While implementing any MCDM approach (VIKOR, TOPSIS, etc), if an alternative gets maximum 1.000 in normalized matrix, and factors have nearly equal weightage, is it necessary this alternative will be first ranked after completion of MCDM process?
please see the attached file for example.
Dear Parveen
In most MCDM factors or criteria, weights play a fundamental role in determining final alternative scores. They can change the ranking, and as a matter of fact this is the procedure used by many models to test the model in a sensitivity analysis.
As per your question, remember that alternative scores are not the result of a mathematical formula, but a consequence of a mathematical procedure, influenced by personal decisions and subjective values, and this is the reason for which a same problem treated with different models usually gives different rankings.
Therefore, the fact that an alternative has the maximum score it does not necessarily mean that it is the best. This is a decision that corresponds to the Decision-Maker (DM), and it is irrelevant if all factors or criteria have the same or different weighs.
Thus, the DM may opt for the alternative which is in the second or even in the third place. To do this he needs information about which are the criteria that affects most each alternative, but not based in their respective weights, but on their potential effects in the future.
Consider for instance that the ranking is C>A>D>B.
At first view it appears that alternative C is the best. Yes, possibly, from the mathematical point of view, but perhaps not from the operating point of view.
Assume that alternative C is strongly linked with criterion ‘Price’ while alternative A is strongly linked with criterion ‘Public opinion’. The problem is that criterion ‘Price’ is known to have strong variations in plus and minus as a function of time and then alternative C is subject to these potential variations, and this could be dangerous.
The DM may decide then not to chose alternative C but A, because this second one, linked with criterion ‘Public opinion’ is more safe (no variations). He must also base his decision by knowing the discrepancy or difference in score values between C and A. Of course he also needs to know the range of criterion variability (observe that I do not refer to its ‘weight’ since it is irrelevant). I am referring on how much the marginal value of each criterion can change without varying the ranking. This is the type of decision that the DM must perform.
Why weight is irrelevant? Because it only expresses a preference between criteria, not the influence of each criterion on each alternative, which is grounded on the amount of information that each criterion contains, in other words, on its entropy.
I hope this answers your question but if you need more details, I can send you a still unpublished paper of mine entitled ‘[250]- Weights for criteria evaluation – Are they truly significant for their intended use? – SIMUS a MCDM model not needing them’
Nolberto
Also, with Vikor method, the alternative with a scoring of 1,0 makes it the worst alternative.
I appreciate the answer given by Nolberto Munie, but as per question asked by Parveen, according to my views the alternative with more numbers of 1 in normalized matrix will be at first position after implementing any MCDM approach.
Dear Dipesh
What happens if you have more than one alternative with the same number of 1s?
Having 1's in normalized matrix is not enough to be the first rank, the final alternatives rankings based on both alternatives' performance (ones) and critetia weights.
Dear Parveen
In your problem, if all factors having equal weight, Alternative 4 having maximum 1.000 with respect to three factors out of five then definitely alternative 4 will be ranked as first after completion of MCDM process.
Saleh
I agree with the first part of your statement but I am afraid that I don't understand the second. Could you pls. elaborate a little more?
In addition to Nolberto Munier answer I could to add that, in the most of the cases, the decisions making task are a part of a more span task and generated solutions are just proposals (or options) to be solved by the last one. In all of the cases the Decisions Maker represent the more span task (or system).