:

Are there any source of downloading free AHP software? - ResearchGate. Available from: https://www.researchgate.net/post/Are_there_any_source_of_downloading_free_AHP_software [accessed Jan 21, 2016].

Data My selected publications (2016-01-05)

See my paper:

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

Dear,

The favorite MCDM depends upon our understanding,  The  favorite will be that one which you can understand easily.

Regards

Parveen Sharma

Im using VIKOR method for decision process. Because it is easier than TOPSIS and the results are quite simlir with AHP, PROMETHEE and TOPSIS.

For group decision making, you can check my paper;

Conference Paper SOFTWARE SELECTION WITH WEIGHTED EXPERT JUDGMENTS APPROACHED...

Every MCDM method has it's own beauty. all MCDM methods are not suitable for each problem due to their own limitations.

Dear sir, you want to know best method in the sense of easy to apply or for more in accuracy in result.

The favorite MCDM depends upon situation, objective, etc. However, I always use an integrated MCDM approach.

BWM Method.

This technique is based on the latest multi-criteria decision-making techniques, which was first presented by Mr. Jafar Rezaei for 2015. This method, based on an optimization model, obtains the weight of the criteria. Mr. Rezaei's 2015 paper included offering a nonlinear optimization model, and an article by Mr. Rezaei in 2016 which included a linear optimization model for this technique. This technique can also be implemented after the creation of the model by softwares like Lingo or GAMS.

Also you can check my novel fuzzy technique in mu applied paper:

Article A fuzzy superiority and inferiority ranking based approach f...

It is interesting. However, why?

Mahmut

I agree that it captures some aspects of real-life better, but it is also very limited,

I adhere to Wojciech question.

Although we do not fully agree with Mr. Munier on his reasons, I think PROMETHEE is one of the most appropriate methods in many situations. My reasons are related to normalization, rank reversal, real life reflection and the ranking characteristic it produces.

As I said, its connection to real life is definitely stronger. There doesn't seem to be a rank reversal issue. Normalization doesn't affect it because it doesn't need it. An important feature is that the alternatives maintain their superiority by making pairwise comparisons. There is almost no RR, and moreover, normalization cannot distort the ranking results it produces. It provides this with the preference function it uses.

There is one more point I agree with Mr. Munier here: Limitation! Yes, many MCDM methods have limitations and they show this by their assumptions, thresholds, or preference functions. Situations that require DM intervention are also a separate problem because each DM sets its own threshold value, normalization type, weight type, data format, and MCDM type. Therefore, we assume that we use the same decision matrix and weighting type when comparing MCMD methods. In addition, methods with minimal DM intervention should be compared as much as possible, in my humble opinion.

Since different threshold values ​​can be used in each study and different DM interventions may be in question, I think DM intervention, that is, DM subjectivity should be minimized. Otherwise we would be comparing apples and pears.

Dear Mahmut

Happy to continue these problems with you.

MB Although we do not fully agree with Mr. Munier on his reasons, I think PROMETHEE is one of the most appropriate methods in many situations. My reasons are related to normalization, rank reversal, real life reflection and the ranking characteristic it produces.

NM- I have always maintain since my far away student days that PROMETHEE is one of the best methods in MCDM.

It has many good properties such as the selection of alternatives is done based on reliable data and using statistical curves. There is the need for reasoning and experience, which is very valuable and it is one of the very few methods that allows for a rational result analysis using the GAIA procedure.

In addition, again, it is one of the very few methods incorporating resources. Therefore, as you can see, I am a defender of the method, because in my opinion, it is really very good.

MB- As I said, its connection to real life is definitely stronger. There doesn't seem to be a rank reversal issue. Normalization doesn't affect it because it doesn't need it.

NM- Yes, it is stronger than others, but this is not enough. I can enumerate a list of real-life situations that it can’t model, the same as the others MCDM methods. Some are:

1- According to some researchers, that prove it with examples, PROMETHEE can generate RR, but I have not experience on that regard. I also believe that in mathematics we can't say that it produces RR only in a few cases. In my opinion, it does or it doesn't.

2. It does mot give any guidelines regarding the weighting of criteria

3. It can’t model aspects such as relationships between alternatives, like precedence.

4. For sensitivity analysis it uses criteria weights that are not adequate for alternatives evaluation

5. In my understanding it can’t treat multiple scenarios

However, since its publication in 1982 it has been enhanced with five versions that address different situations

MB- An important feature is that the alternatives maintain their superiority by making pairwise comparisons. There is almost no RR, and moreover, normalization cannot distort the ranking results it produces. It provides this with the preference function it uses.

NM- I really don’t understand your first sentence. When alternatives maintain their superiority?

MB-There is one more point I agree with Mr. Munier here: Limitation! Yes, many MCDM methods have limitations and they show this by their assumptions, thresholds, or preference functions. Situations that require DM intervention are also a separate problem because each DM sets its own threshold value, normalization type, weight type, data format, and MCDM type. Therefore, we assume that we use the same decision matrix and weighting type when comparing MCMD methods. In addition, methods with minimal DM intervention should be compared as much as possible, in my humble opinion.

NM- I agree

MB-Since different threshold values ​​can be used in each study and different DM interventions may be in question, I think DM intervention, that is, DM subjectivity should be minimized. Otherwise, we would be comparing apples and pears.

NM- I have been saying during years in international conferences, and also published in papers and books, that the main reason for discrepancy between MCDM methods is subjectivity. However, it is necessary.

This is not a contradiction of mine. Subjectivity must not be used to alter or modify original data as all methods do.

It has to be used when a completely objective result has been obtained. There is where we need the opinion, the know-how, the experience of the DM, who can even alter the ranking, because he/she has solid grounds to do it, and even reject the result

Mis metodos favoritos son AHP y FAHP pero desarrollados por mi en excel.

Estimado Christian

Naturalmente, cada investigador puede tener preferencias por algun método en MCDM, por su facilidad, atractividad, posibilidad en representar complejos scenarios, o por cualquier otro motivo

Sin embargo, hay que tener en cuenta que estos métodos no son de aplicacion universal, es decir, normalmente, un método no puede ser aplicado a cualquier escenario. Un escenario puede tener demandas que no pueden ser satisfechas por cualquier método.

Por ejemplo, yo diría que para problemas personales o de selection de personal para una compañía, AHP es uno de los mejores métodos. y tiene sus razones para ello

Sin embargo este método es inaplicable a problemas complejos y que normalmente involucran a mucha gente, y tambien hay multiples razones para comprender este aspecto negativo.

Por consiguiente, en mi modesta opinion, no podemos hablar de preferencias sobre mas de 100 métodos, aunque si entre metodologías similares tales com ELECTRE y PROMETHEE o entre TOPSIS y VIKOR

I think the best method is one that can both calculate weights and rankings like AHP, ANP, SECA.

Dear Faith

AHP and ANP do NOT compute criteria weights; they INVENT them, by intuition, and then, without ANY mathematical support. This is not only my humble opinion, but of many researchers since decades.

Methods such as Entropy and Standard Deviation DO compute them, based on each criterion properties or attributions. These are mathematical supported methods, where there is no room for inventions, and thus, for a certain problem the weights are always the same, independently of the DM wishes

Just think: It is reasonable that the importance of a criterion relies on the opinión of one person, or even in that from

the average of a group of DMs?

What happens if another DM or another group think differently?

SECA or Simultaneous Evaluation of Criteria and Alternatives, evaluates each criterion using statistics, based in its standard deviation, and this is correct, similar to entropy

Then evaluates each pair of criteria using correlation, which is also correct, although I don’t understand why, since the relative importance of criterion was already computed before.

That is, by using statistics considering all the values of each criterion, the relative importance for ranking criteria between criteria is also determined, since the most important criterion is which has the largest dispersion of alternatives values or lower entropy, which allows for ranking criteria according to its importance for evaluate alternatives, based on Shannon Theorem.

This procedure is completely alien in AHP and ANP, which, by the way don’t determine weights, but trade-offs

Bonjour,

la meilleure méthode dépend de la problématique posée, de la disponibilité et de la qualité des données à utiliser. donc "pas de meilleure méthodes" plutôt des méthodes les plus utilisées essentiellement pour des raisons logistiques.

Dear Lasaad

I agree that the best method may depend of the problem posed.

I don't think that it depends on the quality of the data since it is assumed that it is equal for all methods or for logistic reasons. I don't see the connection with the latter

In my opinion, the best method is which can model a scenario the best, and solve it.

In elemental scenarios normally any method is good, but when the scenarios are complex very few methods can model them.

For instance, in scenarios which performance values are expressed in binary format, or when there are relations between the different alternatives.

Dear Nolberto Munier

I respect your point, but I can't entirely agree with it. Why? You said that in elemental scenarios, normally, any method is suitable. However, in reality, one set of alternatives should give one order ranking. When you use some MCDA methods, then you get very frequently different orders of ranking.

Best Regards WS

Dear Wojcieh

What you say is true and very well known

What I meant is that any method can be used in elemental problems, because all methods have well developed algorithms, although there are exceptions.

Any of these methods can give a solution, but it does not mean that the ranking given by Promethee is better for instance, that a solution given by TOPSIS. Perhaps it is, or vice versa, but there is no way to demonstrate it.

Even if the algorithms are based on the same mathematics, the fact that each method applies weights, assumptions, preferences, thresholds, etc., forcefully leads to different rankings. I am quite sure that if all methods use original data without modifying them with subjectivity, all results should be very similar.

I have been saying this for decades. Trouble is that all methods, with exemption of Linear Programming and SIMUS, introduce some kind of personal preferences. No wonder the, that rankings are different.

MCDM is not and exact science, as it has a subjective component, however, if we work with actual values without any modification, the result is exact. The subjective component is at the end, once the theoretical result is known, because we can't take it at its face value, and then, the opinion, experience, and knowhow of the DM is paramount

Well, this is at least, my point of view.

Dear @Nolberto

Well, unfortunately, our points of view diverge. There is a way to verify. It's simulation studies—the need for research with reference rankings. Unfortunately, many decision problems are non-linear, so the methods you point out cannot do well and often suffer from rank reversal paradox (the simple linear methods).

Dear Wojcieh

Thank you for your answer

Sorry, but I don't understand what you mean by saying that there is a way to verify.

To verify what? Could you please explain?

By the way, there has been simulation studies about this, but unfortunately, as far as I know, they reveled nothing.

It is true than many decision problems are not linear, however they can be solved using non-lineal procedures which are included in software such as Solver.

Of course, in these cases, the shadow price is equivalent to the Lagrange multiplier, and then, the solution is only valid for one point.

The methods that I suggest are NOT subject to RR and I can prove it.

The reason is their algebraic structure, where selected alternatives are chosen following the cost of opportunity concept, and then each alternative is analyzed independently from the others; consequently, a new alternative is selected considering its own contribution to the objective function, and in so doing this selection in no way alters or modify the prior ranking

I have made 66 tests using three different examples, with all kinds of deletion or addition of alternatives, even considering more than one alternative at the same time and including pairs of identical alternatives. Remember that the latter is considered the most probable cause of RR

If you want I can send you a copy of these 66 tests, using SIMUS, with the simple linear model, and which there is not a single one with RR

GRA. I think it is effective in employee selection.

I used (fuzzy) AHP, or (fuzzy) ANP to evaluate the weights of criteria and then rank the alternatives by using (fuzzy)TOPSIS/VIKOR/WASPAS.

Because AHP/ANP is too subjective and it's hard to obtain the consistency with large number of criteria. Hence, I might try Entropy in this stage.

As per my knowledge, present MCDM methods do not represent the reality. It is universally true that no method and nobody can assert that a right and reliable result has been attained. But we need modelling a real scenario trying to replicate as close as possible all its features, and this is not done actually. As per my perception To get precise results is based on a) Assuming that the selected method is mathematical sound, and by considering that most of all scenario requirements, characteristics and issues have been plugged in the mathematical modelling.

Dear kumar

UK- As per my knowledge, present MCDM methods do not represent the reality.

NM -Absolutely true

UK - It is universally true that no method and nobody can assert that a right and reliable result has been attained.

NM- Absolutely true

UK- But we need modelling a real scenario trying to replicate as close as possible all its features, and this is not done actually.

NM - Absolutely true, and the problem is that it appears that developers, UNTIL NOW, have developed methods that indeed are far to represent reality, even approximately. Just think: How many methods consider resources? All methods assume that all scenarios are feasible, and then 'select' an alternative that is unfeasible?

UK - As per my perception To get precise results is based on a) Assuming that the selected method is mathematical sound, and by considering that most of all scenario requirements, characteristics and issues have been plugged in the mathematical modelling.

NM- In my opinion most methods are mathematically sound, with the exception of AHP and ANP, based on personal perceptions, that don't have any link with the real world, and most, if not all methods, are unable to conform a realistic modelling

Thank you very much for you clear, concise and valuable interpretation of actual methods

Dear Thanh

First of all, and according to their creator, Dr. Thomas Saaty, it does not have sense using fuzzy in these two methods, because they are already fuzzy in their conception

Second: AHP and ANP evaluate criteria trade-offs, NOT WEIGHTS, and from a personal point of view, and then arbitrarily assign a value to that evaluation.

What is curious is that 'evaluation' is abstract, since they do not take into account the alternatives these criteria have to evaluate. This is certainly strange, because the purpose of any MCDM the method is to evaluate alternatives

Your second paragraph makes a lot of sense, because entropy derived weights really represent the relative importance of each criterion to evaluation.

Just remember not using the entropy (s)value by itself, but its complement (d) to 1, because if you do, you will be doing exactly the opposite. Remember that the higher the entropy the lower the information you get from each criterion, thus, use d=1-s

Dear Nolberto,

techniques such as Entropy, CRITIC, SD, StatVar are used as objective weighting criteria. Of these methods, Entropy does not accept negative values ​​and other methods apply normalization procedures. What I'm wondering is how accurate or appropriate are the normalization techniques these objective criteria use? Because this affects the results. On the other hand, apart from the objective weighting methods we mentioned, do you know any other methods? Thanks

Dear Mahmut

Entropy also applies normalization by dividing each value by the sum of them all.

If not, it would be impossible to determine the probability of each event

I don't know about the effectiveness of normalization for other methods

As I understand, there are other types of weights as those derived by the multiple attribute utility theory or by statistics, or by LP. As I believe, the latter takes criteria as alternatives and determines their scores, that are then considered as weights.

Curiously, in so doing LP does not use any type of weights, and the importance of criteria is determined by solving the transpose of the original problem, called thee 'dual', which generates marginal values for criteria, that are thus considered as 'weights'.

I have explained several times how LP and SIMUS can work without criteria weights.

Interesting. I agree with @Wojciech Sałabun

Respected Dr. Nolberto Munier Sir,

Thank you so much sir for you appreciation on my Interpretations about MCDM techniques . You said that "In my opinion most methods are mathematically sound" . But as per my knowledge some of them still have a scope to modified or enhance Mathematical modelling. For Example we could replace Fuzzy concept ( Fuzzy-AHP, Fuzzy Topsis etc) by beautiful and promising Rough set theory. I am working on it and I need your valuable guidance.

Dear Udaykumar

Thank you sir for your comments

I am not sure I understand your second paragraph, but in my humble opinion no MCDM can fully model a scenario, because they don't have the capacity to mathematically interpret all the characteristics of the scenario. They are no more than simplifications or approximations, in lesser or greater degree, of a problem, and perhaps never will.

You talk about fuzzy applied to several methods, which without a doubt, improves reliability, but that do nothing to interpret reality

I am not proficient in Rough Theory, and therefore my opinion would be useless, however, I understand that tuples, as least in Python, are unchangeable and ordered, and I doubt that said conditions are present in real problems.

But if you need upper and lower approximations, I don't know if for a given class you can define them without ambiguity.

If you need exact lower and upper values, Linear Programming can do that beautifully. Y suggest reading Svetla Stoilova paper recently published in RG on fuzzy systems entitled - 'Fuzzy-SIMUS Multicriteria decision-making method. An application in railway passenger transport planning'

If you read it, please let me know your opinion

Respected Dr @Nolberto

Sir, as I said earlier that Present MCDM methods do not represent the reality and I agreed with it. I want to say that we should try and have a scope to develop enhanced Mathematical model in which real scenarios will be trying to replicate as close as possible all its features.

Sir , Thank you for sharing Svetla Stoilova's paper name. Surely I will go through it.

Respected Dr. Nolberto Sir,

Sorry Sir, before typing "Sir" after your name, I posted earlier msg.

Dear Udaykumar

I adhere a100% to your comments about developing an enhanced mathematical model

As I said, for decades we are trying to improve data without considering that that effort is wasted if it does not apply to representative modelling of the scenario

There is nothing like the best MCDM model. Every MCDM has its advantages and disadvantages. Depending upon the situation, the researchers choose the model or models. But I personally prefer fuzzy MCDM models.

Dear Sukanta

It looks that we continue working on details without considering the whole problem.

What is the advantage, the logic, of improving data, using fuzzy or other techniques, if the methods can't reproduce not even by approximation, a real scenario?

The results are most probably inexact since the methods can't consider all the characteristics of the problem.

Solving a problem in MCDM is not a matter of building an initial matrix with part of data from characteristics of a project, but trying to build a matrix that reflexes as much as possible the real thing. In our days, the practitioner knows about that, but since the methods don't allow him/her to imput them, well, they are just happily ignored

We have to improve the capacity of our MCDM methods to consider at least a large part of those characteristics, that is, we have the improve the modeling.

Dear Mubashar

TOPSIS is convenient according to your sentence.

And it is really a very good method, as there are others such PROMETHEE, ELECTRE or SIMUS

Why do you single one method?

Hi,

I agree with @Nolberto. In my opinion, the best results can be obtained by using few MCDA methods and then looking for compromise. The list of Norberto should be extended. SPOTIS and COMET methods are valuable too, e.g., both are free of rank reversals phenomenon and available in my team's python library pymcmd (for details, please see: https://gitlab.com/shekhand/mcda or https://pypi.org/project/pymcdm/).

Best regards WS

Dear Mahmut

Obviously, you want to go deep into MCDM, and that is very good.

The adjective ‘equivalent’ according to the Merriam-Webster Dictionary, has diverse meanings, to which of them are you referring? Apparently, for you, all methods are equivalent because they don’t produce the same rankings. It appears to mean that two things are equivalent by not producing the desired effect, like a string of failures.

In my humble opinion, none of the following definitions apply.

a- equal in force, amount, or value

b- having the same solution set

c-capable of being placed in one-to-one correspondence

d- related by an equivalence relation

If for you, all methods are equivalent in their goal to make the best selection, I agree, but, in general, they are not equivalent in their algorithms. SAW has nothing to do with AHP, or with ELECTRE, or with TOPSIS.

They don’t produce the same rankings simply because they used subjectivity in different forms.

AHP, selecting weights by intuition

PROMETHEE, selecting thresholds and functions according to the DM, and something similar happens with ELECTRE

TOPSIS selects subjectively the type of distance

BWM, subjectively determines which is the best and the worse criterion, and so on.

Even if you use the same set of weights, results are normally different. Why? Because they multiply them to different entities

AHP and ANP apply them to ratios

PROMETHEE to differences

TOPSIS to criteria, etc.

It is natural that applied to the same problem the rankings will be different, because the algorithms don’t follow a mathematical procedure, and lead to the absurdity that a problem, solved by the same method, may give different results depending on WHO is the DM. What is the solution?

Simply, work only with objectivity, and apply the DM subjectivity, expertise, and know-how, even preferences, on a solid objective result

In my opinion, there are not two PROMETHEE methods but five different procedures that give different results.

I don’t understand why you compare it with SAW; obviously, they are totally different

I disagree with your comment that ‘The advantages or disadvantages of the methods are understood according to the results or scenario’. Why can you assert that, when you don’t know which the ‘true’ result is? If we knew it, all these discussions would be irrelevant.

However, you can select methods according to their advantages and disadvantages in modeling correctly the problem in the initial decision matrixcxx.

Unfortunately, ALL MCDM methods, with the sole exception of PROMETHEE and Linear Programming, that allow for the use of resources, can model correctly.

However, by representing as close as possible a scenario, there is only one method: Linear Programming

I agree with the last part of your last sentence. We are never sure; in fact, the only thing certain is uncertainty

Dear Mahmut

This answer corresponds to a former comment of yours

Dear Mahmut

I don’t believe that it is difficult. I have modelled and solved more that 300 /400 MCDM problems, and the only prtoblem that I couln’t solve using MCDM is Supply Chain, albeit I believe that it is possible. In addition, you know that there are thousands of problems solved by different practitioners. Sorry, I don’t share your theory.

Regarding to solve manually, yes for trivial problems; have yo tried to solve by hand a problem with 15 alternatives and 33 criteria? Of course it can be done, and I did, but on top of being very prone to errors, you get tired, and then, all attempt to be precise is normally lost.

You propose an alternative, one of the more t han 100 methods, but I ask you. On what grounds you say than TOPSIS, PROMETHEE or VIKOR are the best? I share your opinion, but I don’t dare to say that they are the best

As far as my understanting you can’t incorporate AI in MCDM because you don’t have the necessary data base for that task.

PROMETHEE is certainly better than SAW, because the first in based on rationality and since it admits resources, as well as maximums and minimums

You answer your own question; there are more that 100 methods because SAW is very elemental and simple, to address complex scenarios.

Thank you Wojcieh for your support

SIMUS is written in Visual Basic, and I wonder if you would be interested in writing it in Python

Please let me know your answer

Dear Mahmut

In my opinion, yes, you can realize if a method is capable or not capable for a certain scenario

As an example, if the method does not consider resources, it is non-realistic, and probably not very effective.

Yes, there could be two opposite methods in complexity that give the same result, and what does it prove?

It could be because the case es very simple and the complex method can solve it using only a part of its complexity.

Why don't you test the two of them in a complex scenario?

What do you mean by 'capacity' and ‘capability’ of MCDM outputs?

Yes, is the results are coincident in the best selection, and in the ranking, we can say that they are equivalents.

Unfortunately, I don't speak your language but I found that said word has two meanings:

'Respected and highly respected. And also means ‘Early born baby girl'.

P{lease explain you mentioning it in relation to MCDM

In my opinion, the important thing is not the results, but the ways, premises, conditions, and assumptions of how it was obtained