Clusters and pivots for evaluating a large numberof alternatives in AHP

ahp has been successful in many cases but it has a major limitation: a larger number of alternatives requires a high number of judgements in the comparison matrices. in order to reduce this problem,we present a method with clusters and pivots. this method also helps with a further four problems of the analytic hierarchy process. it enlarges the comparison scale, facilitates the construction of a consistent or near consistent matrix, eliminates the problem of the choice of the priorities derivation method and allows the use of incomparable alternatives.