Dear Merve

Thank you very much for your question.

I am not proficiente in fuzzy logic, but I will try to answer your questions, although I am not sure I understand your question.

When you talk about different fuzzy sets, do you mean solving the same scenario with different lower and upper values for each performance value and for an unique MCDM method?

In other words, are you questioning about using different inicial values?

Or are you talking abut using different fuzzy sets as originally and intuitionistic, involving neutrrosophy and Pythagorean?

Thank you for your attention Nolberto Munier

First of all, I want to compare the Pythagorean, Neutrosophic, Spherical and Hesitant fuzzy sets with each other. In doing this I will use a single MCDM method (eg AHP etc.). The problem is to evaluate the performance of these fuzzy sets in the MCDM method. What are the things to be aware of here?

As far as I know, Pythagorean fuzzy sets are the one with the largest grading scale among the other fuzzy sets I've mentioned. This is an advantageous situation when obtaining expert opinion. Is there any way I can evaluate the advantages of fuzzy sets over each other?

Merve

Please send me again a copy of your questionnaire. I received it b ut for some reason I can't find it.

Thank you

Abtin

It is true all what you say, but the most important sentence is your last one : 'it is about how you are modelling the problem'

First of all, thank you for your comment Abtin Ijadi Maghsoodi

"As long as the expert judgement is solid it doesn't matter." The questions I have prepared in order to obtain the decision matrix about this can be formed with different approaches. However, the specialist will feel free when he is given a wide or narrow scale, that is, he can fully reflect his opinion. In this case, another problem arises. Which linguistic scale should I use? At this point, I get the answer that I should choose a Likert scale suitable for my model definition. Definitely, this inference has been useful. Thank you.

So, will the results change as these fuzzy sets provide input to the MCDM method, would it be a logical problem if I want to test it? Because, for example, the algorithm steps of Pythagorean Fuzzy AHP and Hesitant Fuzzy AHP are completely different from each other. So which way should I go to compare these two fuzzy sets?

Dear Nolberto Munier, if you cannot reach my previous comment, it is as follows. However, I did not send you a questionnaire.

First of all, I want to compare the Pythagorean, Neutrosophic, Spherical and Hesitant fuzzy sets with each other. In doing this I will use a single MCDM method (eg AHP etc.). The problem is to evaluate the performance of these fuzzy sets in the MCDM method. What are the things to be aware of here?

As far as I know, Pythagorean fuzzy sets are the one with the largest grading scale among the other fuzzy sets I've mentioned. This is an advantageous situation when obtaining expert opinion. Is there any way I can evaluate the advantages of fuzzy sets over each other?

Dear Merve

I apologize for my past request of a questionnaire. I was confused with another project from another colleague that I am also examining

Lets’ see. As I see your problem, you can have an example, that is, a complete initial decision matrix with crisp values, and you want to apply the four fuzzy sets to this same scenario.

Once you do that, you want to compare the ranking when using, the four fussy sets, and using a MCDM method. Then, you will get four probably different rankings. This appears to be, the same problem that researchers are trying to solve from decades, and it is to determine which is the best method.

Trouble is, that we don not know Which the ‘true’ answer is, and therefore, we don’t have a yardstick to compare methods.

I would like to suggest a method that does not give the solution you are looking for, but that can give you a hint of which of the four fuzzy sets gives the best result.

Suppose your initial scenario has 15 alternatives.

Each fuzzy set most probably will give you a ranking of the 15 alternatives.

In my opinion, you can use entropy to determine the amount of information contained in each ranking, something that is easily done in a couple of minutes, the higher this value the better, and it will allow you to determine which is the fuzzy set that produces the highest amount of information, and this could be something than can be used as a comparison among fuzzy sets.

Remember that entropy indicates disorder or in case of quantities in vectors, it shows the amount of information that each one contains, which is (1 – entropy). The larger this value means that the values are dispersed, there is discrimination, and then it facilitates decisions. Decisions are very difficult to take if the components of a problem have similar values, and it is easier when they have dissimilar value.

Anyway, it is only and idea

Dear Nolberto Munier

Thank you for your valuable ideas and time. If you come across an academic publication regarding the problem I mentioned, please do not hesitate to send it to me.

I wish you success in your work.

Thank you Merve

Dear Nolberto Munier

I read your post and the following sentence called my attention: "I would like to suggest a method that does not give the solution you are looking for, but that can give you a hint of which of the four fuzzy sets gives the best result."

I think I have a suggestion: what about to aggregate the results based on the similarity of the rankings? If method M1 is very similar to M2, they both will have very close importance in the aggregation. If M3 is very different, it will be less important in the aggregation. This similarity can be measured by Kendall tau distance, for example.

We may assume that the methods/approaches that achieves similar rankings are those more valuable to suggest the decision.

Actually, I worked with this idea in my master degree and I just realized that the methodology can deal with your statement.

Dear Marcos

The fact that there is similarity does not necessarily mean that there is a 'correct' ranking

Yes Kendall Tau may give you the correlation between two rankings. As matter of fact it is my preference on correlation, because it measures the ordinal association between two rankings, however and unfortunately, I don.t believe that it can help in deciding which the best solution is

Pls. clarify your last sentence; I don't understand it

Dear Marcos Antonio Alves

I agree with Nolberto Munier . Measuring distance with correlation would still be a choice. I need more specific algorithm and sets comparison.

For example, how do I measure the response of two different fuzzy sets in the normalization steps of two different ranking algorithms?

Dear Merve

The problem it, is that to measure or making a comparison among the rankings of two different MCDM methods, you need a reference, a yardstick, and this is the 'true' value, that we don't know.

I absolutely agree with you Nolberto Munier

Than you Merve

Merve Bulut Dear Merve,

Different types of fuzzy sets have their own advantages in describing the information. For example, hesitant fuzzy sets with several numbers to describe the different opinion of membership degree for the element belongs to sets. Intuitionistic fuzzy sets, which contains the membership and non-membership degree, describe the relationship between element and set. If you want to compare with each, perhaps you could utilize an idea similar to the control variables method, i.e., fix the ranking results of the solutions in one method, then represent the information with different fuzzy sets, and finally compare the differences between the obtained results and the fixed ones. But this also has some problems, if the information form in the actual problem does not satisfy the form of some fuzzy set, then it is not possible to use this fuzzy set form, then the comparison is meaningless. In some methodological innovation literature based on fuzzy set theory, it usually involves the comparison between fuzzy sets, such as the comparison of methods for probabilistic hesitant fuzzy sets and hesitant fuzzy sets. Anyway, it's only and idea.

Good luck for you.

multi criteria decision making in ranking the bus companies using fuzzy rule is proposed. The proposed method uses the application of fuzzy sets and approximate reasoning in deciding the ranking of the performance of several bus companies. The proposed method introduces data normalization using similarity function which dampens extreme values that exist in the data. The use of the model is suitable in evaluating situation that involves subjectivity, vagueness and imprecise information. Experimental results are comparable to several previous methods.

Dear Anas

You say 'is proposed'. Where?

Dear Anas Maaroof

Where the fuzzy rule was proposed?

Dear Abtin Ijadi Maghsoodi

It definitely makes sense. Because in the expert opinion, the quality of the input should be measured, which is why the consistency ratio is there. However, the fact that these sets offer different scales from each other and that the common denominator is not compared may indicate a new consistency ratio calculation.

Dear Merve

A consistency ratio in AHP only measures the transitivity of the DM estimates, and not even that, since the DM, most of the time needs to correct his/her own estimates, according to the 10 % assumption. It is not even good for the DM self-satisfaction..............

But by far more important is that it has nothing to do with the real world, which, in addition, is mostly intransitive.

I would very much like it if somebody can explain to me, why is accepted this absurd transference of information, from the DM mind to the real world. Is there any axiom, any theory, any theorem that supports it? What happens when another DM on the same problem, gets another result?