At the end you have to decide which criteria you regard as objective and which are subjective. I consider it sensible to make a sharp distinction between those two classes, and leave the application of subjectivity-structuring methods like TOPSIS out of the objective part of the approach.

So, I'd return your question with the remark that you should scrutinize any criterion on its nature for the individual optimization problem to solve. If everyone involved would regard it as objectively assessable put it into the basic multi-criteria optimization. If not, leave it to the 2nd layer of subjective single decision taking from the pareto set.

Cheers,

Petra

Yes, we can increase and decrease the number of criteria, but it depends on the nature of techniques ,you are taking. e.g the precision of AHP decreases when criteria is exceeding than 7. in case of large number of criteria , there is issue of pair wise comparisons. there are some mathematical techniques available i.e transitivity etc but still we get issue of imprecision. there is some latest research exist to cope with this large number of criteria.

As Dr. Autran says, your family of criteria must reflect the characteristics of your problem, that should be your main concern about the number of criteria (exhaustivity, cohesion and non redundance).

About the number of criteria, is it not true that AHP precision decrease when you exceeding  7 criteria. (If that was true, then we would be able to resolve a very reduced set of problems with AHP/ANP). That is a misinterpretation of the human psycological issue of 7+-2 elements). You have to cluster the criteria given to them a hierarchy  (or network) system order, and at the same time respect the second AHP axiom of homogeneity, which is the real issue that can make decrease your precision. 

Often a multiobjective optimization problem produces a big set of non-dominated solutions. They can be compared by means of a multi-criteria decision making method (if there are many solutions AHP is not the best method) using a family of consistent criteria (as prof Autran suggests) . It means that the family has to include all the aspects of the problem but at least two situations are possible: a) the multiobjective optimization model cannot include all the aspects (i.e. for the difficult analytical translation) and therefore now they have to be included in the new model; b) all the aspects are included in the multiobjective model and they can be included in the second one using a different way of judgement /information treatment/evaluation/…

Cara Maria Franca,

Is not the number of alternatives what make AHP applicable or not. You may have many alternatives (says 40-50 or even 100), and if the 4 AHP axioms are controlled then you may apply AHP in AM mode. What is really relevant here is the quality of the metric engine you are building and the restrictions you have in relation with the problem you want to resolve. For instance, AHP is clearly not good for the continues problem cases.

Dear Claudio,

I agree, AHP is clearly not good for the continues problem cases. At the same time, if we have not 100 or 40 but only 15 alternatives, the logical consistency of the comparisons (as Saaty indicated in his seminars and included implicitly in the axioms)  is really difficult, and  I had several occasions to verify this situation,

Maria Franca

Dear Maria Franca,

Spite of this topic (number of alternatives in AHP) is quite far from the initial question of Saeed, I´ll try to explain to you a little bit more.

When you have many alternatives is not a good idea trying to compare it all togheter in just one large matrix (as you correctly point it out), that´s why you should use the AM mode (AHP-Absolute Measurement mode, knowing also as Rating mode) and not the traditional RM (Relative Measurement) mode. You can find many examples about this very useful option in the literature. (It also exist the "pivot element process" if for some reason you need to stay in the RM mode). 

By the way, what Tom Saaty says in his seminars is: dont try to compare many alternatives (or criteria) at the same time (same matrix) due to the consistency issue and consequently lack of precision you will face. (This is the result of breaking axiom 2). But, there is no reason to have any limit about the number of alternatives you may evaluate in an AHP/ANP model (if you do it as explained before).

Try to learn more about this option in Tom´s books, there are many examples of this. (it is also an Italian book from Universitá di Cassino (Fabio di Felice, 2011 or 2012).

I´m sure you will find this option very useful in many real problems. 

Hoping have been of some help,

Sincerely,

Claudio Garuti

For multidimensional optimization the method of consecutive concessions was proposed - when criteria are selected subsequently based on their importance, and a each concession is assigned to each minimum value of the corresponding criterion.

A formation of the solution set by first criterion was performed using modernized particle swarm method (PSO-method).

Summary

1The set of solutions Ya is formed from n-dimension vectors ya (y1, y2, ..., yn), which are within the range of permissible concessions delt1 of “minimum first criteria” 

2. The set of solutions Yb is formed within the set of solutions Ya. The set of solutions Yb consists of vectors yb (y1, y2, ..., yn). Vectors yb are in the range of permissible concessions delt2 of "minimum 2" .

3.Also, an next additional criterion  was proposed, based on which the distribution of ranked variables of an unknown vector should be similar to the vector variables with a given analytical dependence yc. Euclidean distance was used as a similarity measure of vectors.

     yc=y0/rbet,  r - rank

Dear Igor, 

Instead of using the classic Euclidean distance formula for the additional criterion, which may present some problems when synthesizing tangible and intangible factors (due to metric scales, weighs and local values close to zero). Try instead with compatibility measure indeces, particularly with Compatibility index G, which I believe is a better estimator of vectors similarity measure. 

Best regards,

Claudio

Dear Claudio.

I ask you to recommend me an article with Compatibility index G

Dear Igor,

There are some articles in the IJAHP journal and at least one Book: Measuring in Weighted Environment: moving from metric to order topology", 2012.  I`m also attaching an article about this topic (sorry for the self reference).

Best regards,

Claudio