Often a multi-criteria decision analysis method is used in a decision making process to determine the best option (alternative). Without proof, we take for granted that the option is the best choice.
It could be better if there could be a proof.
Dear Benito
Very interesting question but which answer is not known yet, and probably never will.
In addition there is very unlikely that you can reach an optimal solution, because normally criteria are contradictory. How can you get an optimal solution when for instance a criterion calls for maximizing benefits while another calls for minimizing costs?
To solve this dichotomy researchers have developed different methods such as AHP, PROMETHEE, ELECTRE, TOPSIS, VIKOR, SIMUS and many others that do not reach an optimal solution but a compromise one.
This procedure aims at finding a result, not optimal, but that satisfies everybody, and this is what MCDM methods do.
In my modest opinion, the only way to assume that a solution is the best, not optimal, is when it derives from a well structured decision matrix that incorporates as much as possible aspects related with the problem under study.
Therefore, a matrix with interrelated and correlated criteria, with provisions for related alternatives, a matrix which incorporates resources and their limits, a matrix that contemplates qualitative and qualitative criteria in any mix and numbers, a matrix that considers that all projects may no start and finish at the same time, etc.
This is related with a method with a very strong participation of the DM, not by inventing preferences but with the capacity to analyze results. Of course, the method must give him reliable information for him to make decisions.
If there are more than one Pareto optimal point, then it's up to you to pick one of the Pareto optimal points look best according to your "selfish" objective. That can be tricky, if your problem is complex - as you may noy be able to visualize (or algebraically represent) every Pareto optimal point. If you can, then you probably can identify the Pareto point that is best for you.
Dear Mr. Osman
SIMUS is able to analyze each one of the Pareto optimal solutions and related with an alternative selected.
After that, using its add-in (IOSA ) it is able to draw the utility curve based on exact data coming from marginal utilities for each objective. Therefore, it provides an utility curve for both, increasing and decreasing values for criteria and for each objective
If for instance a problem has five objectives and an alternative has been selected, IOSA provides five utility curves
There is an interesting result in this aspect presented in a thesis already discussed under my supervison.The idea is simply to have a method to obtain in the convex case that pareto optimal solution whose image in the objective space has the minimum distance from the ideal point.
DEAR BENITO
It is quite difficult to say by comparison with other MCDM methods, which one is the best. However, effectiveness and performance of an MADM method can be tested according to the criteria proposed by Wang and Triantaphyllou (X. Wang, E. Triantaphyllou, Ranking irregularities when evaluating alternatives by using some ELECTRE methods, Omega 36 (2008) 45-63). Go through the paper, you will get some idea.
Regards
Syed Abou Iltaf Hussain
Dear Benito,
I fully support answer of Prof. M. Osman that your solution of MCDM problem depends on method of analysis of the problem. You will obtain the best solution only in exotic case when the solution corresponds to extrema of all criteria of the problem. In other situations you should define formally what means "best solution" for your MCDM problem (for example a specified point from Pareto set or extremal point of generalized criterion etc.) and starting from that construct your proof.
Best regards,
Igor Grebennik
Since MCDM is basically a modeling technique, i would say that you can compare the outputs with the inputs, this might give you an idea about how well the chosen analysis method is performing, also you may consider doing a sensitivity analysis to prove that the results remains reliable when altering the weights of the criteria.
In my opinion, I would rather treat the solution obtained using any MADM method as the solution "that just fits the decision case" because the selection among MADM methods are, indeed, decision-context dependent. And while I agree with the above opinions from Yucheng Dong
Prof. Dong and Bouchaala Mohammed Abdelghani Prof. Abdelghani, instead of understanding whether the selected alternative is a true optimal one or not, it is perhaps the matter to correctly establish the decision problem structure (e.g., the decision hierarchy, constructs, criteria), identify the suitable MADM model, source the precise data which can be computerised (computer data) and precisely probe the weights (human data). As what I may think, this facilitates a 'precise decision-making' process for the encountered selection problems.
This is at least half a century old problem! Yes The methods do not have the same mathematical procedure. They probably don't produce the same ranking results in most cases. If one is different from the other one is either superior or opposite in comparison. Otherwise, you are saying that MCDM methods are uncharacteristic and produce inconsistent results. In short, and therefore, it should be the most appropriate MCDM method according to the situation, and there is. For example, in general, I think the PROMETHEE method is more suitable than the simple SAW method. I think a lot of researcher must have sensed this. Although he cannot prove this situation.
Article An objectıve criteria proposal for the comparison of MCDM an...
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Graphs