Dear Artiom

Yes, they are criteria that can define what method to use.

The bad news is that unfortunately, none, except SIMUS can incorporate them, and this is one of the reasons that nowadays MCDM methods are far from modelling reality, and then their results are inaccurate and biased.

A short list of these criteria just from the back of my mind are:

1. Correlation between criteria.

2. Using resources, except PROMETHEE, Linear Programming and SIMUS, and putting values for those resources’ availability

3. Using restrictions for resources. For instance, lower and upper limits fort air contamination

4. Relationships between the value of resources. For instance, when availability of criterion D depends on availability of criterion A

5. Criteria duality. That is, the same criterion, with identical attributes must be used simultaneously in maximization and minimization, which by the way is a very usual happening in real problems

6. Criteria that change dynamically. This is a common issue in portfolio of projects where there is a criterion for each year of execution of all projects, each criterion for a certain year has its own percentage values, which are different from the values of precedent criterion, with the additions that not all projects start and finish at the same time

7. Criteria which values are expressed in binary format. For instance, to indicate that that alternative A is linked with criterion C8

8. Criteria representing externalities, that is, aspects such erosion, in a logging project

9. Criteria representing equilibrium conditions, as found in oil refinery projects that must consider simultaneously Production, Storage and Delivery

10. When it is necessary to input into the decision matrix that there is a project that must be in the final solution. This is normal when in a portfolio of projects there are some under construction and that must be in the final ranking and with priority

Thank you for an answer, Nolberto Munier

Thus, does it mean that one and only SIMUS should be used?

Dear Artiom

Of course not, because may be there are better methods than SIMUS; but from the ten or more MCDM methods that I know, I can assure you that none of then can handle these conditions, and you can try it by yourself

If you think that the 10 conditions I posted for criteria are realistic (I have real examples for each one of them) just ask yourself which of the methods you know can handle even one of these conditions

You will find the answer you are looking for.

That is why I raised a question. Thank a lot once again.

Dear Venkata

Well, there could be scenarios where different methods can give the same answers, but that is not the normal case, I believe it is rare. There are works by some researchers using the same problem and getting different results. If you like I can give you a good reference.

Even here in RG you should notice the large number of colleagues that are asking why different methods can't give the same results, and this is a proof that it occurs

It would be a miracle if different methods concurs, and this is one of the biggest problems without answer in MCDM

Just think about the fact that two different DM, working on the same problem and with the same method, may give different results. Imagine what then happens when different methods use different approaches.

Since practically all methods rely on sound mathematical principles, it would be logical that a same problem should give the same results. Why this does not happen?

In my humble opinion it is due to the fact of subjectivity, proper of each method.

Regarding your first question, I would say that finding the best alternative is not a matter of time, except perhaps in some methods where it is found by an iterative process. Normally computer time depends on the number of criteria.

I don't understand your second question. Could you pls. rephrase it?

In my opinion understanding the alternatives does not influence selecting the best.

The best alternative, independent of its complexity, is which complies with the largest number of criteria and in a larger proportion than others.

There is a very graphic example about this and that everybody knows: Google.

When you ask for an article in the Web, referred to a certain issue, say for instance 'Passenger traffic in the Auckland Airport in New Zealand.' Google algorithm looks for publications that contain the word ''Auckland', Airport', 'Passengers, 'New Zealand'. Say for instance that there are 20 sites. Googles needs to make a selection of those sites reflecting your choice, that is Passengers, and rank the answers considering the number of times that a site contains this word.

Indeed, thanks Nolberto Munier, for a logical and comprehensive answer.

Best method to evaluate the criteria weights is best worst method because it has highest consistency. further, for ranking of alternative the best method is newly developed proximity index value method (PIV) because it solves the rank reversal problems

Thank you Saif, may you please provide any examples of proximity index value (PIV) method application in practice?

Thank you for writing me, i am attaching a file to look for the example.

regards

saif

thank you

Dear Saif

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

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

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

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

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

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

Why?

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

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

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

If he uses this value to rank for instance between alternative A1 and A3, it is fine.

However, when he analyzed the pair A1 and A4, it is possible that it does not hold, because there is a different trade-off.

Why is this produced?

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

OK, you can say because the comparison is done regarding a main objective.

However, to reach that objective you forcefully need the alternatives, therefore my question is: Where the alternatives enter in this equation?

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

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

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

Dear Prof Munier,

Thank you for your response and healthy explaination and i understand your point. However, i have following queries on your written statement:

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

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

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

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

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

My response:

Are you trying to say that expert advice is necessary for decision making? if so then in Best worst method we take expert advice for the pairwise comparison.

Secondly on your written statement:

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

My response:

Can the problem of RR be eliminated by applying any method in MCDM?

I look forward to hear from you

Sincerely

saif

Dear Saif

SW. My response:

Are you trying to say that expert advice is necessary for decision making? if so then in Best worst method we take expert advice for the pairwise comparison.

NM. No, it wasn’t my intention, I believe that expert advice may be fundamental in many problems, but it does not mean that it is necessary for all scenarios, and of course considering only subjective criteria

I don’t think that experts advise should be related with pair-wise comparison, mainly, as I said before, because that method is highly unreliable, and also because you can’t consider that a preference of trade-off is constant, since it depends on the alternatives, with or without experts. By the way, if experts collaborate, their wisdom appears to be in doubt, since they should know that said comparison may be good for some pair of alternatives, but not for all of them

SW. Secondly on your written statement:

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

My response:

Can the problem of RR be eliminated by applying any method in MCDM?

I look forward to hear from you

NM. Yes, as a matter of fact there are a couple of methods that according to some researchers don’t register RR. One of them is ANP, and if I don’t remember wrong the Preference Selection Method (PSO, Mania and Bhatt, 2010) is another, but I am only replicating what some researchers say. I don’t have any certainty that this is true, because I have not seen any analysis that leads to that conclusion.

However, I can vouch that other method, such as SIMUS, does not produce RR. The most important is that this assertion can be proved, by studying the algebra of this method. It is an iterative procedure, that starts with the worst solution (zero value for the objective function), and is improving it iteratively until it reaches the maximum or the minimum value.

The reason why it does not produce RR is that the selection of a new alternative to enter in the solution in each iteration, is made by comparing opportunity costs or opportunity benefits between each pair of alternatives, and selecting the best.

For that reason, if you introduce a new alternative, or delete one or work with two equal alternatives, the procedure is always the same, and if say, you delete one alternative it does not affect the opportunity cost of the others. and their former ranking. Same is you add a new alternative

I have performed 66 tests, using three different complex scenarios, and in each test, it was considered not one but two or more additions, deletions and identity. There was no RR in any of them.

Both, the algebraic method and the 66 tests are detailed in a book of mine that is published by Springer, and that will hit the shelves in two weeks time.

If you have more queries I will be happy to answer them

Dear Prof,

Now i fully understand the situations and looking forward to receive link of your book.

In addition, i am trying to develop new MCDM technique so i need your help in that, please if possible give me your email to discuss comprehensively

Thank you again

Sincerely

saif

Dear Saif

My email is [email protected]

I am looking forward for your comments

Thank you Prof.

Dear Saif,

Can proximity index value (PIV) method applicable for MCDM methods with incomplete knowledge & Imprecise data .like in fuzzy AHP or D/S theory methods

Dear Udaykumar

Could you please clarify your remark?

As far as I understand your are proposing to use PIV to MCDM. Is that correct?

or is it a question?

I am afraid that I don't understand what a D/S theory method is

Respected Munier Sir,

Yes, I asked question and D/S theory means Dempster–Shafer theory of evidence for uncertainty with basic probability assignment (BPA).

Dear Artiom Volkov ,

As you mentioned in your question that "Some scholars say that the combination of different methods gives a more accurate result".

Sir, Is their any research paper or proof for justifying this statement?. if Yes,then It would be very grateful and helpful for my research reference.

http://www.inzeko.ktu.lt/index.php/EE/article/view/310

Podvezko, V. (2011). Comparative analysis of MCDA methods SAW and COPRAS. Inžinerinė ekonomika, 134-146.

"[...] Therefore, a parallel use of several multicriteria evaluation methods as well as the analysis of the spread of estimates and averaging of the values obtained may be recommended for evaluating complicated multifaceted objects and processes."

Dear Artiom

Many attempts have been made to decide which MCDM is the best, and as you say, there is consensus that there is not a method better than another.

Even if I share that general opinion, I notice that all analysis are performed considering the proximity of rankings, or may be level of discrimination. I have done that using the Tau Kendall Correlation Coefficient in pairs of results, and the most that I was able to deduct is that methods A and B can have better approximation among them that A and C among them, and we can even display those differences in a graphic. And what does it prove?

Nothing, because the ideal situation would be to compare each method with a certified method that gives the best solution. This method exists in mono-criterion, but not in multi criteria, therefore, that analysis is a waste of time.

In my opinion, we err in the sense that we are analyzing a problem according to their results, when in reality we should look for the way in which the initial decision making (IDM) is built, that is, in its origins. In other words, the most important aspect for us to consider is how the scenario is modelled. We can improve data using better estimates or fuzzy logic, but if the model is incomplete or faulty, we only well get, with luck, an approximate result.

If this IDM is the product of personal references, it is possible that results will not coincide with solved by a different DM, and using the same method. This is not an axiom, but it is evident that different preferences most probably will give different results. This is a paradox, because the problem is the same!

It is a fact that even with hybrid methods such as for instance AHP and TOPSIS, and using AHP derived weights, there is no guarantee that the result of both method for the same problem will coincide.

It is my opinion that the best way to compare different methods solving a problem is to inspect in each one, how the mathematical model of IDM is built in relationship with the scenario. If one of the methods takes into account as much as possible the different aspects of the problem, most likely this method is better than another which does not. It is similar to the trivial case of purchasing a car and selecting between different makers and models. Most probably, the best car will be that which represents our expectations, and it does not matter what method we use for this selection.

I would say that the question about which is the best method, has a simple answer. Check which method permits building the most complete IDM, that is, the one than best represents a scenario, and then select it.

To do that, I suggest:

First: Analyse the scenario and write down all its aspects, for instance:

· Kind of scenario. Is it a personal or corporate problem directly affecting the DM or is it a problem affecting thousands of people, large capital expenditure, that is, a complex problem?

· In a portfolio of projects, are they related or independent? Is there any restriction linked with time of execution, that is, can they start or finish at the same time, or these are different?

· Can a project be partitioned to be built in two or more places, or must only be one location?

· The scenario is simple one or a multiple one?

· Which are the characteristics of the different potential places, land, or water, for instance, for wind turbines to generate electric power? or may be both at the same time?

· In site selection for instance, all projects have the same facilities for import/export?

Second: Inspect the characteristics of criteria and determine:

· Restrictions needed, that is limits, such as for total capital, environment, social needs, transport, annual budget restrictions, construction schedule, etc. If a method does not consider resources, then most probably you have to disregard it.

· Determine existing relationships between criteria; if they exist, then you know that some methods can’t be used, that is, those that work only with independent criteria.

· Examine alternatives or ask the respective department that selected them, to verify their relationships, that is, inclusive, exclusive, dependency, etc. If they are for instance dependent, choose a method that can consider it.

· How are qualitative criteria values determined? Etc.

These are the main aspects, although of course not all of them. Then, just select a MCDM method that best approximate to the conditions imposed. We have to admit that most methods are mathematically sound, consequently, the method that allows for a better representation of reality, will be the best.

If we can’t model a scenario properly, it does not matter what method we use, since all of them will be biased by default, for they will give a solution to a scenario which is different from the one of our interest.

The best team or individual becomes the champion in sports competitions. Let's look at the example of football. 3 points for a win and 0 points for a loss and 1 point for a draw. In the alternative case, it would be the rule to give one point for each goal scored. But it didn't. There are two different approaches here. Both are mathematical. But which one is correct? The difference between outranking methods and other utility / value / global sum methods can be compared to this.

Dear Mahmut

MB - The best team or individual becomes the champion in sports competitions. Let's look at the example of football. 3 points for a win and 0 points for a loss and 1 point for a draw.

In the alternative case, it would be the rule to give one point for each goal scored. But it didn't. There are two different approaches here. Both are mathematical. But which one is correct? The difference between outranking methods and other utility / value / global sum methods can be compared to this.

NM- In your example I understand that whatever the number of goals, a 3 is given to the team that wins and 0 for the loser.

In all honesty, I know nothing about football, because I never liked the game or played it - something unusual for an Argentinian - and thus, your word is good for me, but it appears that the first is unfair, because it does not consider the relative effort of each team materialized in the number of goals.

I am glad with the alternative you mention because that is exactly how my SIMUS method works.

To determine alternatives scores, it follows three steps:

1. For each alternative adds up the scores corresponding to the criteria that it satisfies. These scores are optimal, because are obtained by Linear Programming. Normally, not all criteria are fulfilled considering a given alternative, and even it can happen that no criteria are satisfied.

2. It counts how many criteria are complied (the equivalent of number of goals), gives a value 1 to each criterion satisfied, adds up the 1s (or goals), and divides this sum by the total of criteria. This is a weight for each alternative.

3. The sum of optimal scores found on 1) are multiplied by the normalized weight in 2), and this is the score of that alternative.

You talk about outranking and this is also incorporated in SIMUS, processed and gives a second ranking, which is identical to the first obtained by weighted sum. In this way. These two different procedures check one another.

Dear Nolberto, you can help us further to fully understand the SIMUS method you have produced. Is it the compromise solution of the outranking method and the global sum method? Does it have formulas, for example? Is it ranking or classifying? MCDM method or not? Let's start with the matrix. I have 25 company alternatives and I have 5 financial criteria. I would like to measure the annual firm performance with these quantitative criteria. I want to determine the best company. How can SIMUS help me?

Dear Mahmut

It will be my pleasure to share SIMUS with a learned colleague.

First let me answer your questions:

1- In reality a compromise solution for one heuristic MCDM method is to reach an agreement, a compromise, between the alternatives and the criteria, because normally it does not exist an optimum solution in multi criteria. SIMUS also reaches a compromise.

2. There are no formulas like in AHP, PROMETHHE or TOPSIS. SIMUS is an algorithm.

3. It can classify (sort), and rank alternatives

4, It is a hybrid MCDM method.

5. Yes, it can solve your problem

Let me to make an introduction to SIMUS, since obviously, and because your questions, you need to know how something works, which for me is the correct way.

SIMUS is based on Linear Programming (LP), which is its most important component, not only because LP can find optimums, if they exist, but because its algebraic infrastructure using inequalities, and by not needing weights, because the relative importance among criteria is internally computed by the LP Simplex algorithm - which by the way, is in each computer as an Excel add-in - and based in data inputted, therefore, there is no subjectivity.

This means that you can apply SIMUS methodology ‘by hand’, as I did at the very beginning years ago, although not recommended, since its software allows solving large initial decision matrices, may be 150 x 45 or larger, in minutes, at least in my computer which is an ordinary ACER laptop.

It starts with modelling the normal initial decision matrix, as used in all MCDM methods, however, because it works with inequalities which represent geometrical spaces instead of lines, it allows for a large range of characteristics from the scenario to be modelled.

This is one of the most important features, because with LP you can model many different demands either in criteria and in alternatives, or combining both, such as assigning simultaneously maximums and minimums values to a criterion, as for instance a minimum acceptable IRR, and at the same time the potential maximum that it can reach, considering all other criteria.

You can model relationships between alternatives, which is normally done using binary notation that can be mixed with the normal decimal, integer, negative and positive numbers, as well as algebraic formulas.

That is, in the same initial matrix you can have two kinds of data, normal and binary.

SIMUS procedure is simple:

1- Model the initial decision matrix. No weights or assumptions are needed, and it can be formed by any mix of quantitative and qualitative data, the last one, coming of course from statistics, surveys and experts estimates, as well as crisps value using fuzzy logic.

However, if you want, you can establish a preference to alternatives and criteria, either independently or jointly, and the software will take those into account, but for criteria, this is not part of the SIMUS software, and then you need to make a prior simple operation to input them into the initial matrix.

2 – Press the start key, and you will be asked the normalization method you wish, among four, further, it will ask you if you want to see partial results or just the final result. The partial results ate those by each iteration.

3- Here enter SIMUS. It will select the first criterion, remove it from the matrix, use it as objective function, and then apply the Simplex algorithm to determine- if they exist - optimal scores, and at the same tine, if the project is feasible, with that objective factor and the set of criteria. If it is not, the software will inform you, in writing.

That is, that first objective is subject to the balance of the remaining criteria. Then SIMUS replaces the function as a criterion and selects the second to be used as an objective function, and reinstate it again into the matrix. It proceeds this way as many times as number of criteria, irrelevant if they are 5 or 500, as well as the number of alternatives. Computing times depends on the number of criteria.

4- The partial optimal scores are saved in a new matrix called ERP (Efficient Result Matrix), because it has all Pareto efficient results, per criterion. This is the fundamental SIMUS matrix, which is in reality the mapping in a new space of the initial one with raw numbers. Again, this ERP matrix is formed only with optimal scores.

5.- From here, SIMUS applies the Weighted Sum procedure. For each column or alternative, it adds up the corresponding scores (SC). Since for each alternative each score represents how the corresponding criterion is satisfied, it assigns a 1 to each, adds them up, and divide this sum by the total number of criteria (This is called Participation Factor,) (PF), which is then normalized (NPF), by considering all alternatives.

6. The final score for each alternative is found with the product SC x NPF, normally, the higher the better. At the same time, the software prints the corresponding ranking.

7. From here, SIMUS applies outranking.

It computes for each row of ERM the difference between the maximum scores in each row, and, if there are more scores, the difference between them. That is, the positive differences between all the scores in a row; these differences are added up and the result salved in another matrix called Project Dominance Matrix (PDM). It is a square matrix composed by alternatives. The sum of the differences in a row gives the value of the alternative to which that rowed belongs, and then, expresses the value of its dominant on the others.

The sum of the differences on each column gives the value of the alternative the column belongs, and then, expresses the values by which it is dominated by others.

8. For a same alternative the difference between its row and its column shows it score.

The software also prints the ranking.

The scores from the PDM matrix are different, since two different methods were used, however, their rankings are identical. By the way, when there are ties in the scores of the alternatives, the DM can use these score differences to determine which alternative is better.

This is in essence how SIMUS works. There is more interesting characteristic for instance, it can determine the shadow price of a stock, meaning how much an investor is willing to pay for it.

I hope that I have answered your questions, and yes, SIMUS can address your problem of 25 alternatives and 5 financial criteria, whatever they might be, IRR, NPD, Payback period, etc., and even all at the same time.

For your information, SIMUS is completely free world-wide, in all its power, and I will be happy to send the software to you if you so wish.

I am eager in making SIMUS known and used in many different applications, and therefore, I am at your disposal for helping you if you decide using it.

Best regards

Nolberto

Thank you for the very comprehensive and descriptive explanation. But I suggest you design a user-friendly interface for SIMUS method. I want to get results by pressing 3-5 keys and I can't wait for that. Also an online SIMUS method course would be nice. Or at least an application video might be useful.

Dear Mahmut

Yes, it was a detailed explanation for SIMUS, and I did it because I don't wan t anything taken for granted, or having the user to have doubts about the rightness of the method. You noticed that I did not use a single formula, which indeed would have been easier for me; I used common language that everybody can understand

In SIMUS you only need to press three keys, one for selecting normalization, the second for selecting step-by-step or continue, and the third for the system to start . That is all, and it can take 4 seconds. Do you want more user friendly that this?

I don't understand when you said that you can't wait. Wait for what?

Probably a matrix like yours will take in SIMUS 4 or 5 minutes or even less time. Is it too much?

I am not to compare SIMUS with other MCDM software, but with it you have no weights, no assumptions, no thresholds, no decisions.. You write your matrix in Excel and then electronically transfer it to SIMUS

I don't think that an interface is really needed. The only thing you have to do, as any other MCDM method, is to fill the initial decision matrix

In the SIMUS software, just by pressing a key, you have access to an extensive tutorial, 120 pages, with 12 examples solved

I don't think that this is too complicate. I am sure that it is simpler that computing the NPV for a project, which I guess you are familiar with.

I wish you luck in your endeavour, and hoping in hearing from you

If you are looking for easiest one (easy calculation) then go for AHP..but I personally prefer fuzzy integrated MCDM approaches.

Dear Sukanta

Yes, AHP is probably the easiest method to use, and it is also the most subjective and artificial of all methods and completely irrational. To use AHP is a waste of time, and it makes you believe that you can solve a problem with preferences, which are good for choosing a car, a movie, or a restaurant, that is, trivial problems, but useless for complicated scenarios. If you need more information, I will be happy to oblige

Dear Artiom

I believe that there are indeed criteria that can define the MCDM method to use.

For instance, and in your field, an agricultural project for different crops. There is usually for water needed a lower limit and a high limit for maize, wheat, barley, etc., and different for each one.

The first establishes that as a minimum the crop must receive a certain amount of water, while another establishes that the same crop must receive no more than a certain amount.

Which MCDM method can handle that?

Another example is a criterion that works with binary values such as 0 or 1

In another example, a criterion can establish for instance that the alternatives must satisfy at least n criteria

Which method can handle these criteria: Only two: Linear Programming and SIMUS

Dear Dr. Nolberto Sir,

I think, SIMUS would be more effective than Linear programming. Also I would like to suggest CLFPR with D- Number theory method which can be used to design mathematical model of given scenario to attain all constraints.

Dear Udaykamar

Thank you for your answer, but remember that SIMUS gets its strength from LP.

I don't know if it is more efficient than LP, but certainly, it has the de advantage to work with as many objectives you want and by using qualitative criteria

Thank you for your suggestion to using CLFPR theory that is unknown to me

By the way, have you tried SIMUS in a prtoject?

Dear Dr. Nolberto Sir,

I have gone through SIMUS , but not apply in my any project because as you pointed out Fuzzy ness is not going to handle previously by SIMUS and also we can't apply for dependant criteria. But surely I will try to apply it at proper place if I get a chance in my project

Dear Udaykamar

SIMUS can also be used with fuzzy. You can check the procedure by reading a recent paper from Stoilova, published in RG, where a complex railway problem is analyzed and solved by FSIMUS

Regarding depending criteria, you can apply the 'IF.... then... '' or perhaps correlation, both can be managed by SIMUS.

Dear Dr. Nolberto Munier Sir,

Sure, I will refer the paper from Stoilova.

-I think MCDM methods are comparable,

-One of the MCDM methods might be better,

-And of course, one of the MCDM methods can be selected.

That's what our article below considers,

Article AN OBJECTIVE CRITERIA PROPOSAL FOR THE COMPARISON OF MCDM AN...

Suggest reviewing this paper for MCDM methods:

https://www.sciencedirect.com/science/article/abs/pii/S092583881732827X