Evidential reasoning in large partially ordered sets

Annals of Operations Research

Volumn 195, Issue 1, 2012, Pages 135-161

  Denœux, Thierry ^a   Masson, Marie Hélène ^b  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

^b UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Belief functions; Classification; Clustering; Dempster Shafer theory; Evidence theory; Lattice intervals; Lattices; Learning; Preference relation; Preorder

Indexed keywords

EID: 84858703834     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-011-0887-2     Document Type: Article

References (39)

1. Charon, I., & Hudry, O. (1998). Lamarckian genetic algorithms applied to the aggregation of preferences. Annals of Operation Research, 80, 281-297.
2. Charon, I., & Hudry, O. (2010). An updated survey on the linear ordering problem for weighted or unweighted tournaments. Annals of Operation Research, 175, 107-158.
3. Cobb, B. R., & Shenoy, P. P. (2006). On the plausibility transformation method for translating belief function models to probability models. International Journal of Approximate Reasoning, 41(3), 314-330.
4. Dempster, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38, 325-339.
5. Dempster, A. P. (1968). Upper and lower probabilities generated by a random closed interval. Annals of Mathematical Statistics, 39(3), 957-966.
6. Denœux, T. (1995). A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Transactions on Systems, Man, and Cybernetics, 25(05), 804-813.
7. Denœux, T. (1997). Analysis of evidence-theoretic decision rules for pattern classification. Pattern Recognition, 30(7), 1095-1107.
8. Denœux, T. (2001). Inner and outer approximation of belief structures using a hierarchical clustering approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(4), 437-460.
9. Denœux, T. (2006). Constructing belief functions from sample data using multinomial confidence regions. International Journal of Approximate Reasoning, 42(3), 228-252.
10. Denoeux, T. (2008). Conjunctive and disjunctive combination of belief functions induced by non distinct bodies of evidence. Artificial Intelligence, 172, 234-264.
11. Denoeux, T., Younes, Z., & Abdallah, F. (2010). Representing uncertainty on set-valued variables using belief functions. Artificial Intelligence, 174(7-8), 479-499.
12. Dubois, D., & Prade, H. (1986). A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. International Journal of General Systems, 12(3), 193-226.
13. Fred, A., & Jain, A. (2002). Data clustering using evidence accumulation. In Proceedings of the 16th international conference on pattern Recognition, Quebec, Canada (pp. 276-328).
14. Fred, A., & Lourenço, A. (2008). Cluster ensemble methods: from single clusterings to combined solutions. Studies in Computational Intelligence (SCI), 126, 3-30.
15. Gonzales-Pachon, J., & Romero, C. (2007). Inferring consensus weights from pairwise comparison matrices without suitable properties. Annals of Operation Research, 154, 123-132.
16. Grabisch, M. (2009). Belief functions on lattices. International Journal of Intelligent Systems, 24, 76-95.
17. Grabisch, M., & Labreuche, C. (2005). Bi-capacities-I: definition, Möbius transform and interaction. Fuzzy Sets and Systems, 151, 211-236.
18. Hornik, K., & Leisch, F. (2005). Ensemble methods for cluster analysis. In A. Taudes (Ed.), Interdisciplinary studies in economics and management: Vol. 5. Adaptive information systems and modelling in economics and management science (pp. 261-268). Berlin: Springer.
19. Liu, L. (1996). A theory of Gaussian belief functions. International Journal of Approximate Reasoning, 14, 95-126.
20. Masson, M.-H., & Denœux, T. (2009). Belief functions and cluster ensembles. In C. Sossai & G. Chemello (Eds.), Proceedings of the 9th European conference on symbolic and quantitative approaches to reasoning with uncertainty (ECSQARU), Verona, Italy (pp. 323-334). Berlin: Springer.
21. Masson, M.-H., & Denœux, T. (2011). Ensemble clustering in the belief functions framework. International Journal of Approximate Reasoning, 52(1), 92-109.
22. Monjardet, B. (2003). The presence of lattice theory in discrete problems of mathematical social sciences. Why. Mathematical Social Sciences, 46(2), 103-144.
23. Owsinski, J. W. (1994). Preferences agreement, consensus-measuring, aggregation and control. Annals of Operation Research, 51(5), 217-240.
24. Oztürk, M., Tsoukiàs, A., & Vincke, P. (2005). Preference modelling. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multiple criteria decision analysis: state of the art surveys (pp. 27-72). Berlin: Springer.
25. Perny, P. (1998). Multicriteria filtering methods based onconcordance and non-discordance principles. Annals of Operation Research, 80, 137-165.
26. Shafer, G. (1976). A mathematical theory of evidence. Princeton: Princeton University Press.
27. Shafer, G., Shenoy, P. P., & Mellouli, K. (1987). Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning, 1, 349-400.
28. Shenoy, P. P. (1997). Binary joint trees for computing marginals in the Shenoy-Shafer architecture. International Journal of Approximate Reasoning, 17, 239-263.
29. Smets, P. (1990). The combination of evidence in the Transferable Belief Model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5), 447-458.
30. Smets, P. (1993). Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate Reasoning, 9, 1-35.
31. Smets, P. (2005). Belief functions on real numbers. International Journal of Approximate Reasoning, 40(3), 181-223.
32. Smets, P., & Kennes, R. (1994). The Transferable Belief Model. Artificial Intelligence, 66, 191-243.
33. Tritchler, D., & Lockwood, G. (1991). Modelling the reliability of paired comparisons. Journal of Mathematical Psychology, 35, 277-293.
34. Trohidis, K., Tsoumakas, G., Kalliris, G., & Vlahavas, I. (2008). Multi-label classification of music into emotions. In Proc. 9th international conference on music information retrieval (ISMIR), Philadelphia, PA, USA.
35. Wilson, N. (2000). Algorithms for Dempster-Shafer theory. In D. M. Gabbay & P. Smets (Eds.), Algorithms for uncertainty and defeasible reasoning: Vol. 5. Handbook of defeasible reasoning and uncertainty management (pp. 421-475). Boston: Kluwer Academic.
36. Yager, R. R. (1987). Set-based representations of conjunctive and disjunctive knowledge. Information Sciences, 41, 1-22.
37. Younes, Z., Abdallah, F., & Denœux, T. (2009). An evidence-theoretic k-nearest neighbor rule for multi-label classification. In LNAI: Vol. 5785. Proceedings of the 3rd international conference on scalable uncertainty management (SUM), Washington, DC, USA (pp. 297-308). Berlin: Springer.
38. Younes, Z., Abdallah, F., & Denoeux, T. (2010). Evidential multi-label classification approach to learning from data with imprecise labels. In Proceedings of IPMU, Dortmund, Germany, July 2010.
39. Zhang, M.-L., & Zhou, Z.-H. (2007). ML-KNN: a lazy learning approach to multi-label learning. Pattern Recognition, 40(7), 2038-2048.