Hi Mehdi,

AHP is itself  a fuzzy decision making tool.  I doubt making it more fuzzier add value. AHP has been used with some success in various fields. See my paper

https://www.researchgate.net/publication/272144498_Subsea_technologies_selection_using_analytic_hierarchy_process

However, many  researcher have tried to include fuzzy numbers into this process.  The  calculation is slightly more involved but not difficult. I don't believe it adds value to the basic AHP.  There is no empirical evidence that FAHP is better than AHP. 

You can read different views on this subject below. 

http://www.nus.edu.sg/nurop/2010/Proceedings/FoE/Does%20the%20Fuzzy%20Analytic%20Hierarchy%20Process%20Improve%20the%20Quality%20of%20Multi-Attribute%20Decision%20Making.pdf

http://www.ticaret.edu.tr/uploads/Kutuphane/dergi/f11/M00178.pdf

http://www.diva-portal.org/smash/get/diva2:120251/fulltext01

Article Subsea technologies selection using analytic hierarchy process

According to " no free lunch" theorom, neither AHP nor FAPS performs better in all cases. I suppose that we have to evaluate their performance on a case by case basis.

You may refer to section 6.3 of following thesis:

"This research works on the comparison of classical AHP and fuzzy AHP with 240 randomly generated data. By building a series of statistic models, this research concludes that criteria weights given by fuzzy AHP follow the same tendency as the ones given by classic AHP approach"

Hi Behrouz,

I tried to read the thesis that you have attached. I have no patience to read 90 pages hence I went directly to the conclusions. I could not make head or tale of it, perhaps I am too hasty and don't read carefully. 

Do you think he reinforced my belief that FAHP is just more numerical torture without adding value? Or I must revise my opinion?

Dear Mehdi,

I agree with Sirous, FAHP (in my experience), do not add any extra value to the classic AHP. the fundamental scale of AHP (which by the way is not a nominal scale ) it is already fuzzy, so fuzzyfing something already fuzzy do not make sense to me.

By the way, I test the results of both methods in few simple problems with the compatibility index "G" (a compatibility index built especially for weighted environments) and AHP always gave  better (or at least equal) results than FAHP.

If you are interested, I can send you the file with the comparison of results of both methods by means of index G.

Dear freinds

Thanks a lot for answers espcially from dear freinds that send attach files.

I have a sugession. First, determine whether or not AHP method  have weaknesses ? If AHP method have weaknesses, FAHP will upgrade it? Or with FAHP only calculations has increased ? So  Please determine whether or not AHP method  have weaknesses ?

Regards

Mehdi Zandebasiri

Hi Mehdi,

This road is well traveled. AHP is a qualitative method and very much dependent on the assessors point of view. In an unbiased experience you will find that  consistency index is far from ideal. Those who the method and have time, they will tinker with numbers until they get  a good CI.  AHP is not brilliant, but nothing else to replace. 

Fuzzy AHP is not an upgrade it is more of the same thing. 

Dear sirou

Thanks for your answer

Do you think presentation of  crisp number is  a weaknesse  in comparable to fuzzy number?

That is right. Calculations in FAHP is very difficut bur FAHP uses fuzzy numbers and  fuzzy number have priority than crisp number. Zade, Zimmerman and Yager have presented this subject ago. Even though FAHP has difficult mathematics but has fuzzy numbers also.

Regards

Mehdi

Hi Mehdi,

You asked a couple of questions which I have alluded to them in my previous posts. Here I answer them again.

Your question: Do you think using crisp number is a weakness  compared to fuzzy number?  

My Answer:  What you are calling crisp is really fuzzy, as there is no hard calculation behind it. You just assign a number to the criterion based on experience. Thus, the classical AHP is really a fuzzy approach.  What I said was that adding another layer of fuzziness doesn't make your decision better.  The best way to understand this point is take a simple case and  go through the numbers.

Your question: is it right. that calculations in FAHP is very difficult  since FAHP uses fuzzy numbers and fuzzy number have priority than crisp number. 

My Answer: Doing Fuzzy AHP is not difficult  but you need to do more number crunching.  You might ask why I am doing this.  My point was you expect by spending more time on a decision tool to get a better results. This is not going to happen. More calculations doesn't help to make a better decision. Since  you may loose the sight of the original issue by doing mindless calculations. 

Somebody already suggested  in this thread that you take a couple of simple cases and do both AHP and FAHP and come up with your own conclusions.  The subject of AHP/FAHP and many other decision  making tools (TOPSIS/FTOPSIS, VICTOR and so on. ) is very well explored.  Just read the single paper as Professor Aliyeh Kazemi suggested to see the forest for the tree. 

Hi Mehdi, 

Multi-attribute decision-making methods such as AHP, ANP, TOPSIS and PROMETHEE used for assessment problems in the literature and all of them have some different advantages. 

Some of these methods are systematic approaches to the alternative selection and justification problem by using the concepts of fuzzy set theory and hierarchical

structure analysis. We can not say AHP or fuzzy AHP is better than the other. However fuzzy AHP has a big advantage: decision makers usually find that it is more confident to give interval judgements than fixed value judgements. 

So as a researcher, you can collect more confident data with fuzzy AHP. 

For details see my paper:

Article A Fuzzy Multi-Attribute Decision Making Model for Strategic ...

Dear sirous

Thanks for 2 answers

Regards

Mehdi

Dear Rabia 

Thanks for your answer.

You noticed the Interesting subject. I agree with you.  we can not say AHP or fuzzy AHP is better than the other. We must define each method workplace. Where do you think the FAHP method work better ? also AHP? Where fuzzy numbers work better?

Regards

Mehdi

Dear Mehdi,

In my view, data types are so important to identify decision-making method. So I think the question is should be "When?", instead of "Where?". If we use survey results or subjective observations of peoples, FAHP will work better. While traditional AHP is inadequate in the evaluation of subjective values, FAHP tries to eliminate the vagueness. If you have a very organized or numeric dataset, you do not need to use FAHP. So, the researcher's first decision is about using AHP or not, if you are positive the second decision will be using fuzzy or not? 

Regards

Rabia

Dear Rabia

Thanks for your answer

What you know the software appropriate for FAHP?

Regards

Mehdi

Dear Sirous

What is your opinion about Rabia view that  we can not say AHP or fuzzy AHP is better than the other?

Regards

Mehdi

As i wrote in my previous response, according to No Free Lunch theorom, neither AHP no FAHP outperform each other in all cases.

Wolpert and Macready give two NFL theorems that are closely related to the folkloric theorem. In their paper, they state:

We have dubbed the associated results NFL theorems because they demonstrate that if an algorithm performs well on a certain class of problems then it necessarily pays for that with degraded performance on the set of all remaining problems.

Wolpert, D.H., Macready, W.G. (1997), "No Free Lunch Theorems for Optimization", IEEE Transactions on Evolutionary Computation 1, 67.

Wolpert, David (1996), "The Lack of A Priori Distinctions between Learning Algorithms", Neural Computation, pp. 1341-1390.

Dear Behrouz Thanks for your attention

I agree with you

neither AHP no FAHP outperform each other in all cases

Thanks for your refrences also

Regards

Mehdi

Dear Mehdi,

I have already used "superdecision" and "MATLAB", and don't know much about others. But I exactly prefer and recommend MATLAB. It is flexible, user-friendly and also has many additional functions.

Regards

Rabia

Dear Rabia

Thanks for your guide in FAHP software.

Do the MATLAB software calculate the Consistency Index (CI) similar to the Exper Choice in AHP?

Regards

Mehdi

Also, the new methods such as; BWM, Linmap, IDOCRIW and SWARA can be used. All these methods are presented in the last ten years. Of course, along with the methods mentioned above, auxiliary methods should be used. These methods include; VIKOR, TOPSIS, ELECTRE, PROMETHEE, SAW, WASPAS, MultiMOORA, ARAS, COPRAS, EDAS and CODAS.

Dear Mehdi,

It depends on your case study.

Regards,

Hi there!

Just a quick question on this topic.

Is AHP an Operations research method?

I just need to know whether we can count AHP as a method in the O.R field?

Regards,

Soroush

Hi Soroush,

Any procdure to assistnt the decsion making mightbe consided as an OR method.

Sirous Yasseri

Hi dear Sirous,

Thank you for your answer.