Dear Morteza Yazdani 

I hope this example can be well for you

Best regard

Thank you Luis.

best

Morteza:

The paper that Luis Perez recommended you is an excellent publication

There are more, for instance:

1- Wang, X., and E. Triantaphyllou, "Ranking Irregularities When Evaluating Alternativesby Using Some Multi-Criteria Decision Analysis Methods,"Handbook of Industrial andSystems Engineering (A. Badiru, Editor), CRC Press, Taylor & Francis Group, Boca Raton,FL, U.S.A., Chapter 27, pp. 27-1 to 27-12, 2006. 

JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS

J. Multi-Crit. Decis. Anal. 10: 11–25 (2001)

2. Two New Cases of Rank Reversals when the AHP and

Some of its Additive Variants are Used that do not Occur

with the Multiplicative AHP

EVANGELOS TRIANTAPHYLLOU*

 Mathematical and Computer Modelling

Volume 49, Issues 5–6, March 2009, Pages 1221–1229

3. On rank reversal in decision analysis

Ying-Ming Wanga, b, , ,

Ying Luoc

I have been working lately on this subject and proposing a new method based in Linear Programming that does not produce Rank Reversal.

If interested and since you are in Madrid and I am in Valencia, you can telephone me at 96 336 0841 or e- mail me to [email protected]. I will be happy to share with you my findings 

Good luck

Dear Professor Munier,

thank you very much for your information and explanations. I have great source now. Lets talk some days later. Now i have a very compact days of my thesis defense in Madrid and so very soon i will back my main research. It would be great to work together. Valencia is a lovely city like Madrid!:)

Rank reversal is a concept there are good contribution and we can go forward to do effective works. I was working on Normalization tools and their effect on MCDM, so now rank reversal is a term can influence MCDM outcome and it is interesting to be worked.

best and keep in touch.  

You can find some papers to measure distance or difference between orders.

I can recommend these. 

Dear Morteza,

This can be of interest in your analysis: (pairwise) rank reversals in outranking methods. Some useful theorems and conditions, with particular (but not limited) analysis of the Promethee method.

Conference Paper Rank reversal in the PROMETHEE II method: Some new results

Article Some results about rank reversal instances in the PROMETHEE methods

Actually the rank reversal depends on the assumption you make on your value scale. If you use the original Saaty's scale, then you implicitly assume that utility (the scale of a criterion)  is something you "distribute" to alternatives. A typical example is money. Assume that the rector of the university decides to distribute a certain amount of money for research achievements and some amount for teaching achievements to departments. If we delete or add a new department, then rank may change. It is very natural, because the rector has fixed the amounts for research and teaching achievements.

However, if the utility is something which is not restricted, then the rank reversal is not natural. Then you cannot scale the criteria such as Saaty originally made. Then you cannot change scale in the middle of the process. For instance, one way to scale the criteria is to use the scale where the maximum value is one. If you delete or add alternatives, you cannot change the original values.

Rank reversal occurs because the collection of rankings, called a profile, contains what Don Saari calls Condorcet n-tuples.  For example, a Condorcet triple is A ≻ B ≻ C, B ≻ C ≻ A, and C ≻ A ≻ B where ≻ means “is preferred to.”  Any positional voting scheme aggregating this set of rankings will yield a tie.  If one of the candidates is removed or another is added, however, the tie is broken.  If a profile contains Condorcet n-tuples, it can result in inconsistencies of this type.   An excellent reference is Donald G. Saari, Disposing Dictators, Demystifying Voting Paradoxes: Social Choice Analysis, 2008, Cambridge University Press: New York.

Note that any attempt to avoid rank reversal generally involves discarding critical information provided by the rankings, for example, looking only at the relative position of two alternatives and ignoring any that are in between.  In other words, when comparing A and B, failing to differentiate between A ≻ B ≻ C ≻ D and A ≻ C ≻ D ≻ B.  This can result in an overall or aggregate ranking that is nontransitive or irrational!  Saari has examples. 

This issue is related to a property called Independence of Irrelevant Alternatives (IIA).  Saari showed that this property negates another property, transitivity of outcome, and substitutes one called Intensity form of Independence of Irrelevant Alternatives (IIIA) that considers not only the relative position of two candidates but also some measure of the strength of preference.  In the case of the Borda Count, the number of alternatives between the two being considered is the measure of strength of preference.

I refer you to a paper I coauthored entitled “Deflecting Arrow by Aggregating Rankings of Multiple Correlated Criteria According to Borda.”  It appears in the Journal of Multi-Criteria Decision Analysis http://onlinelibrary.wiley.com/doi/10.1002/mcda.1568/full.

Article Deflecting Arrow by Aggregating Rankings of Multiple Correla...

Dear Morteza

I am wondering why you relate normalization with Rank Reversal, or at least that is what I understood

As I understand it the normalization method should not influence a ranking, that is, whatever the normalization method used, the ranking should be the same.

I have performed many examples where I use the sum of row method, the largest row value method, the Euclidean method and the maximin method, and whatever the method used I got the same ranking. However, perhapss there is something that IK am missing and I will apprecaite your comment

Dear Nolberto, 

yes normalization methods will change the ranking. Now we are working on a paper which proposes a new logarithmic normalization tool for VIKOR and TOPSIS, so it is observed that the results have changed. This is a very interesting discussion and one of my co-authors performed one, please see the file. 

For more info i would like to hear from you. Thank you for your following. 

morteza

Dear Morteza

Thank you for your answer and for the interesting paper .

In my opinion normalization can change ranking in methods that use  weights for criteria.

In my case I do not use any weights and I can demonstrate that I do not have any changes using different normalization methods

Look at this example:

Alternatives in columns and criteria in rows

6200  6050  4800  5100   3800  Maximize

3         4.2      2.8     6.1    3.01  Maximize

20       20       21      20       32   Minimize

4         3        2.5       3        5     Maximize

Ranking using Euclidean:          4 > 5 > 3 > 2

Using Suma of Row:                   4 > 5 > 3 > 2

Using Máximum Row Value:       4 > 5 > 3 > 2

In the three cases the scores for alternatives are exactly the same as shown:

Alternative 4 = 0.25

Alternative 5 = 0.25

Alternative 3 = 0.17

Alternative 2- 0.08

Alternatice 1 = 0

If you want I can e mail you the computer screenshots of these results.

Dear Morteza,

The following articles may help you:

1. The Characteristic Objects Method: A New Distance-based Approach to Multicriteria Decision-making Problems, Wojciech Sałabun, Journal of Multi Criteria Decision Analysis, Volume 22, Issue 1-2, 2015, pp. 37–50.

2. Ranking irregularities when evaluating alternatives by using some ELECTRE methods, Xiaoting Wang, Evangelos Triantaphyllou, Omega 36 (2008) 45 – 63.

3. A Comparison of the REMBRANDT System with a New Approach in AHP, Journal of Industrial Engineering 6(2010)7-12.

4. Rank reversal and Rank Preservation in ANP method, Feng Kong, Wei Wei & Jia-Hao Gong, Journal of Discrete Mathematical Sciences and Cryptography, Volume 19, 2016 - Issue 3, pp. 821-836, 2016.

5. Eliminating rank reversal in multicriteria analysis of urban transportation system alternatives, Luiz F. A. M. Gomes, Journal of Advanced Transportation, Volume 24, Issue 2, pp. 181–184, 1990.

6. On rank reversal in decision analysis, Ying-Ming Wang, Ying Luo, Mathematical and Computer Modelling, Volume 49, Issues 5–6, pp. 1221–1229, 2009.

7. Some results about rank reversal instances in the PROMETHEE methods, Céline Verly; Yves De Smet, International Journal of Multicriteria Decision Making (IJMCDM), Vol. 3, No. 4, 2013.

With best regards

Prasenjit