Multi-criteria Axiom Ranking Based on Analytic Hierarchy Process

Axiom ranking plays an important role in ontology repairing. There has been a number of criteria that can be used in axiom ranking, but there still lacks a framework for combining multiple criteria to rank axioms. To provide such a framework, this paper proposes an analytic hierarchy process (AHP) based approach. It expresses existing criteria in a hierarchy and derives weights of criteria from pairwise comparison matrices. All axioms are then ranked by a weighted sum model on all criteria. Since the AHP based approach does not work when a pairwise comparison matrix is insufficiently consistent, a method is proposed to adjust the matrix. The method expresses the adjustment problem as an optimization problem solvable by level-wise search. To make the proposed method more practical, an approximation of it is also proposed. Experimental results show that the proposed method is feasible for small pairwise comparison matrices but is hard to scale to large ones, while the approximate method scales well to large pairwise comparison matrices.

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