Graphoid properties of qualitative possibilistic independence relations

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 13, Issue 1, 2005, Pages 59-96

  Amor, Nahla Ben ^a   Benferhat, Salem ^b  

^a UNIVERSITY OF TUNIS   (Tunisia)

^b UNIVERSITÉ D'ARTOIS   (France)

Author keywords

Graphoid properties; Plausibility relations; Possibilistic independence

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; SET THEORY;

GRAPHOID PROPERTIES; PLAUSIBILITY RELATIONS; POSSIBILISTIC INDEPENDENCE; POSSIBILITY THEORY FRAMEWORK;

UNCERTAIN SYSTEMS;

EID: 17444386018     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021848850500331X     Document Type: Article

References (27)

1. N. Ben Amor. Qualitative Possibilistic Graphical Models: From Independence to Propagation Algorithms. PhD thesis, Institut Suprieur de Gestion, Tunis, 2002.
2. N. Ben Amor, S. Benferhat, D. Dubois, K. Mellouli, and H. Prade. A theoretical framework for possibilistic independence in a weakly ordered setting. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10/2:117-155, 2002.
3. B. Bouchon-Meunier. Fuzzy inference nd conditional possibility distributions. Fuzzy Sets and Systems, 23:23-41, 1987.
4. B. Bouchon-Meunier, G. Coletti, and C. Marsala. Independence and possibilistic conditioning. Annals of Mathematics and Artificial Intelligence, 35:107-123, 2000.
5. R. R. Bouckaert. Bayesian belief networks and conditional independencies. In Technical report RUU-CS-92-36. Department of computer science, Utrecht University, 1992.
6. C. Boutilier, R. I. Brafman, H. H. Hoos, and D. Poole. Reasoning with conditional ceteris paribus preference statements. In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI'99), pages 71-80, San Francisco, CA, 1999. Morgan Kaufmann Publishers.
7. A. D. Dawid. Conditional independence in statistical theory. Journal of the Royal Statistical Society, 41:1-31, 1979.
8. L.M de Campos and J. F. Huete. Independence concepts in possibility theory: Part i. Fuzzy Sets and Systems, 103:127-152, 1999.
9. L.M de Campos and J. F. Huete. Independence concepts in possibility theory: Part ii. Fuzzy Sets and Systems, 103:487-505, 1999.
10. G. de Cooman. Possibility theory ii: Conditional possibility. International Journal of General Systems, 25:325-351, 1997.
11. G. de Cooman. Possibility theory iii: Possibilistic independence. International Journal of General Systems, 25:353-371, 1997.
12. A. Dempster. Upper and lower probabilities induces by multivalued mappings. Annals of Mathematics and Statistics, 38:325-339, 1967.
13. D. Dubois. Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and Artificial Intelligence, 5:403-416, 1986.
14. D. Dubois and H. Prade. Conditioning in possibility and evidence theories - a logical viewpoint. In B. Bouchon-Meunier, L. Saitta, and R.R. Yager, editors, Uncertainty and intelligent systems, Lecture Notes in Computer Science, volume 313, pages 401-408. 1988.
15. D. Dubois and H. Prade. Possibility theory: An approach to computerized, Processing of uncertainty. Plenium Press, New York, 1988.
16. D. Dubois and H. Prade. Numerical representation of acceptance. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI'95), pages 149-156, San Francisco, CA, 1995. Morgan Kaufmann Publishers.
17. P. Fonck. Conditional independence in possibility theory. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI'94), pages 221-226, San Francisco, CA, 1994. Morgan Kaufmann Publishers.
18. P. Fonck. Rseaux d'infrence pour le raisonnement possibiliste. PhD thesis, Universit de Lige, Facult des Sciences, 1994.
19. P. Fonck. A comparative study of possibilistic conditional independence and lack of interaction. International Journal of Approximate Reasoning, 16:149-171, 1997.
20. N. Friedman and J. Halpern. Plausible measures and default reasoning. In Proceedings of American Association for Artificial Intelligence Conference (AAAI'96), pages 1297-1304, Portland (Oregon), 1996.
21. E. Hisdal. Conditional possibilities independence and non interaction. Fuzzy Sets and Systems, 1:283-297, 1978.
22. J. Pearl. Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmman, San Francisco (California), 1988.
23. J. Pearl and A. Paz. Graphoids: A graph-based logic for reasoning about relevance relations. In Technical report 850038 (R-53-L). Cognitive systems laboratory, University of California, 1995.
24. M. Studený. Semigraphoids and structures of probabilistic conditional independence. Annals of Mathematics and Artificial Intelligence, 21:71-98, 1997.
25. B. Vantaggi. Conditional independence in a finite coherent setting. Annals of Mathematics and Artificial Intelligence, 32:287-314, 2001.
26. J. Vejnarová. Conditional independence relations in possibility theory. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 8(3):253-269, 2000.
27. L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning. Information science, 9:43-80, 1975.