I am seeking to carry out a simple AHP to identify which features are the most important for guest visiting a particular Hotel. Though, I have a question concerning the values in the Saaty matrix if the matrix is based on preferences stemming from several people. It is clear that the average of the answers is to be computed based on the geometric mean for each pairwise comparison. However, if I compute the geometric mean, then the importance of a particular i dimension over an other j dimension can be a non-integer value. My question is how to handle this values in the Saaty-matrix? It is recommended to round them to the next integer (or to the reciprocal of one of the integers originally used in the matrix) and use only integer values in the aggregated matrix, or can one leave even the non-integer values as they were obtained after computing the geometric mean?
Thank You in advance!
I would be careful in your use of the analytical hierarchy process (AHP) as it has known and serious issues with preference rank reversal which change the overall priority ranking when an alternative is added or deleted from the initial set of alternatives. In axiomatic decision analysis and utility theory rank reversal in is related to the concept of irrelevant alternatives as given by the following axiom: Adding new acts (alternatives) to a decision problem under uncertainty, each of which is weakly dominated (preferred) by or is equivalent to some old act, has no effect on the optimality or non-optimality of an old act (Luce and Raiffa 1957, p. 288). In stead I would use a multi-objective value hierarchy such as the one used by Parnell, 2013. I know this does not answer your question about the Saaty matrix, but I believe the use of AHP will result in flawed or sub-optimal preferences.
Hi Mr Árva,
You can solve this problem using a software. I suggest you the Expert Choice trial version is apllied to make AHP process easly.
Good job!
Hi Árva,
Yes it is true that when it comes to several people in filling up the questionnaire, we need to find the geometric means which most of the time in the decimal forms. However, eigen vector will give us the answer which criteria is the most important. For me, I will let the value in the geometric means (decimal) and will calculated until I get the Eigen vector.
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix