A method to estimate results of unknown comparisons in the binary analytic hierarchy process

In this paper we propose an algorithm to estimate results of unknown comparisons in binary AHP. For incomplete comparison case, which includes unknown pairwise comparisons, there are various methods to calculate weights, for example, Harker method, Two-Stage method and so on. However these methods are to estimate weights of activities but not to estimate results of unknown comparisons directly. We intend to estimate results of unknown comparisons directly. For this purpose we introduce a kind of syllogism which is to connect two activities with unknown comparisons by an arrow so that there are no cycles in the graph corresponding to the given comparison matrix. We apply our algorithm, first, to estimate results of unknown comparisons and compare our weights with Harker’s and Two-Stage’s, for four examples, respectively. Next, we also apply our algorithm to construct comparison matrix using a personal computer and the performance of our algorithm is discussed based on simulation. From results of these examples and simulation, we can illustrate the effectiveness of the proposed algorithm.