As we know that AHP and TOPSIS both are multicriteria decision maing methods. many times I found that these methods used for same kind of problems. Even people applied the combination of AHP and TOPSIS for many selection problems. I want to know that: What are the basic and technical diferences between AHP and TOPSIS? Can we use AHP and TOPSIS saperatly for same problem?
Please suggest me.
Dear Saty
Regarding your question AHP and TOPSIS are methods based on different concepts. AHP is based on weighted aggregation and its criteria and alternatives weights are obtained by pair-wise comparison and DM preferences.
It starts with ordering hierarchically the objective, then criteria and lastly the alternatives
TOPSIS is based on distance. That is, it is assumed that there is an ideal and non-ideal solution. The method works aiming at finding the shortest distance to the positive ideal solution and the farthest distance to the ideal negative solution. It is based in Linear Programming.
TOPSIS can work with criteria weights or without them. In the first case, weights are normally obtained using the first stage of AHP that determines subjective criteria weights. These weights can also be objective (that is , no depending on the DM but on the data inputted), when are obtained by other processes such as entropy.
When TOPSIS uses AHP weights it is known as AHP/TOPSIS.
Both methods can be used independently for different types of problems. However, many researchers consider that TOPSIS, because its clear and mathematically sound structure is preferred over AHP which mathematical structure has been, and is very criticized, however, AHP is by far the most used method.
Dear resercher,
The both methods are built on a different principle. AHP method use hierarchical principle, TOPSIS method use distance principle. Using AHP method you can determine the criteria weights and rank the alternatives. In AHP method is used pairwise comparison between criteria and pairwise comparison between alternatives for each criterion by applying Saaty’s scale A rating scale (Saaty’s scale ) and an index of consistency (CI index) of expert assessments are used in AHP method. The consistency index allows to assess and correct the expert responses. This is also the positive of this method. In TOPSIS method you can set criteria weights, after that to determine the rating of alternatives. The positive of TOPSIS method is that the type of optimization is set for each of criteria (max or min). This is not done with the APP method. For TOPSIS method is should to set the criteria values for each of the alternatives. For AHP method the criteria values are not set (are not necessary). In AHP method you may have the criteria values for each of the alternatives but this is not set when using the method.The alternatives are evaluated using Saaty’s scale. The combination of both methods is a good solution because on the one hand you define the criteria weights and you use a consistency index using AHP method and on the other hand you set the criteria values and the type of optimization by TOPSIS method. This reduces subjectivity when decision making. In addition in both methods, you need to make sensitivity analysis when making a decision, i.e. at what interval of criteria changes the optimal solution is retained.
Dear Saty
In my case, I used a combination of the two multicriteria analysis methods: AHP (Analytic Hierarchy Process) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). The model is based on the AHP method to determine the weights for the sets of selected elements. The TOPSIS method was used to obtain the final ranking of the alternative closest to the ideal solution.
Dear Saty:
Any decision making tools has advantages and drawbacks. When we choose to select one of them or to combine some we are assuming some guiding principles.
I am a strongly believer in AHP as a useful tool. In my opinion it is its usefulness that drives it's popularity. I also believe that AHP has enough but controversial mathematical development to support it's use and in consequence I recommend to use it as an AHP supporter.
I am also an admirer of Nolberto juice and arguments then my answer is not pretended as a denial of his. But in his line of argumentation it is not rational to mix AHP/TOPSIS because the hybridization will suffer the same drawbacks of stand alone AHP.
The open questions to reflect on when choosing TOPSIS are: (1) How could any one set valid weights in using it? and (2) On what base we qualifies one of the solutions at hands as ideal positive/negative?
In summary as an advice for a young researcher choose any one of them (including hybridization) by means of accepting their guiding principles and prepare your self to epistemic justify your compromise without ignore the drawbacks associated.
Best wishes,
Manuel
Dear Svetla
SS . The both methods are built on a different principle. AHP method use hierarchical principle, TOPSIS method use distance principle. Using AHP method you can determine the criteria weights and rank the alternatives. In AHP method is used pairwise comparison between criteria and pairwise comparison between alternatives for each criterion by applying Saaty’s scale A rating scale (Saaty’s scale ) and an index of consistency (CI index) of expert assessments are used in AHP method. The consistency index allows to assess and correct the expert responses. This is also the positive of this method.
NM. Excellent summary of the AHP method. However, I disagree on your last paragraph (bolded). I don’t think that you can say that it is a positive aspect of AHP.
Quite the opposite, what the DM is doing is correcting his/her own assessment based on what a formula tells him/her (which I would say is not very orthodox!)
The correction indeed maybe small but also maybe large. For instance, if the DM assigned 6 to A over B, in his best, honest and supposedly knowledgeable preference, and then has to change to 4, he is modifying his judgement in more than 33%. The problem is that if he has to discuss it with his colleagues, he has not solid arguments to justify his preferences, or maybe he has, but then the CI >0.1.In other words he has to accept what a formula says. What about if he is right and really there is no transitivity?
However, in my opinion all of this is maybe rather useless, because it is supposed that the DM has to mimic reality as close as possible, and there is nothing on that in this procedure.
Instead, the DM is creating some sort of universe of his own which is probably detached from the true universe. I base this assertion in the fact that HE IS LOOKING FOR TRANSITIVITY, when normally, the universe that he is trying to replicate is NOT TRANSITIVE.
SS. In TOPSIS method you can set criteria weights, after that to determine the rating of alternatives. The positive of TOPSIS method is that the type of optimization is set for each of criteria (max or min). This is not done with the APP method.
NM. I agree with you, and this is serious because you probably will never know what was in the mind of the DM. For instance in a maximization criterion as benefits, it can be said that the higher the better, which is the opposite in a minimization criterion such as cost, where naturally the lower the better. No wonder that in AHP he has first to have everything maximized!
SS. For TOPSIS method is should to set the criteria values for each of the alternatives. For AHP method the criteria values are not set (are not necessary.
NM. No, it is not necessary in AHP because values are invented. I may agree with subjective preferences when dealing with qualitative criteria, but not when dealing with quantitative criteria. If you have fixed and homologated prices from a vendor related to different equipment, which is the purpose of the DM preferences? Where is the rational of this?
His preferences will express reality more accurately that reliable data?
SS. In AHP method you may have the criteria values for each of the alternatives but this is not set when using the method.The alternatives are evaluated using Saaty’s scale. The combination of both methods is a good solution because on the one hand you define the criteria weights and you use a consistency index using AHP method and on the other hand you set the criteria values and the type of optimization by TOPSIS method. This reduces subjectivity when decision making. In addition in both methods,
NM. In my opinion it is too optimistic to say that you reduce subjectivity using AHP derived weights and applied to TOPSIS, since there is nothing more subjective than DM preferences. What about another DM preferences for the same problem? This fact puts in evidence the weakness of using pair-wise comparisons.
SS. You need to make sensitivity analysis when making a decision, i.e. at what interval of criteria changes the optimal solution is retained.
NM. Of course you need to perform sensitivity analysis, but based on what? On the variation of subjective weights that do not have any relationship with their quality to evaluate alternatives as it is done at present?
If you use OBJECTIVE criteria weights for instance from entropy, then you can use those weights for sensitivity analysis since they represent the relative criteria importance based on their capacity to evaluate alternatives.
Svetla, if you think that I am wrong, please tell me it without 'anesthesia', I am not the owner of the truth and I am not a mathematician either. I am only using common sense and reasoning
Dear Prof. Munier,
I have read and taught from many you books which I have great respect. In my response to the researcher, I only give separate elements to compare the two methods according to their methodology. I approve the SIMUS Method. I am honored for you answered.
Yours sincerely,
Svetla
Dear Professor Svetla
Thank you so much for your answer.
It is a pleasure for me to debate on this subject with a scholar of your experience and knowledge.
I am pleased you like SIMUS, and since you know it, I will very much appreciate your judgement about the method. I can send you, if you wish, the last version, v.3.13, which includes IOSA (Input-Output Sensisitivity Analysis).
Sharing link,
http://ieeexplore.ieee.org/document/7479937/
Regards!
Dear Dev,
AHP and TOPSIS are two MCDM methods as you have said. Say for example there are 10 students and you have to select the best student among them on the basis of 5 criteria. What AHP does is that it takes 2 students at a time and compare their criteria one by one which is called comparison matrix. By doing so AHP finds out the best among the 10 students. Total no of combination becomes 10C2 = 55 i.e. you have to make a total of 55 comparison matrix. The criteria also need some weightage because each criteria shall not contribute equally in choosing the best student. Hence a comparison matrix of the criteria is also needed. As a result a total of 56 comparison matrix is created which is a lengthy process. If in case, there are 60 students in the class, the no of comparison matrices would become (60C2 + 1). Moreover of the lengthy calculation there is one more problem in AHP is selecting of decision makers.
In case of TOPSIS, all the students will be taken at a time as alternatives and they would be given score on the basis of the criteria which is called the decision matrix. By using TOPSIS method, from the decision matrix we can find out the best alternative. The calculation part is lessen as we can compute the best alternative from the decision matrix. But one problem encountered in TOPSIS or other MCDM method is computation of the weightage of the criteria. This problem is tackled by various ways like AHP, cross-entropy, fuzzy preference programming etc etc. As I have already mentioned in the first para that we can compute the weightage of the criteria by forming a comparison matrix for the criteria and following the steps of AHP.
As per the second part of your question, we can use the two method separately for the same problem but again in TOPSIS for criteria weight computation we have to depend on AHP. We can use some other methods for weight computation but as we have already computed the criteria weights by AHP so, it is useless to go for some other method once again for the same step.
For more you can go through the links:
Conference Paper A Hybrid Approach of AHP-Cross Entropy Model to Select Beari...
Conference Paper Entropy based MCDM approach for Selection of material
Chapter A Holistic-Based Multi-Criterion Decision-Making Approach fo...
Conference Paper Developing a Decision Making Model Using Interval Valued Int...
Article Decision Maker Priority Index and Degree of Vagueness Couple...
Dear Saty
I read with interest the explanation given by Syed, and I think that he put very clearly the differences bentween AHP and TOPSIS, and also informed you about their combination as a hybrid method, something that is normally done. His reasoning coincide with mine
I would like to emphasize the last paragraph from Syad as extremelly important. If you want to compare results between AHP and TOPSIS, but using AHP, you will get a biased result since you are inroducing in TOPSIS a partial solution already found by AHP
I would suggest you to solve your problem using AHP and then use TOPSIS using weights from entropy, that does not belong to any method, or by statistics.
Dear Prof Munier
I am honored that a researcher of your calibre has acknowledged my answer. Could you please share the link for downloading the latest version of SIMUS. I shall remain ever grateful for your help.
Thanking you
With regards
Syed Abou Iltaf HUssain
Dear Svetla
Thank you for your interest on my paper on sensitivity analysis
In the Valencia Polytechnic University we have been studying that subject dor a while because we understand that the way it is performed nowadays does not give any useful information
We will be honoured in sharing our findings with you your colleagues . These materialized in the IOSA (Input-Ouput Sensitivity Analysis) that is the lasted addition to SIMUS and incoporated in the software version I sent you. Our infomatic is studying the problem you have in uploading it.
Anyway, if we can help you in your project or if for some reason or another you will not be able to upload SIMUS we will be happy to load in our domputers and solve it, if you send us the decision matrix. In that case we don't need to know neither the projects nor the criteria, only the decision matrix.
Another aspects that we are working right now is in suggesting new procedures for MCDM, since we believe that actual methods, whatever they might be, don't reflect reality. We can help in that issue too and again will be happy in sharing our finfings
Dear Syed
Give me you email address so I can send SIMUS, cause I can't do that in this platfom
Dear Saty
From my side your are most welcome and I believe that this recflect the opinion of many people.
I also believe that RG spirit is to connect people interested in technical issues, and that can use it as a gigantic encyclopaedia where there is always somebody able to help and collaborate the best she/he can, without any further interest
However, I believe it is a two-ways road ,because at least from my point of view, I feel enriched with the questions posed, since some of them deal on aspects that perhaps never were in my mind
Syed Abou Iltaf Hussain Good evening, please I have a quick question, is it possible to calculate the weight of criteria by using AHP, and in a second step used this weight in the application of TPSIS. thank you
Dear Amina
Yes, that is normally done, however, in so doing you are inputting in a very good and rational method as TOPSIS, subjective weights, that depend on the intuition of one person. If another person or DM thinks differently, you will have different weights and probably different result from TOPSIS
If l may, I would suggest using objective weights from entropy, something very easy to do, if you have the data for your matrix. If you need information about how to compute entropic weights, I will be glad to help.
Nolberto Munier
Dear Munier
In the case of our research we must have the opinion of experts to generate weights and classify elements generated by our conceptual framework, to operationalize them, hence my choice of AHP, which implies subjectivity. But if I correctly understood entropy is also a method that can also generate weight, but on what basis? Expert opinion? The data collection is made from what support? I would be very grateful if you could suggest me some literature on the method, or how to calculate the weight with entropy.
Thank you
Dear Amina
All MCDM methods, except AHP, start from an initial decision matrix with objective and subjective values.
Each criterion has thus a series of data according to the alternatives. That is all you need for getting significant and useful weights using entropy.
AHP generates trade-offs, NOT weights. Thus, they are useless to evaluate alternatives, simply because they are |NOT connected to the real problem. They are a representation of what is in the DM mind.
Objective weights are based on Information Theory using the Shannon theorem, hand have the quality of being able to evaluate alternatives.
AHP trade-offs are only inventions, that may be useful only to the DM
The fact that the DM can't explain the reasons for his/her preference is enough to understand their utility
Many differences can be found, however, the main one is that criteria can be weighed subjectively using AHP. While the original version of TOPSIS is used for ranking alternatives/solutions only.
Amina
I don't know what your project is, but if you, for some reason MUST have the opinion of experts, that is fine.
However, why to complicate your life making pair-wise comparisons when what you need is the weight of each criterion?
Most projects have alternatives and criteria to evaluate them. You may have a mix of quantitative criteria as well as qualitative ones.
For the first, you may have reliable data since they normally refer to money, demands, percentages, prices, which are very well known
For the second you can have criteria such as 'Quality', 'Usefulness', 'Market penetration', etc.
For these subjective criteria why don't ask each expert to put a value on each criterion using a simple scale such as 2 (Bad), 4(Good), Very good (6) and Excellent ()?
'
Each expert assigns a number between 2 and 8 to a criterion such as 'Quality', another to criterion for 'Demand', for each alternative, and so on. No comparisons are needed.
Once you get several quality values for say 'Quality', find the arithmetic average or still better use the simple formula of the mean for beta distribution. Thus you have an average value for each criterion and each alternative. Once you have it you can find the entropy of each criterion, and its complement to 1 measures its importance.
But whys to use weights? There are MCDM methods that don't use them at all and instead compute the relative importance of each criteria using the data initially inputted
I will send you an example to compute entropy. It is really easy
Nolberto Munier Professor, I really appreciate your help and thank you in advance for the document.
With Gratitude
Dear Amina
AC- Thank you very much for your answers Mr., due to my background in urban and tourism studies, I don't master very well all the statistical and mathematical aspects, but I am doing my best to understand which method is the most suitable for my research, so please if it is possible to answer and enlighten me on the subject:
If I understand correctly, the weight of the criteria defined by entropy is generated in relation to the data we have on the alternatives? In this case we need to have alternatives, cases such as data on cities if we want to determine which city is the most touristy in relation to another.
NM - Yes, this is correct
AC- However, in my case study, there is no precise context, let me explain the situation, we have defined the elements that determine the tourist attractiveness of cities in a general manner, and we want to rank these elements in order of importance, in other words, order of influence, from the most influential to the least influential. That's why I think AHP is appropriate, because the primary objective is to rank the elements in a general context, not specific to a particular city.
NM- First of all you can’t use AHP because most aspects or criteria related with tourism are related among them such as roads, hotels and infrastructure. AHP demands that all criteria like these must be independent. Second, in my opinion, you are looking for characteristics that are site-specific, therefore these criteria are not to be used in any city or site
For instance, you don’t need any criterion for large cities such’s as Paris, London, Buenos Aires or Moscow, because they have everything, such as sight-seeing, entertainments, restaurants, cultural events and museums, all kinds of hotels, many routes and airports to reach them etc.
However, if you are analysing tourism sites there are differences.
There are those sites that have a unique feature and nothing else, like the Great Wall in China, the Grand Canyon in USA, or the Masada monument, in Israel. In these cases, there is only a one-day trip. Maybe you need a restaurant, sanitary facilities, but nothing else.
There are cities like Cairo where you have the pyramids, the many mosques, the market, the Nile, etc. where people stay a couple of days and then you need hotels, restaurants and transportation
There are sites where people just go to relax, but you need roads to access them, a market and a health-care centre.
There are sites like the Cancun beaches where people stay may be for weeks and that on top of the beaches, they offer scuba diving, sea bikes. Then you need many hotels, restaurants, bars, entertainment transportation, hospital, roads and airport, teachers, etc.
There are mountain places for skiing, of difficult access and where you need a strong infrastructure in hotels, sky lifts, restaurants, etc.
In all these examples the characteristics or criteria change, since you don’t need to consider access roads in Paris, or scuba-diving in the Great Wall
AC- The objective of this step is to produce a general, universal evaluation tool that determines the elements (criteria) of attractiveness and their weight, independently of a specific location. Given the objective, we do not have data on specific alternatives (cities in our country) to be able to apply the entropy, and thus weight the elements (criteria).
NM – I understand what you are aiming to, but in my humble opinion it is not real.
I agree on what you say about entropy.
AC- It is only in a second step that the choice of alternative this fact, to compare between cities we intend to apply the TOPSIS, to determine which alternative (city) is the most touristic and thus guide the choice of decision. Hence my question is whether we can use the weights generated in the first phase, for the application of TOPSIS, in a second phase where there are alternatives
NM – If you want to apply TOPSIS your need real values for each place. Where are you going to get them?
In my opinion, considering that different destinations need different criteria, the next step would be finding out what measures or projects you need to satisfy those criteria.
Again Amina, I am not an expert in tourism although long time ago I had a tourism agency, long time gone, and my observations were possible influenced by what people asked when there came to the agency.
If you think that I can help you, pls. don't hesitate in contacting me again
Dear Albhari
You are right, however AHP is also used to select alternatives.
In reality determining criteria weights is the first part of the method, and by using those weights it selects alternatives in a second step
However, in my opinion, the real difference is that AHP is a method where no rationality is used, only intuitions, while TOPSIS is rational and has a mathematical correct algorithm, while AHP is grounded on assumptions which are not based in any mathematical principle, except, in using the Eigen Value method for a reduced number of alternatives
AHP for weighting criteria ad topsis for ranking is a good combination
Maikel
AHP can be used for both purposes. In a first step in determines criteria weights, and in a second step it uses those weights to determine alternatives ranking
TOPSIS determines alternatives ranking either using AHP weights or those from entropy
The largest difference between AHP and TOPSIS is that the first is irrational, because reasoning is absent, and replaced by arbitrary preferences, while the second is rational, based in actual values and reasoning.
Dear Saty Dev
In my point of view, TOPSIS is used for ranking the alternatives based on the distance between the positive and negative ideal solution. The input data could come from real data or expert judgment. Meanwhile, AHP can be used for determining the subjective weight of criteria or ranking the alternatives in MCDM problems based on the pairwise comparison matrices from experts.
Attached for more references:
Article A Two-Stage Multiple Criteria Decision Making for Site Selec...
Article Assessing Renewable Energy Production Capabilities Using DEA...
Dear Thanh
If you don't have the performance values to build the initial matrix you can use AHP.
Its first stage, as you say, determines the subjective criteria weights.
In s second stage using pair-wise comparison of alternatives and the weights found in the first stage for criteria, you can build the ranking of alternatives.
TOPSIS instead, starts with a known decision matrix and can use AHP weights for criteria, from the AHP first stage, or use entropy derived objective weights, and also produce a ranking
Dear Nolberto Munier
Thank you for your sharing. Can I ask in case that some criteria are quantitative type, and others are qualitative type. What should we handle with this?
No problem at all with most MCDM methods. Usually, that is usually the case. In every problem normally there is a mix of both
Dear Nolberto Munier
It means we can use both real data and expert judgment in one integrated matrix. Thank you for your suggestion.
Yes, you are right, however, in my opinion, it depends on the problem. If the subjective data affects a large number of people, for instance, I prefer to use a survey to consult people, rather than the opinion of experts, since they can't replace what thousands of people want or wish, or how a project can benefit or harm them.
If you could tell me what your problem is, perhaps I can help you
Nolberto Munier I am just reading related papers and thinking about my future research. I will ask for help if any next time. Thank you so much, Prof.
Thanks, Nolberto, during the start of my analysis we met and you, discussed using TOPSIS anyway I have done my research using AHP and now comparing using TOPSIS all that you mentioned above is true of AHP and TOPSIS...TOPSIS ranking of alternatives is made easier using AHP where criteria weight has been determined considering both qualitative and quantitative data.
Welcome to all MCDA users
Thank you Abiola
The fact the AHP is easy, is true, as is also true that its weights are just a product of the DM's mind and moods. Another DM could have different values. Is thus rational to assume what DM1 say is true and DM2 false?
Is it rational to assume that the weights derived from the DM's mind can be applied without hesitation to real-life problems and assuming that they are transitive? Who said or demonsdtrated that? Surelly not Saaty or other researcher supporting AHP.
In addition, I remind you that AHP does not generate weights but trade-offs, that are completely different. Ther latter are good for making comparisons betweenn criteria, but not for evaluating alternatives
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