Dear Julia

The fuzzy logic purpose is to convert a diffuse or fuzzy numerical value or linguistic variable, in such a way that different possibilities are considered.

For instance, a linguistic expression such as 'At 38, he is not very young'  is not a deterministic but a diffused information because at that age this person still belongs to the young people universe but at the same time is beginning to be a part of the mature people universe. With fuzzy logic you can convert that expression in a number that considers his/her participation in the two universes. This is an independent procedure.

However, you can put the resulting number as data in most MCDM methods.

The fuzzy logic is the way you express your variables so you need to use it with one of the MCDA approaches. For instance, Fuzzy AHP means you are using AHP but the variables are expressed in a fuzzy way. However, you cannot say I am using fuzzy for MCDA because in itself fuzzy is not an analysis approach. 

I hope I could give you some idea.

Thank you very much to you Nolberto Munier and Hossein Baharmand for the timely response. It is now clear that Fuzzy set theory cannot be used on its own. I will look at another MCDA method. I do appreciate it. Thank you

Dear Julia

You can use Intuitionistic fuzzy set alone please let me know how I can help you

Luis Perez, I would like to rank alternatives using the fuzzy set theory, like I would do with different MCDA techniques. Is that possible? Is software required or can it be done manually? I would like to get assistance, thank you.

Dear Julia 

In order to help you

Let me know how many criteria and alternative do you want to evaluate

Luis Perez it is a collection of case studies so I want to evaluate them with another or alternative MCDA method to see if the ranking of alternatives is any different. Krishnendu Mukherjee, I have looked at your work and your discussion. Can I use Fuzzy set theory as an independent  MCDA tool or can it be used in conjunction with other methods?

I see from the discussion that FST can be used with qualitative data

Dear Julia

I believe that FST is designed to be used with qualitative data, because if you have deterministic data, such as for instance the final costs for each equipment, in a case where you need to select one of them, there is no need to use FST

If you have a collection of case studies solved with a certain method, you certainly can also solve them with another method/s. However, there is no guarantee that the results agree, not because their different mathematical procedures, which are considered sound (although not everybody agrees in this point), but because the subjectivities that each model introduces into the system. Even if you use the same weights for criteria for all models,  each model has its own additional subjective rules, such as comparing alternatives according to criteria in AHP, or establishing thresholds and transfer functions in PROMETHEE, or assuming any of the three distances in TOPSIS. It would certainly would be a miracle if the different models coincide in results.

Thank you Nolberto. That is what I am trying to achieve in my research. I have collected a number of mining related case studies and I am ranking the alternatives using AHP, ELECTRE, PROMETHEE, VIKOR, SAW, TOPSIS, Yager's method and then FST. I will then compare the different rankings from each method then establish a trend. Of course certain assumptions had to be made due to different requirements of each technique. I am kindly asking for assistance with whether it is justifiable to use FST independently, as one of the techniques. The different case studies contain both qualitative and quantitative data.

Dear Julia

It appears that I misunderstood your question. Sorry

Regarding what you now put as ' whether it is justifiable to use FST independently, as one of the techniques' I don't think so. FST was not designed as a selection tool, but as a tool with which you can feed MCDM models with more reliable data, when there are vagueness. It was not designed to rank alternatives

Thank you very much Nolberto. This has been so helpful, I really do appreciate it

Dear Fausto

I don't think that you can use fuzzy logic as a MCDM tool, because the technique is not designed for that.

You can use it to refine data for MCDM but not for selection