You asked about the most popular method, therefore in my opinion that's all. These methods are most commonly used
ANP is an evolution of AHP, and solve problems in cycle. The AHP solve the most problems.
I agree with Mr. Salabun's list, and I have to point out that AHP is the most popular by a Bibliometric procedure. You can confirm it in the paper below.
VAIDYA, O. S.; KUMAR, S. Analytic hierarchy process: An overview of applications. European Journal of Operational Research, v. 169, n. 1, p. 1–29, fev. 2006.
In second place, I wolud try ELECTRE Family, in particular, ELECRE TRI, because there is not a lot of methods for classifications.
The orthers are not spread as these two I told you.
I agree with Mr. Hora's comments. However, I would avoid establishing the strict ranking. Additionally, I would like to say something about WSM and TOPSIS method.
WSM(Weighted Sum Model) is unfortunately the most frequently used method in practice (applications for research, government tenders, etc.). In practice a many institutions establish a group of criteria. Each alternative is evaluated with respect to the particular criterion (scoring phase). Finally, the scores are summed with adequate weights index. The best solution has the most points. This approach is rare in literature, but it is often practiced in reality.
TOPSIS is a little similar to the WSM method. The main difference is a normalization step and measured distance to Positive Ideal Solution (PIS) and Negative Ideal Solution (NIS). However, in ScienceDirect Base we can find results for particular acronyms (word; results):
AHP; 13650
TOPSIS; 1863
ELECTRE; 1602
and in ISI:
AHP; 10384
TOPSIS; 1685
ELECTRE; 481
Once again I would like to emphasize, that I would like to be very careful with establish ranking of the MCDM methods. This is just another MCDM problem.
Please refer
Kumar Sanjay, Parashar Neeraj and Haleem Abid, 2009, Analytical Hierarchy Process Applied to Vendor Selection Problem: Small Scale, Medium Scale and Large Scale Industries, Business Intelligence Journal, Vol. 2, No. 2 pp 355-362.
Thanks,
The paper is about application of AHP in vendor selection problem. I think AHP is the most applied technique that proposed by Prof. Saaty.
I agree with Seyed Mohamad Mohsen Emamat that AHP has been among the most applied techniques.
AHP, TOPSIS, ELECTRE I-II-III, PROMETHEE, VIKOR are the most popular ones. Also, you can check this publication to see that how to apply TOPSIS and ELECTRE I
Article Financial Performance Analysis by Using TOPSIS and ELECTRE M...