On the analytic hierarchy process with conflicting criteria

In the Analytic Hierarchy Process (AHP) developed by T. L. Saaty elements from one hierarchical level (such as alternatives) are pair-wise compared with regard to each element from immediately higher level of hierarchy (e. g. by criteria) on 1-9 scale. By this procedure weights of criteria are established by the eigenvalue method and the best alternative is found with regard to a given goal. However, in real-world multiple criteria decision making (MCDM) problems some criterion might be in conflict with other criteria, but this problem is completely neglected in the standard AHP. The aim of the article is to propose a new method for the evaluation of criteria weights based both on their pair-wise comparisons and the degree of a conflict/agreement among criteria. This degree for each pair of alternatives is expressed by a value from [-1,1] interval, where positive values denote an agreement, while negative values denote a conflict, and all the degrees form a conflict matrix. Information from the conflict matrix is converted into criteria (sub) weights, and the final weights of criteria are given as an aggregation of weights from pair-wise comparisons and from the conflict matrix. The use of the method is illustrated by an example.