Abstract
The essence of AHP is to evaluate objects in terms of the eigen vector of the comparison matrix. But when the number of objects, n, is too large, it causes often worse reliability for an observer to evaluate all paired comparisons at a time. So it is necessary to decompose the whole set of pairs into several classes, and for each class to be evaluated by one observer. We propose the decomposition by BIBD (balanced incomplete block design) well known in the field of experimental design or combinatorics. We show by simulation experiments that our method gives better evaluations than the ordinary AHP. In connection with these, we show that the logarithmic least square method, which has been proposed by several authors, gives very good approximation to the eigen vector method when n is rather small, and that the former completely coincides with the latter when n &ie; 3, surprisingly.
