Dear Seyed:

Your question:

Is Entropy Shanon a good technique for weighting in Multi-Criteria Decision-Making?

As you know we use Entropy Shanon for weighting criteria in multi-criteria decision-making.

.Is "Entropy Shanon" a good technique for weighting in Multi-Criteria Decision-Making?

I think it is not a good technique for weighting in real world because:

It just uses decision matrix data

My answers in bold:

That is just its main advantage because it works with quantitative data supposed reliable, and qualitative data, also assumed reliable, because it comes from statistics, surveys, etc. Weights used in MCDM are subjective; whatever the system used for their computation.

If you want a proof of their importance think that two different DM addressing the same problem can develop different weights. It does not happen with entropy derived weights, because they do not depend on a person but on data. But the problem is that it is wrong to develop subjective weights for criteria, and then using them to qualify criteria foralternatives evaluation. The only way you can do that is when you use entropy derived weights, because then they truly represent criteria capacity for evaluation

If we add some new alternatives, weights change.

Of course, because you are adding new performaces values. Consider that it is new problem. Remember that entropy measures discrimination or dispersion of numbers. If you add a new alternative you are modifying all criteria series of performances

If we change period of time weights change.

Where ‘period of time’ enter in this? If it is in a criterion, again values will changes,  as well possible discrimination

For example we have 3 criteria: price, speed, safety

In several period of time weights of criteria vary

For example if our period of time is one month"

You are changing values. Each set of values for a criterion is a different problem

This month may price get 0.7 (speed=0.2, safety=0.1)

Next month may price get 0.1 (speed=0.6, safety=0.3)

It is against reality! What is your opinion?

Why is against reality?

 Remember that entropy is the sum of the product of variable times its natural logarithm and everything divided by the natural log of the number of variables

By the way, criteria weight is DERIVED from entropy. Entropy in itself means ‘Lack of information’ ‘Disorder’ where anything can happens, because there is complete uncertainty. The higher the entropy the less the information. In reality entropy derived weighs are (1 – entropy)

If in July price is 0.7, Speed 0.2 and safety 0.1, its entropy is 0.109 and the weight 1-0.109 = 0.89

If in August price is 0.1, speed 0.6 and safety 0.3, its entropy is 0.33 and the weight  1–0.33= 0.67

In the first case your information content is 0.89 and in the second is 0.67.

Therefore, the first criterion has a higher weight than the second

Pls. see example of entropy calculation in the attached file

Hi:

  weights are a way to express decision maker preferences on the criteria. And there are many many ways to do this. I suggest you to check surrogate weigths.

Regards

David

Hi,

if you have no information on decision makers' weights, you can use Shannon entropy and assign the higher weights to a decision maker who provides more specific }less vague] information.

Dear David

In small problems such  as deciding for a car to purchase or for company hiring, I agree with you because the beneficiaries of the project are the DM or the company, and  therefore DM preferences are very valuable because he knows very well what he or the company needs or wants.

But in complicated problems where you have reliable quantitative data and even qualitative data from say a survey of 5000 people, the DM cannot override the numbers, and then establish through eigen value analysis the corresponding weight. This is  ilogical.

He cannot assume to be more knowledgeable that a manufacturer that indicates for instance, in a quantitative criterion calling for maximizing output the homologated value for his equipment. In a qualitative criterion, when the DM has the opinion in percentage of 5000 people, on what grounds he can ignore what they say, especially when  is not he, by them, who will benefit or will suffer the consequences of his decisions?. This is from a rational point of view.

From the mathematical point of view the Arrow’s Impossibility theorem clearly states that a group cannot take decisions on behalf of a collective. Therefore, in so doing when the DM overrides the preferences of thousands of people and uses those of his own, he is violating this theorem.

I know first hand this problem when a project I was working was stopped, after spending 1200 million dollars, because the DMs did not pay attention at what the affected people said. If you want I can give you the source of this that had a very strong resonance in Canada. And this is only one of the many examples that I have.

Of course you can use subrogate weights, and in fact there are a couple of models than use them, but again they are based on a subjective ranking of the importance of criteria. On what grounds? On what authority you as a DM can affirm for instance that criterion ‘water availability’ is more important than ‘transportation’? Based on what?

However, the main point is that sauf in the personal or company case as mentioned, weights are useless, because the fact that they establish relative degrees of importance between criteria, does not mean that they are suitable to rank criteria importance to evaluate alternatives, let alone for a sensitivity analysis of the solution.

Nolbero:

   I agree with you 100%.

Gracias David

Si tienes interes en intercambiar puntos de vista, lo cual me agradaria, este es mi telefono en Valencia:96 336 0841

Un abrazo

Thank you all for answering.

I have another question. "What is the philosophy of entropy method?"

for example, in this decision matrix we have:

                  C1          C2        C3

A1              4            10         0.4

A2              4             1          0.5

A3              4             5          0.6

I think C1 will be 0 and C2 will the most important criteria.

I think the philosophy of entropy method says: more differences = more importance.

differences between 10,1,5 are more than others, then c2 is the most important criteria.

I said the philosophy of entropy method is: "more differences = more importance".

Is that correct?

I think it is a good technique for weighting in real world because:

because it is based on objective research

Shannon Entropy method is a good technique to give the priority importance to the attribute because it always gives objective weight.

Dear Aqib

I don't know what you mean for objective 'research'.

Shannon entropy is indeed based on objectives or criteria, but on their performance vales

Dear Chiranrib

You are right, Shannon entropy measures the relative importance of criteria, and that is fundamental for selecting alternatives. That importance is based on the discrimination existent between each criteria performance values

Chiranjib Bhowmik can you send me some online manuscript link, where the ''Shannon Entropy method'' with illustration is given?

Just follow my Paper

Article The effect of normalization tools on green energy sources se...

Dear Raju

Please find attached an example of entropy on the same problem: one with a large dispersion of values and the other with low dispersion

Remember that entropy means disorder, noise or loss on information in a message, consequently, we are interested in its complement, that is (1 - entropy), which is quantity of information

In the first example with larger dispersion you get and entropy s = 0.64 and then quantity of information is 0.36

In the second example with very little dispersion, the entropy s =0.998 and quantity of information = 0.002

As another typical example assume that you cast a die, since all numbers have the same probability of occurrence, the entropy s = 1 and then quantity of information is 1-1 = 0

If you alter the die to show for instance the number 6, its probability will be higher than the other numbers, and the the entropy will be less than 1, consequently, the quantity of information is greater than 0

Nolberto Munier Thanks sir.

Chiranjib Bhowmik Thanks a lot.

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 Mohammed

Very interesting your question

If you use questionnaires for questions in order to get weight values I believed that what you can do is to average the answers.

Some months ago this problem was examined here in RGin some extent

Of course I agree plenty on the use of entropy derived weights instead of the subjective weights.

I don't have any doubts that your results were closer to reality when using entropy derived weights, however I would like if you can explain how you reached to that conclusion related with the real world

Dear Nolberto

Thank a million because of your answer

We were working on the efficiency of intra-urban public transportation. We used three different method for doing that. First of all we calculated the efficiency through DEA which gives you detailed information about unit analysis. This is what exactly is going on the reality. Because, DEA is a method which is based on the inputs and outputs and it really works in these situations. Then, we need some other methods to examine the results. Hence, we designed a questionnaire based on the mutual comparison and we asked related experts to fill it out and the variables weights were calculated by questionnaire results via AHP. After seeing the results, I was not satisfied because it seemed that results are somehow bias. That is why I used Entropy which its result were quite close to DEA.

Dear Mohammad

Thank you for your excellent explanation.

I am glad that you used DEA because it is a tool you can trust, because it is based on Linear Programming, and using real data.

Which is still better is that results using entropy were close to those of DEA, while those using subjective weights, were not so good, not only because preferences, but also, as you say, because biases, which is probably very common, since as defenders of AHP affirm, weights are intuitive, very curious way to address technical issues, indeed!

This clearly shows that preferences have not room in real-life studies and that we should use methods that work with realities.

I believe your work should be published in a paper, if possible, because there are not too many papers addressing the use of entropy or other objective weights instead of arbitrary weights, which unfortunately is the norm in excellent methods such as Promethee, Electre, Topsis, etc. This is an aspect that I have been fighting for years.

By the way, I am working on a paper on urban planning and related with several areas, such as Education, Public Health, Transportation, Safety, Housing, etc., with the objective of minimizing costs for this set of projects. It has the number 298, and will be published shortly in RG.

I would be very happy if you can review it and make me know your comments, and of course, criticism.

Dear Nolberto

That is Nice of you and I really appreciate it.

That would be my pleasure to review your paper for sure that would be perfect. I am also ready to have a cooperation with you on related papers if you agree.

Dear Mohammad

I appreciate your comment regarding my work, but my friend, remember that no human activity is perfect. It is not for us.

My modest contribution lies in using common sense and trying to make the best possible use of the tools and experience that we have, and most of this effort is directed to represent reality as much as possible.

It will be my pleasure if both can work together in a paper. Do you have any specific subject in minds?

Dear Nolberto

For sure you are right. There is no 100 percent perfect human activity. We are in our ways and we are trying our best. This is what matters.

There are lots of subjects that we could work together. Could you possibly send your email address to me?

Dear Mohammad

My email is [email protected]