Abstract
Belief merging operators combine multiple belief bases (a profile) into a collective one. When the conjunction of belief bases is consistent, all the operators agree on the result. However, if the conjunction of belief bases is inconsistent, the results vary between operators. There is no formal manner to measure the results and decide on which operator to select. So, in this paper we propose to evaluate the result of merging operators by using three ordering relations (fairness, satisfaction and strength) over operators for a given profile. Moreover, a relation of conformity over operators is introduced in order to classify how well the operator conforms to the definition of a merging operator. By using the four proposed relations we provide a comparison of some classical merging operators and evaluate the results for some specific profiles.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baral, C., Kraus, S., Minker, J., Subrahmanian, V.S.: Combining knowledge bases consisting of first-order analysis. Com. Int. 8, 45–71 (1992)
Everaere, P., Konieczny, S., Marquis, P.: The strategy-proofness landscape of merging. J. of Art. Int. Research 28, 49–105 (2007)
Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 191–236. Springer, Heidelberg (2005)
Hunter, A., Konieczny, S.: On the measure of conflicts: Shapley inconsistency values. Artificial Intelligence 174(14), 1007–1026 (2010)
Konieczny, S.: On the difference between merging knowledge bases and combining them. In: KR 2000, pp. 135–144 (2000)
Konieczny, S., Lang, J., Marquis, P.: DA2 merging operators. Artif. Intell. 157(1-2), 49–79 (2004)
Konieczny, S., Pino-Pérez, R.: On the logic of merging. In: KR 1998, pp. 488–498 (1998)
Konieczny, S., Pino-Pérez, R.: Merging information under constraints: a logical framework. J. of Logic. and Computation 12(5), 773–808 (2002)
Konieczny, S., Pino-Pérez, R.: Logic based merging. Journal of Philosophical Logic 40(2), 239–270 (2011)
Liberatore, P., Schaerf, M.: Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering 10(1), 76–90 (1998)
Lin, J., Mendelzon, A.: Knowledge base merging by majority. In: Pareschi, R., Fronhoefer, B. (eds.) Dynamic Worlds: From the Frame Problem to Knowledge Management. Kluwer Academic (1999)
Liu, W., Qi, G., Bell, D.A.: Adaptive merging of prioritized knowledge bases. Fundam. Inform. 73(3), 389–407 (2006)
Marchi, J., Bittencourt, G., Perrussel, L.: Prime forms and minimal change in propositional belief bases. Ann. Math. Artif. Intell. 59(1), 1–45 (2010)
Revesz, P.Z.: On the Semantics of Arbitration. Journal of Algebra and Computation 7(2), 133–160 (1997)
Yager, R.R.: On the dempster-shafer framework and new combination rules. Inf. Sci. 41(2), 93–137 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pozos-Parra, P., McAreavey, K., Liu, W. (2013). On the Merit of Selecting Different Belief Merging Operators. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds) Scalable Uncertainty Management. SUM 2013. Lecture Notes in Computer Science(), vol 8078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40381-1_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-40381-1_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40380-4
Online ISBN: 978-3-642-40381-1
eBook Packages: Computer ScienceComputer Science (R0)