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Multi-criteria Axiom Ranking Based on Analytic Hierarchy Process

  • Jianfeng Du
  • Rongfeng Jiang
  • Yong Hu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 406)

Abstract

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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References

  1. 1.
    Aguarón, J., Moreno-Jiménez, J.M.: The geometric consistency index: Approximated thresholds. European Journal of Operational Research 147(1), 137–145 (2003)CrossRefzbMATHGoogle Scholar
  2. 2.
    Barzilai, J.J.: Deriving weights from pairwise comparison matrices. Journal of the Operational Research Society 48, 1226–1232 (1997)zbMATHGoogle Scholar
  3. 3.
    Cao, D., Leung, L.C., Law, J.S.: Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach. Decision Support Systems 44(4), 944–953 (2008)CrossRefGoogle Scholar
  4. 4.
    Deng, X., Haarslev, V., Shiri, N.: Measuring inconsistencies in ontologies. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC 2007. LNCS, vol. 4519, pp. 326–340. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Du, J., Qi, G., Shen, Y.-D.: Lexicographical inference over inconsistent DL-based ontologies. In: Calvanese, D., Lausen, G. (eds.) RR 2008. LNCS, vol. 5341, pp. 58–73. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Du, J., Qi, G., Shen, Y.: Weight-based consistent query answering over inconsistent SHIQ knowledge bases. Knowledge and Information Systems 34(2), 335–371 (2013)CrossRefGoogle Scholar
  7. 7.
    Du, J., Shen, Y.: Computing minimum cost diagnoses to repair populated DL-based ontologies. In: Proceedings of the 17th International World Wide Web Conference (WWW), pp. 575–584 (2008)Google Scholar
  8. 8.
    Ergu, D., Kou, G., Peng, Y., Shi, Y.: A simple method to improve the consistency ratio of the pair-wise comparison matrix in anp. European Journal of Operational Research 213(1), 246–259 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Forman, E., Peniwati, K.: Aggregating individual judgments and priorities with the analytic hierarchy process. European Journal of Operational Research 108, 165–169 (1998)CrossRefzbMATHGoogle Scholar
  10. 10.
    Huang, Z., van Harmelen, F., ten Teije, A.: Reasoning with inconsistent ontologies. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 454–459 (2005)Google Scholar
  11. 11.
    Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR), pp. 358–366 (2008)Google Scholar
  12. 12.
    Kalyanpur, A., Parsia, B., Sirin, E., Cuenca-Grau, B.: Repairing unsatisfiable concepts in OWL ontologies. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 170–184. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Lam, S.C., Pan, J.Z., Sleeman, D.H., Vasconcelos, W.W.: A fine-grained approach to resolving unsatisfiable ontologies. In: Proceedings of the International Conference on Web Intelligence (WI), pp. 428–434 (2006)Google Scholar
  14. 14.
    Li, H., Ma, L.: Detecting and adjusting ordinal and cardinal inconsistencies through a graphical and optimal approach in ahp models. Computers & OR 34(3), 780–798 (2007)CrossRefzbMATHGoogle Scholar
  15. 15.
    Michiels, W., Aarts, E., Korst, J.: Theoretical aspects of local search. Springer (2007)Google Scholar
  16. 16.
    Mu, K., Liu, W., Jin, Z.: A general framework for measuring inconsistency through minimal inconsistent sets. Knowledge and Information Systems 27(1), 85–114 (2011)CrossRefGoogle Scholar
  17. 17.
    Qi, G., Hunter, A.: Measuring incoherence in description logic-based ontologies. In: Aberer, K., et al. (eds.) ISWC/ASWC 2007. LNCS, vol. 4825, pp. 381–394. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Qi, G., Ji, Q., Pan, J.Z., Du, J.: Extending description logics with uncertainty reasoning in possibilistic logic. International Journal of Intelligent Systems 26(4), 353–381 (2011)CrossRefzbMATHGoogle Scholar
  19. 19.
    Saaty, T.L.: The analytic hierarchy process: planning, priority setting, resource allocation. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  20. 20.
    Vaidya, O.S., Kumar, S.: Analytic hierarchy process: An overview of applications. European Journal of Operational Research 169(1), 1–29 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Xu, Z., Wei, C.: A consistency improving method in the analytic hierarchy process. European Journal of Operational Research 116(2), 443–449 (1999)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jianfeng Du
    • 1
  • Rongfeng Jiang
    • 1
  • Yong Hu
    • 1
  1. 1.Guangdong University of Foreign StudiesGuangzhouChina

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