Multiple-Criteria Decision Analysis - Science topic

Akram

Could you explain what yo say?

Are you asserting that if you have say 10 criteria, it is enough computing the weights of only two of them?

And what wejghts do you assign to the other 8 criteria?

Difficult to understand.

I suggest 10.1016/j.ejor.2009.10.018.

I used it on http://www.podesenvolvimento.org.br/inicio/index.php?journal=podesenvolvimento&page=article&op=view&path%5B%5D=421, but it is in Portuguese.

There is no strict limitation on the number of experts required in a Fuzzy Delphi Method study. The number of experts you involve can vary based on several factors, including the complexity of the problem, the diversity of expertise needed, and the resources available. However, a common range is typically between 10 to 15 experts.

The goal is to have a sufficiently diverse and knowledgeable group of experts to provide valuable input and reach a consensus or convergence on the topic under study. Too few experts may lead to limited perspectives, while too many experts may make the process unwieldy. The key is to strike a balance that best suits the specific research question and objectives of the Delphi study.

No, a Pareto front produced by an evolutionary algorithm does not necessarily include both global and local optima. The Pareto front represents the set of non-dominated solutions in multi-objective optimization problems. These solutions are not dominated by any other solution in terms of all the objective functions simultaneously.

In a multi-objective optimization problem, there can be multiple optimal solutions, known as Pareto optimal solutions, that represent trade-offs between conflicting objectives. These solutions lie on the Pareto front and are considered efficient solutions because improving one objective would require sacrificing performance in another objective.

The Pareto front typically contains a mixture of global and local optima. Global optima are solutions that provide the best performance across all objectives in the entire search space. Local optima, on the other hand, are solutions that are optimal within a specific region of the search space but may not be globally optimal.

The evolutionary algorithm aims to explore the search space and find a diverse set of Pareto optimal solutions across the entire front, which may include both global and local optima. However, the algorithm's ability to discover global optima depends on its exploration and exploitation capabilities, the problem complexity, and the specific settings and parameters of the algorithm.

It's important to note that the distribution and representation of global and local optima on the Pareto front can vary depending on the problem and algorithm used. Analyzing the Pareto front and its solutions can provide valuable insights into the trade-offs and optimal solutions available in multi-objective optimization problems.

I agree with the idea of Wadie Abu Dahoud.

there are other normalization methods for the "nominal-is-better" case besides the normalization possible through grey relational analysis (GRA). Some commonly used normalization methods in MCDM for nominal scale data include:

Each normalization method has its advantages and disadvantages, and the choice of method will depend on the specific characteristics of the decision problem and the nature of the data.

Dear José de la Garza

I don’t think that AHP has a limit for alternatives, however, in your case, dealing with 350 alternatives involves a tremendous workload, and, if for whatever reasons and after you finish, you add or delete and alternative or a criterion, as ususually happens, you have to start all over again.

I would suggest not making pair-wise comparisons of criteria, but simply, the group may evaluate each criterion separately, and then finding the average. Consistency or lack of it, is a property of AHP, and in my opinion useless, since the DM may be forced to adjust something that he/she believed, and assuming that there must be transitivity with a 10 % of tolerance. And all of this trouble to gain what?

Nothing, because they can’t assume that the scenario in the real-world is transitive. Maybe it is, or may be not.

I believe that your group criteria is OK but short.

For instance, don’t you think that it is important a criterion that qualifies each supplier regarding compliance history in time and in quantities?

You can have a hint of it by researching the history of each supplier, and asking your competition. What about type and age of machinery? Are your potential suppliers metal foundries for Aluminium, Iron, Precision casting?) (I guess it since you talk about casting).

If it is so, it appears that in level 2 criteria, they may be related. For instance, I don’t think that you can address the manufacturing capability independently of product capacity and cost. A foundry with small capacity most probable will have higher production costs that a large one.

If this is the case, you are not allowed to use AHP, because in this method all criteria must be independent. This was specifically established by its creator, Dr. Thomas Saaty.

What I would suggest is computing weights independently and apply them to a decision matrix that responds to real issues, for instance production capacity in kgr/day, costs per unit, expertise, financial capacity, size of technical department, etc.

Once you have that you can applied methods like PROMETHEE, TOPSIS, ELECTRE,VIKOR, etc., to find the best supplier, or else a method that does not use weights, like SIMUS.

I hope it helps

I think these shall help you...regarding calculations of ELECTRE-III scheme..

The impact of overlapping drainage density and waterbodies in LULC (Land Use and Land Cover) in determining groundwater can be significant. Drainage density and waterbodies can impact the amount of runoff and infiltration, which ultimately affects the amount of groundwater available. For example, areas of high drainage density, such as urban areas, can lead to rapid runoff and less infiltration, resulting in less groundwater recharge. Similarly, waterbodies such as rivers, lakes, and wetlands can act as barriers to infiltration, reducing the amount of groundwater that can reach deeper aquifers. Therefore, careful consideration of LULC in the watershed can help to ensure adequate groundwater availability.

I'd stick with QGIS as it is 100% free. There are examples on Google about MCDA using QGIS, for example: (https://gis.stackexchange.com/questions/25976/performing-multicriteria-analysis-using-qgis). Generally speaking, it's a good practice to work with raster layers when performing MCDA.

Suggest reviewing this paper for MCDM methods:

Suggest reviewing this paper for MCDM methods:

There is nothing like the best suited MCDM method to be applied for any sustainable problem. Since it would appear that the selection of the technique was due to the authors' familiarity with it, rather than to the theoretical or practical reasons associated with the specifications of the problem situation, I would recommend explaining the strengths of TOPSIS, as Prof. Munier says.

Dear Marcos Antonio Alves

My book "Uses and Limitations of the AHP Method', Springer, addresses exactly what you are requesting.

In 130 pages you will find the comments and analysis of 105 researchers, including, of course, Saaty and his co-authors, Vargas and Harker

Dear Mahmut

Thank you for considering that I can answer your question.

However I don't have an answer because I don't know in detail the method our friend Thanh posed.

I already mentioned Thanh that it is improbable that after 0.5% the selected alternative holds, because most probable the intervening criteria are decreasing their Lambda as long as the Lambda of one criterion is changed, and then, their margins of variation are decreasing simultaneously, until a moment where the selected criterion ceases to be important for the best selection, and then, a new criterion is now responsible, and most probably producing a change on the initial ranking.

This can be clearly seen when the original straight line of a certain objective, changes to another straight line, but with a lower slope, corresponding to a lower marginal cost, and then originating a convex curve, which represents the utility curve

Trying to answer your specific question, and always according to my reasoning, it appears that it is not natural that the same procedure produces alternatives changes for lambda values below 05, which agrees with what I said above, and suddenly, from 0.5 > lambda< 1, it remains constant. I would check this

I am attaching the resulting curves produced by SIMUS/IOSA, published in one of my books, for solving a problem, where the best alternatives was subject to two criteria C3 and C5, and their simultaneous variation. The curve of the left is from increasing criteria C1 and C5 at the same time. That on the left is for decreasing.

Observe that the curve on the left shows a straight line and for a certain value changes forming a convex curve

This may be recommended: https://www.tandfonline.com/toc/tgis20/current

A free journal

Hello Lasantha Bandara . You may want to look at Colombo Metropolitan Area with regards to land-change intensity, gradient analysis and land-change modeling.

Good luck

Samarth Bhatia yes, you can do it in IDRISI TerrSet using land change modeler and IDRISI GIS analysis.

If I were the decision analyst working this problem and I had to choose between AHP or simple multi-attribute rating technique (SMART) I would choose smart because I can ensure it adheres to axiomatic decision analysis (which AHP does not) and I can use methods such as value focused thinking (VFT) and swing weight matrices to ensure that I am assessing the right objectives and applying weights to the objectives that adhere to the decision maker's preferences. Thus I can use SMART to better model the decision maker's preferences.

The wastes like chippings from blocks I use the to backfill trenches, and improving on the road.

Dear Delano

As far as I know you need the performance values for the alternatives in each criterion, and I believe that AHP is the only method that allows you to 'fabricate' those performances, which needless to say are fake, because they are only in the mind of the DM

In my opinion you need first to select the alternatives or suppliers.

Second, decide about the criteria for which they are subject to

Third, use statistics, or consult people in your same industry about their experience with these suppliers, and simple rank responses for each criterion and each alternative from 1 to 10.

Fourth, with this data complete use weights derived from entropy, and then you will have your decision matrix.

Fifth, use a MCDM method such as PROMETHEE, TOPSIS, VIKOR, ELECTRE, etc.

Your question helped me too. Thanks for asking here.

Hello Silvia! Thank you for indicating my software, and it can also solve Electre TRI problems. https://github.com/Valdecy/J-Electre

Dear Yuriy

100% close.

Please send me your email, I would like to send you the SIMUS software

Dear Sanchit Saran Agarwal , Here is the answer

A Bayesian network, Bayes network, belief network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.

An example of a Markov random field. Each edge represents dependency. In this example: A depends on B and D. B depends on A and D. D depends on A, B, and E. E depends on D and C. C depends on E.

In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be Markov random field if it satisfies Markov properties.

A Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it can't represent certain dependencies that a Bayesian network can (such as induced dependencies). The underlying graph of a Markov random field may be finite or infinite.

This would be of great help with only 13 pages http://www.cs.cmu.edu/~epxing/Class/10708-07/Slides/lecture3-BN&MRF.pdf

Alessandro is correct, however, I caution you on the use of AHP due to known issues with the methodology. Unfortunately APH does not follow the rules of axiomatic decision theory, and thus can result in inconsistent preferences and orders when options added or removed. I would recommend the use of multi-objective decision analysis either using utility or value depending on your preference.

Hi,

you definitely want to review this journal

https://onlinelibrary.wiley.com/page/journal/10991360/homepage/forauthors.html

B.R.,

Ari

You're right

I considered normalization of 1-E

It still makes result not good

It has slight difference between criteria

but when I calculate just entropy value (E)

and normalize this: E/sum(E)

result becomes dramatic and useful for research

Is this formula changeable? or unchangeable?

In my thought, I think I can change this formula because Shannon's entropy is just calculation of log.

I want to hear others' opinion

Dear Rafael,

I'm currently engaged with the same challenge in my hometown, Isfahan. Here, the problem is to provide an integrated CDW management plan to allow managers to track it from the very beginning (generation) to very end (final disposal). We did the following process. That might be hint for you as well:

- A wide literature review and studying experiences of other similar cities

- Doing a broad study regarding the current situation (statistics, dumping site conditions, illegal procedures, current key players, etc).

- Developing a modified process in Isfahan Municipality

- Developing a system to help managers monitor the process

-Approval of required bills in city council

- Running a pilot in selected regions of the city

- Organizing the dumping site

Considering the market situation for recycled aggregate products

- Enforcing regulations for using recycled aggregates in constructions where applicable

- Preparing the situation for establishing a CDW recycling plant (especially concrete wastes to recycled aggregates).

I hope this could be useful for you.

Hello Nolberto,

thank you for letting me know. I've sent you a mail with another adress.

Dear Fatih

It can never happen in LP or SIMUS. You can have in the decision matrix a mix of positive and negative values, you can even have all the values in the matrix being negative, but the result, if it exists, will also be positive

Why?

Because when the system of equations is solved you express the condition that the values of alternatives must be positive.

However, in the solution, you can have negative values for the criteria marginal values.

If you are maximizing a criterion, a negative marginal value means that increasing the criterion value will produce a decrease in the result and vice versa.

This is the information used for a rational sensitivity analysis

Dear Nouran,

You can find the answer in this paper:

https://www.mdpi.com/2073-8994/12/2/243

Best regards,

Sarbast

Dear colleague, You can easily use TOPSIS or any other MCDM methods to solve many research questions even in construction research. The main point here is that you should be able to establish a criterion/alternative matrix in accordance with the nature of MCDM in a research design. If this condition is met, you can conduct your research with MCDM methods.

Laura

I can send you the software of SIMUS, a MCDM model based in LP, as Goal Programming

Click on Multiple criteria decision analysis below your questions and you come to a place in RG where this question is discussed: https://www.researchgate.net/topic/Multiple-Criteria-Decision-Analysis

Dear Sir,

As per Saaty who formulated the AHP approach, Aggregating Individual Priorities is the best approach when compared to aggregating individual judgements. Since, the underlying concept of both SAW and AHP are the same, it's better to follow the former approach. The justifications are provided in the following papers:

Basak, I., & Saaty, T. (1993). Group decision making using the analytic hierarchy process. Mathematical and computer modelling, 17(4-5), 101-109.

Saaty, T. L. (2008). Decision making with the analytic hierarchy process. International journal of services sciences, 1(1), 83-98.

Srdevic, Z., Blagojevic, B., & Srdevic, B. (2011). AHP based group decision making in ranking loan applicants for purchasing irrigation equipment: a case study. Bulgarian Journal of Agricultural Science, 17(4), 531-543.

Basically, in AHP they advice to combine final priorities of each experts through Geometric Mean. Following this route will give the investigator a provision to even rank and prioritize the experts based on their competence and even by considering the inconsistencies in their initial judgments.

Hope the information helps.

-Vishnu

Many thanks for the question and responses. We have an easy-to-use MS Excel based program for 10 different MCDM methods such as TOPSIS. It is free of cost. Please contact me at chegpr@nus.edu.sg if you are interested to have this program.

Excellent answers

Once I was working on several variables and I wanted to weight them. At this time, people usually say that we'd better provide a questionnaire and then through AHP, ANP or other related methods define the weights for variables. That's quite common but how about the bias of the those who fill the questionnaire. Therefore, I looked for some other methods to weight variables based on the reality and I came across with Entropy. In fact, I weighted variables based on the each of these methods and then I compared the results. Entropy results were much closer to what is going on in real world.

Dear Ali,

Yes, it is the same model. Be careful about its properties though, mainly those of incomparability across attributes' units (e.g. adding "apples" and "oranges" - hence, normalization/standardization is probably needed, unless you are adding attributes of the same unit) or compensation between attributes (e.g. proportionate to the ratio of their weights).

You can have a look at Section 2.2.1 of this book (but also more or less any MCDA theory-related book) for more:

Triantaphyllou, E. (2000). Multi-criteria decision making methods. In Multi-criteria decision making methods: A comparative study (pp. 5-21). Springer, Boston, MA.

All the best,

Menelaos

Dear Alejandro

As far as I understand the eigen value method does not distribute weights amongst criteria. This is done when each weight is divided by their sum, that is, when eigen values are normalized

Reading the Saaty publication that you mention, he effectively mentions the ‘idealized priorities’. In reality I don’t know why he used that expression that apparently means ideal or relevant priorities. In fact that method consisted in dividing by the highest value, was suggested to Saaty by Belton and Gear in an attempt to cope with the rank reversal phenomenon, discovered by Belton and Stewart

Now, you say that idealized priorities are those used for ratings. May I remind you that all priorities are used for ratings?

Really I can’t understand what you say about that the lowest level of the hierarchy ratings could be high, medium or low. Compared to what? Are you talking that there could be that the differences in scores between the highest values and the lowest values is high, medium or low?

What is an ‘aggregated’ score? Are you talking about a composite indicator for environment, which is indeed a very reasonable objective?

Sorry, I don’t understand your explanation in the second paragraph. However, it appears that your reasoning goes against which is normally accepted in MCDM, that is, the larger the score the better, does not matter if you are maximizing or minimizing.

I agree that for certain criteria the are to be minimized, for instance risk, and if you use negative values, obviously, the higher negative the better. However, how can you to take that in consideration in AHP, as it was discussed not so long ago?

In MCDM methods, and as far as I know, the best is always considered the highest. In the case of risk apparently is does not have sense, however it does, because the highest score indicates the alternative, that all thinks considered has the best performance, including perhaps the lowest risk

As an analogy, say in the race track, it is aimed at running in a circuit and in the least time, and then the runner that do I, gets the higher marks

hello there

No, it should be less (or equal) to 1 and can't be above 1.

check all your calculations again, maybe you made a mistake somewhere.

Dear Benito

Very interesting question but which answer is not known yet, and probably never will.

In addition there is very unlikely that you can reach an optimal solution, because normally criteria are contradictory. How can you get an optimal solution when for instance a criterion calls for maximizing benefits while another calls for minimizing costs?

To solve this dichotomy researchers have developed different methods such as AHP, PROMETHEE, ELECTRE, TOPSIS, VIKOR, SIMUS and many others that do not reach an optimal solution but a compromise one.

This procedure aims at finding a result, not optimal, but that satisfies everybody, and this is what MCDM methods do.

In my modest opinion, the only way to assume that a solution is the best, not optimal, is when it derives from a well structured decision matrix that incorporates as much as possible aspects related with the problem under study.

Therefore, a matrix with interrelated and correlated criteria, with provisions for related alternatives, a matrix which incorporates resources and their limits, a matrix that contemplates qualitative and qualitative criteria in any mix and numbers, a matrix that considers that all projects may no start and finish at the same time, etc.

This is related with a method with a very strong participation of the DM, not by inventing preferences but with the capacity to analyze results.

I start to use http://www.diviz.org/.

Dear Lambart,

Ighravwe is right in his views.

Dear Pooya,

Please follow the links below.

Sánchez-Lozano, J. M., Teruel-Solano, J., Soto-Elvira, P. L., & García-Cascales, M. S. (2013). Geographical Information Systems (GIS) and Multi-Criteria Decision Making (MCDM) methods for the evaluation of solar farms locations: Case study in south-eastern Spain. Renewable and Sustainable Energy Reviews, 24, 544-556.

Chen, Y., Yu, J., & Khan, S. (2010). Spatial sensitivity analysis of multi-criteria weights in GIS-based land suitability evaluation. Environmental modelling & software, 25(12), 1582-1591.

Dear Ozcan

May be it is a problem in AHP but not in other methods.

Once yo place the performance values in the decision matrix there is no difference for the method

Regarding how to tackle this issue in AHP I have posed this question a couple of times.

Apparently the process is dismiss the quantitative criteria and consider all of them as qualitative, which in my opinion is absurd, because in so doing the DM is overriding reliable and certain information

Curiously non AHP defender responded to my queries

As I see there are researchers who need help on the VIKOR method steps, I have modified the file.

You can find an explanation of the method in the pdf file, as well as complete implementation process in the excel file.

Hope it is useful.

Thanks Adriana. Wondering the Vikor method (as with this article) uses the same direction as with compromise programming in its computational way?

Thanks!

1) Both of these methods belong to the same group of MADM methods, but they are based on different algorithms.

2) VIKOR as well as TOPSIS takes into consideration negative aspects of evaluation through R value (minimum individual regret) so this cannot be considered as difference.

But to answer (or not) to your question related to selection of more appropriate MADM method for problem solving. There is just no simple answer to that question, as it is raised so many times. You cannot say which method is better if they are yielding different results applied to the same problem, simply because you do not have a reference point for comparison of methods. The only thing that you can be sure about is that there are differences between methods. Generally speaking, the problem that you are solving is the one which will determine preferred method. In order to do so, you have to be familiar with different methods and their specificity.

So, I gave you a rather philosophic answer, certainly the one you did not hope for. But that is the reality.

Best luck in your work.

Greetings

My colleague thinks he will get a zero value because the VIKOR method is the best zero and the worst one.

I published research using Likert scale for AHP in DSS, it may help you in devolving your DSS research

Dear Fran

I have a complete (step by step) video tutorial about Susceptibility mapping and validation (success and prediction) using ArcGIS and Excel only. The comprehensive tutorials are on Udemy website.

- How to Produce Prediction Map in GIS With ArcGIS and Excel?, link: https://goo.gl/6c8A1H

- Prediction Maps & Validation using Logistic Regression & ROC, Link: https://goo.gl/y5EnLn

Happy learning!

Energy planning refers to providing sufficient power to human societies while at the same time underlies resource, economic environmental, social and technological constraints. The complexity of the task renders Multi-Criteria Decision Analysis (MCDA) techniques a useful tool in the decision process. MCDA techniques offer a transparent way of elaborating on decision problems which include many criteria and different Decision-Makers (DMs). This paper presents a multi-criteria decision analysis methodology and software for renewable energy applications. The software, (MCDA-RES) provides for a step-decomposition of the decision-making process:

Problem Identification & Initial Data Collection, Identification of Stakeholders,

Creation of Alternatives, Establishment of Criteria, Criteria Evaluation & Preference

Elicitation, Selection of the MCDA Technique, Model Application, and Stakeholders’

Analysis of the Results & Feedback. The applicability is illustrated through a real case-study for an island in Greece where the performance of alternatives on a set of different criteria and the preference of the DMs is assessed. The analysis showed that no group consensus could be directly established; still some alternatives performed better than others and a way towards a compromise solution could be revealed.

For academic use, you may download Visual PROMETHEE for free. http://www.promethee-gaia.net

Dear Victor,

Judging by your question, you possibly have a situation with ordered criteria: you are looking for a solution that is optimal with respect to the first criterion and amongst these solutions, you are looking for a solution that is optimal with respect to the second criterion.

If my description is valid, then the terminology question has the following answer. The above approach to solving multicriteria problems is called an ordered criteria approach or a lexicographic approach.

Please, be careful: you should guarantee that the found solution is really optimal with respect to the second criterion amongst all solutions that are optimal with respect to the first criterion. To guarantee this, you should prove, for example, that IN EACH STEP, your ALGORITHM GENERATES ALL POSSIBLE ALTERNATIVES for the first criterion. Otherwise, the final solution may not be optimal with respect to the second criterion.

More than that, even if you generate all alternatives, you should guarantee, that the local choice in each step gives a global optimum with respect to the second criterion. If you have no such guarantees, you cannot speak about solving a multicriteria problem and your approach has no any special name.

Multi-Criteria Decision Analysis, or MCDA, is a valuable tool that we can apply to many complex decisions. It is most applicable to solving problems that are characterized as a choice among alternatives. It has all the characteristics of a useful decision support tool: It helps us focus on what is important, is logical and consistent, and is easy to use. At its core MCDA is useful for:

Dividing the decision into smaller, more understandable parts

Analyzing each part

Integrating the parts to produce a meaningful solution

When used for group decision making, MCDA helps groups talk about their decision opportunity (the problem to be solved) in a way that allows them to consider the values that each views as important. It also provides a unique ability for people to consider and talk about complex trade-offs among alternatives. In effect, It helps people think, re-think, query, adjust, decide, rethink some more, test, adjust, and finally decide.

MCDA problems are comprised of five components:

1. Goal

2. Decision maker or group of decision makers with opinions (preferences)

3. Decision alternatives

4. Evaluation criteria (interests)

5. Outcomes or consequences associated with alternative/interest combination

Arvind

There is not doubt that the DM needs data for establishing his preferences.

That applies nicely  for instance, for a company contracting new personnel

One of the criteria could be for example 'quality level' (according company standards), or 'lowest performance accepted' (tolerance to company needs), or 'level of expertise' (according to complexity of a work position).

In this case the DM knows what he or his company wants, and also he needs data. This data may come in the form of presentations made by potential candidates. Then studying potential candidates background the DM can make sound decisions.

This is the way used by entreprenerurs, headhunters and Human Resouces Departments to contract new personnel, although probably they don't use much MCDM methods

However, if in the case of purchasing equipment for instance, the DM gets from the purchaqsing or engineering department firm values for say three different equipments, which is the function of the DM?

Is he going to modify firm values according to his experience?

That is, what can the DM say about the criterion 'Cost of equipment'? Is he going to correct homologated values from suppliers because his preferences?

For another criterion such as 'Performance of equipment from other users', the DM will also may have information perhaps not quantitative but linguistics, as 'very good', 'reliable', 'por performance' and so on. He can translate those values into cardinals by different methods, but where are his preferences?

I would like very much if somebody could explain me this, because I never undrestood the role of the DM when there are quantitative values, nor when he is addressing aspects that he CAN'T have complete information, that is involving a large quantity of people.

How can he decide for thousands?

In addition, and as other colleagues suggest, the selection can be based on 'related literature', I am afraid that I disagree, because each project is unique, each project has its own demands and restrictions, and projects can involve different fields such as Medicine, Geology, Environment, Social issues, etc, at the same time, nor shared by others

In my modest opinjon practitioners must study  their projects very consciously and then select the criteria according to them. Of course, he can extract information from other SIMILAR projects, but this is only illustrative.

The DM has to créate his own criteria considering posible and even unforfeseen aspects of the projects, no matter if he needs 5, 10 or 78 criteria for that.

Muham

It appears that this scenario is similar to a portfolio of projects, where you have some projects going and then you want to add five more projects.

If I were you I would solve the problem building a decision matrix with the projects already in operation and the new ones. All of them subject to the same restrictions, that is, profit, social issues and change in employment, or others, for instance social profit, environment, risk, etc

I would not use weights, especially because, as you said, the five projects are almost equally profitable, and therefore, a weight for profit is useless, or if there is any, it will have the least importance.

I suggest using TOPSIS without weights, that is assuming that all criteria have the same weight. If at the end, getting the result, you consider that in reality; say social issues are not well represented give a weight to that criterion, considering what the government really wants. You can also give a weight to change in employment, if you find it is relevant, and then run the model again.

Regarding your question, MCDM is mainly a system to solve a problem with alternatives that are subject to certain criteria, and the model gives you which alternative is the most desirable.

Weights may or may not be utilized in MCDM, it depends of the method used.

TOPSIS, SIMUS and other methods don’t use them, and for me they are the most reliable because not subjectivity is involved.

Of course, normally criteria do not have the same importance and for that reason people must use weights which are in general subjective and can vary from one decision-maker to another. You probably will be asking yourself that if it recognized that normally criteria have different importance measured by weights, why these methods do not consider this importance?

The answer to this legitimate question, is that these methods DO CONSIDER CRITERIA IMPORTANCE, but not using weights, but their capacity to evaluate alternatives, which does not depends on weights.

They do not rely in arbitrary weights but work with the initial data and without any bias.

I hope it helps

Thank you Gireesha

With your question and your experiment comparing results using the same data, the same criteria weights and different MCDM models, and your more that logical question, you gave me more motives and reasons to maintain what I have been promoting here in RG as well as in papers and international conferences, the last one two weeks ago in Ottawa, Canada, and sponsored by the International MCDM society.

Bluntly, as I mentioned in this conference, the way Sensitivity Analysis is performed nowadays - irrelevant of the MCDM model used - produces wrong results that in addition are almost useless. You illustrated it very well when using three different methods and the same weights you got three different rankings. This is unconceivable.

However, the models are not to be blamed for this. The problem lies in using weights that are not appropriate, or still better, the problem lies in using criteria weights. They should not be used, or at least using weights that are relevant and true, not artificial.

You really put the finger in the wound.

Your observation is very valuable because it clearly shows the inadequacy of using criteria weights to perform a sensitivity analysis, irrelevant of the method used.

As I said before, changing criteria weights, which are artificial, indeed changes the ranking, simply because it is arithmetic operation.

Regarding why the ranking changes for different MCDM models even using the same weights, it is due, in my opinion, to the fact that they affect differently the values of the algorithms and involving not only multiplications but also additions and subtractions.

For instance in ELECTRE you use these weights when comparing two alternatives regarding one criterion, and then you give the alternative a weight equal to the criterion weight subject to the action (concordance matrix).

In the same model the discordance matrix computes the absolute differences between performance values.

Both matrices are computed as dominance matrices and then compared and a raking obtained.

For PROMETHE method, each pair of alternatives is compared regarding each criterion and using preference functions for each criterion, which in turn are multiplied by criteria weights.

For TOPSIS method you don’t need to use weights, and most probably if you do there will be no change, because if you multiply each performance value for a weight, the same increse applies to all performance values in that criterion and their relative difference remains constant. Because TOPSIS is based in Linear Programming, these weights are irrelevant.

In VIKOR the best performance value for each criterion is found as well as its worst performance value. Then the difference between the best value and any performance value for each criterion is computed. This difference is then divided by the difference between the best and worst values and this ratio multiplied by the criterion weight

In AHP each alternative is compared regarding each criterion and a value of preference multiplied by the corresponding criterion weight.

As you can see because the different ways that criteria weights are inputted in each algorithm it would be a ‘miracle’ if rankings coincide, and in my opinion it does not depends on the nature of the weights, because even if you use entropy generated weights, probably the result will be the same.

This is one of the reasons that different models, treating a same problem, with the same data, yield different results, and this is also the reason by which I believe that weights should not be used in MCDM. Of course, it means assuming that all criteria have the same importance which is not realistic. However, if we run all models without using weights and analyze the final results it is likely that these coincide. At this point the DM opinion, expertise and know how can be put to work, and because his knowledge and experience he could be inclined to assign weight to certain criteria, but he will be doing this based on actual results, not on blind preferences.

Linear Programming, works without any weights, so perhaps it could be considered as the technique delivering the most suitable solution, not the optimal, but one that satisfies the DMs.

Again, I want to point out that TOPSIS is considered one of the best models as well as  DEA (Data Envelopment Analysis),  with wide recognition for determining optimal efficiencies are based in Linear Programming. Is this a coincidence? I doubt it.

Your first question was: How can the ranking obtain from VIKOR method be justified?

I believe that the ranking obtained by any method can be justified by the method itself. Again, the use of criteria weights without any mathematical foundation obviously alters the results producing not comparable results.

As a proof, the SIMUS method based in Linear Programming, with no weights, utilizes two completely different approaches (Simple additive weighting, similar to SAW), and (Outranking, similar to PROMETHEE), both starting at a Pareto efficient matrix, and producing two identical rankings.

Draw your conclusions.

Boris

Thank you for your contribution to this debate.

BY. 1. Prof. Thomas Saaty, as the Author of AHP, and AHP-followers stress that AHP was and is used in applications and “…is the only accurate and rigorous mathematical way….”; for the measurement of intangible’

NM. Let’s analyze this sentence

Accurate: The Dictionary defines ‘accurate’ as: ‘Free from error’ or ‘Carefully precise’.

Accuracy is related with consistency; a system may be accurate in some results, but to be credible it also needs to be consistent in all results; it cannot be accurate in some and inaccurate in others.  If Dr. Saaty says that his system is accurate, why then AHP includes the consistency ratio to compensate for lack of consistency or error? Doesn’t it involve a contradiction?

Rigorous?  Saaty’s fundamental scale of absolute numbers is an invention based on a psychiatric opinion; there many scholars that have criticized it. It might be reasonable, but not rigorous since it does not have any mathematical foundation.

Intangible. By definition it is something incapable of being perceived by the sense of touch, as incorporeal or immaterial things; impalpable.

I believe that this word is incorrectly used in this context. It appears that AHP can measure intangibles as human intelligence, or intangible effects such as erosion due to logging, or losing natural capital due to oil extraction, or people desperation when they are moved because a large project needs their land?

I would really appreciate it if somebody can explain me how AHP can measure them, because these are normal and current aspects that a MCDM problem should consider. My guess is that AHP cannot rationally address these criteria, because they are components of a complex scenario for which the model is not prepared for.

BY. 2. Prof. Waldemar Koczkodaj presents and proves in his papers the serious shortcomings/drawbacks of AHP; and. Prof. Nolberto Munier discuss the pros and cons of this method. I want to say (reading his works), I appreciate very much Nolberto’s efforts concerning the use of MCDA methods within decision-making process and regarding correct implementation in applications.

NM. Thank you Professor Yatsalo for your comment; that is in effect my goal. It does not matter what model we use, but it must replicate reality as much as possible

BY. Therefore, I’ll discuss some other questions around AHP.

1. I teach MCDA at my Uni for many years. My students (bachelors, undergraduates) ask me each year: Which MCDA method is the “best” and the most popular…

NM. Yes, I also got that question many times and even here in RG. My answer to my students was that they shouldn’t ask about which the best model is because it does not exist; they should instead ask: ‘Which is the MCDM method that best model my reality and satisfies my needs?’ irrelevant if it is popular, easy or complicated.

BY. I say there is no the “best” method…! However, there is the most popular one… In addition to other analyses, I mention my paper from 2015… I analyzed there the usage of different MCDA meth and software (using Scopus, WoS, and ScienceDirect data for 2000-2014) within the multicriteria problems associated with risk management. According to my analysis, AHP was the post popular meth … with big advantage (AHP>TOPSIS>PROMETHEE>MAVT/MAUT).

NM. I think that you are absolutely right. There is not a ‘best’ method, none of the existing models can replicate reality and probably never will, and certainly AHP is the most popular. Now that you mention risk management, I wonder how AHP can handle risks expressed in percentages. Or do we have to admit that the DM can establish that alternative A is say ‘n’ times more risky than alternative D, and if he can, on what grounds?

BY. 2. Each year, I ask my students to vote for the one MCDA meth, which they would use for analysis of a serious MCDA problem. The results is presented below.

[My students know 9 methods, and each year they make presentation at an open Seminar with analysis of their own multicriteria problem using several MCDA meth].

2.1 Ranking (MCDA methods) by IST students (for the last 2 years, 55 students): MAVT/MAUT (~45%)> AHP (~25%)>TOPSIS (~12%)~Promethee (~12%) [for the previous years the AHP votes were <20%].

NM. Very interesting question for your students!

It shows that MAVT/MAUT gets 80% more votes than AHP. I wonder why, and I think that you know the answer when you add ‘Serious problems’

May be, and just may be, your students  chose MAVT/MAUT in lieu of the more popular AHP because they realized that AHP is not designed to handle serious problems, which by the way is also my opinion.

BY. 2.2 Students from the Economic and Management department prefer TOPSIS (~ 45%) [because “it is the most simple and quick method”], and AHP (~30%).

NM. See my point? They don’t care about which method will fit their needs. They look for the easiest way, which of course is natural to any human being

BY. 3. Students ask me: Why AHP is the most popular meth (among classical ones)?!?

I discuss with them (and they agree with me…) the following reasons:

BY. 3.1 AHP allows the users to compare criteria and alternatives in a simple verbal scale;

NM. Agreed

BY. 3.2 Users (especially those, who don’t understand/feel good enough partial value functions and weighting process, compare 2.1 and 2.2 above) implement comparisons without problems found in other methods requiring weighting and value functions setting;

making pairwise comparisons of criteria, they think that they avoid weighting process: computer is clear, and it implements weighting itself using my simple judgements…

NM. And don’t they realize that simple judgement may be inaccurate? It appears to me that they adopt the law of the minimum effort

BY. 3.3 The Expert Choice Software (thanks to Prof. Saaty and his pupils) was the 1st in MCDA and is well-known and popular still now (and CD+, etc);

NM. Agreed, but there are also available easy to use software for PROMETHEE and TOPSIS; I employed them in my university. The problem, as I see it, is that these models demand more research and self commitment, especially PROMETHEE. Here the DM must take decisions such as selecting the transfer functions and thresholds, and he must be able to justify the reasons for his choosing.  In AHP the DM has nothing to justify, it is his preference, period, as I was told by a AHP professor…..

BY, 4. I had several talks with my (best) students when they presented their MCDA problems.

Student: - I don’t like AHP…

Me: - Why, it’s simple, understandable…

Student: - I don’t feel AHP. It’s a black box for me,…. in contrast to MAVT, TOPSIS.

I see the formula (as for MAVT), but the results of weighting and scoring go to me from a black box… I can do weight sensitivity analysis, as for MAVT, but...how can I transform pairwise comparison matrix to have the weights I see in this tool for weight sensitivity analysis in AHP!?

NM. That is also my main question when analyzing the so ‘called sensitivity analysis’ in AHP.

BY. From your lectures, I know fuzzy approaches and linguistic variables, so I understand the verbal AHP scale for pairwise comparisons. However, I don’t understand, why this method is so popular!?. And, I don’t like to fill a lot of matrices and improve their CI….

NM. Can you blame this guy?

BY. 5. After discussion of AHP and its popularity, students ask me:

- Do U use/like AHP?

I give my answer to this question in the very end of my course and after students’ voting concerning “MCDA method they would choose”.

NM Naturally!

Usually I say: I don’t use AHP in my\our research and applications. The only case was in my paper with USA colleagues in 2006 (we used in that paper different methods in a problem on multicriteria analysis of remediation actions).

NM. Professor Yatsalo, I understand that you are doing serious research and handle complex problems. Your honest answer regarding that you don’t use AHP, confirms what I said about AHP ability to MODEL, let alone to SOLVE complex problems.

BY. 6. I don’t say about the causes of that. It’s a complex of reasons they were discussed above and in some papers; though, I’ve not analyzed AHP “drawbacks” so deeply as prof. Koczkodaj and some other opponents of AHP.

In any case, I don’t consider Ranks Reversal Problem (RRP) as a defect of AHP.

NM. Neither do I; Rank Reversal is not an AHP monopoly. Most models have the same problem

BY. Almost all classical MCDA methods are encountered with RRP (see, eg, papers by prof. Nolberto Munier with a survey by RRP for different MCDA meth as well as and his method SIMUS).

I do research in ranking of Fuzzy Numbers (FNs) and know that the most intuitively clear ranking methods pay for their understandability just by violation of transitivity (Axiom A5 from the survey by Wang&Kerre 2001) and/or by violation of axiom A5 (absence of rank reversal). MCDA methods may be considered as Methods for ranking alternatives (I say here about the ranking problematique). [and intransitivity and RR is a part of our real life /relations, and we /human Beings are often not under rational behaviour and rules; and such intransitive or RR relations should be explored].

NM. Sure enough about transitivity. AHP is notorious for its lack of transitivity, and I agree with your last paragraph.

 I reckon that intransitivity is part of our life, however apparently that is ignored by AHP when they say that if preference A is better that preference B, and this one is better than preference C, then preference A must be better that preference C, with a 10 % margin. Wouldn’t be better to assume that sometimes transitivity cannot be achieved, in lieu of forcing it?

Thus, RRP, which I considered as a big drawback in the very beginning of my R&Ds within MCDA, isn’t a drawback in fact (as I think now, it’ my, subjective, point of view). Moreover, the cases of RR may be considered, if we seriously analyze a topical multicriteria problem, as a helpful case to pay more attention to these (i.e., under RR) alternatives within the Decision Making Process.

In my opinion, RR is a big drawback because robustness of a ranking is important, and RR can destroy it. I think it is well considering

However, I believe that in many cases what is deemed to be RR in not such, but a logical consequence of an added alternative being better than others. The problem is to decide when this happens. Nobody can assure by simply examining the performance vector of a new alternative, if it is better or worse than another because the trade-offs between alternatives.

Nevertheless, when an alternative vector is identical to another existent it shouldn’t produce RR, however it does.

Thank you Professor Yatsalo for your detailed comments

Sewer network construction costs are dependent partially on the costs of the installed pipes, but depend more on the initial costs of trenching and back-filling. The underground plant is expensive to replace, and so it must be regarded as an asset to be carefully managed. Sadly, maintenance is usually reactive rather than proactive. Greater reliability is achieved (at greater costs) by trenching deeply. Redundancy is not used to ensure greater reliability as it is in other networks. Good record keeping and communication with other network providers ensures that they will not inadvertently damage your assets during their network repair and expansion. Toll-free numbers should be well advertised to minimise damage and repair time. Tree roots and inadvertent rain flooding cause the main problems. Depending on the area, pollutants may enter the system. 

If you were to "sell" the network to a commercial company, how much would you charge for the parts of it? These are your assets.

A municipality will typically recover their investment costs many times over in the lifetime of the network. Interestingly, as with other networks, they charge all customers of the same class the same monthly fees, irregardless of the length of the shared network actually needed to connect the customer to the processing plant. This is regarded as being "fair", and the municipality pays off its investment borrowings faster via the customers close to the processing plant. All customers in a particular class (domestic, industrial..) are regarded as being equal sources of revenue.

The other big investment goes into the processing plant, which, by necessity is placed at low points. The processing is mainly mechanical, resulting in low maintenance costs.

 I attach a reading list for you. Follow also the links to the links!

Dear Khubaib 

All MCDM methods are suitable for large number of evaluation criteria, but the selection an appropriate MCDM method or why this method is better than another are depend on your circumstances and MCDM problem.  For example, if the relationships among criteria is important for you you need to use ANP. While, if the calculation time is important for you; you need to avoid use Pairwise comparison methods such as (AHP, ANP, decision matrix, ELECTRE, MACBETH, REMBRANDT, PAPRIKA). for example, in your case,the MCDM problem includes 6 alternatives and 45 criteria, therefore, complete pairwise comparison can be extremely time consuming especially when you have multi-level. 

At the end, none of MCDM methods is perfect and each of them has limitations and benefits. Also, evaluation MCDM methods is different research area and it will make you confused, so I advice you to keep using the method that you select FAHP or I can recommend FSAW method to handle your problem.

I attached two papers that I feel they will help you....

All the best... 

in MODM you have more than one goal (objective), so you want to optimize something AND something else... In MADM you have one goal, but more than one criterion (attribute).

A little late but...You can use J-Electre-v1.0 (it's free), that is a java based software that solves the following MCDA problems: Electre I, Electre I_s, Electre I_v, Electre II, Electre III, Electre IV, Electre TRI and Electre TRI ME. 

You can download the software here: sourceforge.net/projects/j-electre/files/

If the payoff variable is non-negative, you can use square root for risk aversion and square for risk seeking. If the payoff can be negative, then you first have to add a constant to make it non negative.

Dear Lafifi

thank you so much for the complete answer.

Comment on:

Assume for instance that selecting equipment the ranking is D>A>B>C. This is a purely mathematical approach, and then the DM can say, “OK the best equipment selected by the model is D, but in my opinion I would reverse the ranking and select equipment A. Why? Because I have worked with equipment A and I know it is reliable, sturdy, and with reasonable maintenance costs, while equipment D incorporates a new technology that I don’t know if it has been sufficiently tested”.

My view of the above statement is that your MCDM should have a criteria regarding reliability/ sturdiness and maintenance costs.

Hi Khubaib,'

You can easily found some implementation of Fuzzy Vikor in Github.

Some of them are here:

Good luck

Dear Siyu

Brief comment on the ELECTRE four methods

ELECTRE I: Selects a satisfactory set of alternatives, and works with concordance indexes. They measure the intensity of the arguments favouring the assertion that action (a) outranks action (b). There is also a discordance index, that is, the quantity or intensity of opposed arguments within the criteria under analysis, which challenges the assertion that (a) outranks (b) (Flament, 1999).

ELECTRE II: Selects an ordering of alternatives and adds thresholds to the latter matrixes.

ELECTRE III: Similar to ELECTRE II but also adds evaluated outranking relationships and utilizes pseudo criteria, that is attributes which use preference and indifference thresholds.

ELECTRE IV:  Similar to those already commented on, however, an important consideration is that it does not require weights for criteria, which is a step further against subjectivity. The interpretation of this lack of weight, is, according to Flament (cited) that “This doesn’t imply that all criteria have the same importance, but that none of them has an inferior category in its relationships with others”.

I do not share this opinion because consider that not all criteria have the same category or importance. For instance, it is obvious that if a project includes the Internal Rate of Return as a criterion, and as another criterion the payback period, the former is more important than the latter, for it defines the project’s profitability, while the second criterion may be negotiated

Regarding what method to use for environment, in my opinion all depends on what are your needs and what are you looking for. I would recommend to have a look at ELECTRE IV for the reasons that it does not need weights for criteria..

As in all models, there are doubts with ELECTRE. Some researchers have reservations and apparently, with reasons, e.g. that fixing thresholds may lead to finding that the corresponding nucleus is empty. This entails modifying these thresholds until a nucleus is generated, which constitutes a manifest arbitrariness or biasness of the system.

Good luck

Nolberto

Dear Mr. Tran,

I reveived you message and I will answer It here to help others researches.

It depends how your hiearchy is strutured. Once you use sub-criteria, the pairwise comparisons decrease a lot.

I received you draft and I think it is not that complicated.

Let's work together.