Analytic hierarchy process (AHP) has been criticized considerably for possible rank reversal phenomenon caused by the addition or deletion of an alternative. While in many cases this is a perfectly valid phenomenon, there are also many cases where ranks should be preserved. Our findings indicate that using the geometric mean reduces the variance in ratings substantially; hence, yielding lower i...

analytic hierarchy process (ahp) has been criticized considerably for possible rank reversal phenomenon caused by the addition or deletion of an alternative. while in many cases this is a perfectly valid phenomenon, there are also many cases where ranks should be preserved. our findings indicate that using the geometric mean reduces the variance in ratings substantially; hence, yielding lower i...

Analytic hierarchy process (AHP) has been considerably criticized for possible rank reversal phenomenon caused by the addition or deletion of an alternative. This paper looks into the cause of rank reversal phenomenon and finds that rank reversal is caused by change of local priorities before and after an alternative is added or deleted. An approach is therefore proposed to keep the local prior...

The problem of aggregating multiple criteria to form an overall measure is of considerable importance in many disciplines. The ordered weighted averaging (OWA) aggregation, introduced by Yager, uses weights assigned to the ordered values rather than to the specific criteria. This allows one to model various aggregated preferences, preserving simultaneously the impartiality (neutrality) with res...

For some multi-criteria decision aiding methods, the relative ranks of two actions may be inverted when the original set is altered. This phenomenon is known as rank reversal. In this contribution, we formalise rank reversal for the Promethee II method and derive the exact conditions for its occurrence when one ore more actions are added or removed from/to the original set. These conditions eve...

PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the question of rank stability and choice of the damping factor (a parameter in the algorithm) is clearly important. We investigate PR as a function of the damping fa...