A view on conditional measures through local representability of binary relations

International Journal of Approximate Reasoning

Volumn 47, Issue 3, 2008, Pages 268-283

  Coletti, Giulianella ^a   Vantaggi, Barbara ^b  

^a UNIVERSITY OF PERUGIA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Conditional belief functions; Conditional necessities; Conditional plausibilities; Conditional possibilities; Local representability; Weakly additive ordinal degree of belief

Indexed keywords

FUNCTION EVALUATION; UNCERTAINTY ANALYSIS;

CONDITIONAL BELIEF FUNCTIONS; CONDITIONAL PLAUSIBILITIES;

BINARY CODES;

EID: 38149045817     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2007.05.007     Document Type: Article

References (45)

1. Aumann R.J. Utility theory without the completeness axiom. Econometrica 30 3 (1962) 445-461
2. Ben Yaghlane B., Smets P., and Mellouli K. About conditional belief function independence. Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Lecture Notes in Comput. Sci. 2143 (2001), Springer, Berlin 340-349
3. Bernardi S., and Coletti G. A conditional decision model. Approaches to Reasoning with Uncertainty. Lecture Notes in Comput. Sci. 2143 (2001), Springer, Berlin 108-119
4. B. Bouchon-Meunier, G. Coletti, C. Marsala, Possibilistic conditional events, in: Proc. Information Processing and Management of Uncertainty in knowledge-based systems (IPMU 2000), Madrid, 2000, pp. 1561-1566.
5. Bouchon-Meunier B., Coletti G., and Marsala C. Independence and possibilistic conditioning. Ann. Math. Artif. Intell. 35 (2002) 107-124
6. Bouchon-Meunier B., Coletti G., and Marsala C. Conditional possibility and necessity. In: Bouchon-Meunier, Gutierréz-Rions, Magdalena, and Yager (Eds). Technologies for Constructing Intelligent Systems (2002), Springer-Verlag 59-71
7. Capotorti A., Coletti G., and Vantaggi B. Non-additive ordinal relations representable by lower or upper probabilities. Kybernetika 34 1 (1998) 79-90
8. A. Capotorti, G. Coletti, B. Vantaggi, Preferences representable by lower expectation: some characterizations, Theory and Decision, in press (A short version is in Proc. FUR 06, Rome, 2006).
9. Coletti G. A weak coherence condition for conditional comparative probabilities. In: Bouchon-Meunier, et al. (Ed). Uncertainty in Intelligent Systems (1993), Elsevier Sci. Publ. BV 195-201
10. G. Coletti, Non-additive ordinal relations representable by conditional probabilities and its use in expert systems, in: Proc. of IPMU'96, Granada, 1996, pp. 43-48.
11. G. Coletti, M. Mastroleo, Conditional belief functions: a comparison among different definitions, in: Proc. of WUPES 2006, Mikulov (Czech Rep.), 2006, pp. 24-35.
12. Coletti G., and Regoli G. Probabilitá qualitative non archimedee e realizzabilitá. Riv. Mat. Sci. Econom. Soc. 6 (1983) 79-99
13. Coletti G., and Scozzafava R. From conditional events to conditional measures: a new axiomatic approach. Ann. Math. Artif. Intell. 32 (2001) 373-392
14. G. Coletti, R. Scozzafava, Locally additive comparative probabilities, in: 2nd Int. Symp. on Imprecise Probabilities and Their Applications (ISIPTA'01), Ithaca (New York), 2001, pp. 83-92.
15. Coletti G., and Scozzafava R. Probabilistic logic in a coherent setting. Trends in Logic vol. 15 (2002), Kluwer, Dordrecht/Boston/London
16. Coletti G., and Scozzafava R. Toward a general theory of conditional beliefs. Int. J. Intell. Syst. 21 3 (2006) 229-259
17. G. Coletti, B. Vantaggi, Comparative conditional possibilities, in: Godo (Ed.), Lecture Notes in Computer Science, LNAI 3571, 2005, pp. 872-883.
18. Coletti G., and Vantaggi B. Possibility theory: conditional independence. Fuzzy Sets Syst. 57 (2006) 1491-1513
19. Coletti G., and Vantaggi B. Representability of ordinal relations on a set of conditional events. Theory and Decision 60 (2006) 137-174
20. Coletti G., and Vantaggi B. Comparative models ruled by possibility and necessity: a conditional world. Int. J. Approx. Reason. 45 (2007) 341-363
21. Cox R.T. Probability, frequency and reasonable expectation. Am. J. Phys. 14 1 (1946) 1-13
22. De Baets B., Tsiporkova E., and Mesiar R. Conditioning in possibility theory with strict order norms. Fuzzy Sets Syst. 106 (1999) 121-129
23. De Baets B., and De Meyer H. Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity. Fuzzy Sets Syst. 152 (2005) 249-270
24. De Baets B., De Meyer H., De Schuymer B., and Jenei S. Cyclic evaluation of transitivity of reciprocal relations. Social Choice and Welfare 26 (2006) 217-238
25. de Finetti B. Sul significato soggettivo della probabilità. Fundam. Mat. 17 (1931) 293-329
26. de Finetti B. Les probabilites nulles. Bull. Sci. Math. 60 (1936) 275-288
27. De Schuymer B., De Meyer H., De Baets B., and Jenei S. On the cycle-transitivity of the dice model. Theory and Decision 54 (2003) 264-285
28. Dempster A.P. A generalization of Bayesian inference. The Royal Stat. Soc. B 50 (1968) 205-247
29. Denoeux T., and Smets P. Classification using belief functions: the relationship between the case-based and model-based approaches. IEEE Trans. Syst. Man Cybernet. B 36 (2006) 1395-1406
30. Dubois D. Belief structure, possibility theory and decomposable confidence measures on finite sets. Comput. Artif. Intell. 5 (1986) 403-416
31. Dubois, and Prade H. Possibility Theory (1988), Plenum Press, New York
32. Dubois D., Prade H., and Sabbadin R. Decision-theoretic foundations of qualitative possibility theory. Eur. J. Operat. Res. 128 (2001) 459-478
33. Ferracuti L., and Vantaggi B. Independence and conditional possibilities for strictly monotone triangular norms. Int. J. Intell. Syst. 21 3 (2006) 299-323
34. Jaffray J.Y. Bayesian updating and belief functions. IEEE Trans. Syst. Man Cybernet. 5 (1992) 1144-1152
35. Klement E.P., Mesiar R., and Pap E. Triangular Norms (2000), Kluwer, Dordrecht
36. Koopman B.O. The axioms and algebra of intuitive probability. Ann. Math. 41 (1940) 269-292
37. Kraft C.H., Pratt J.W., and Seidenberg A. Intuitive probability on finite sets. Ann. Math. Stat. 30 (1959) 408-419
38. Krantz D.H., Luce R.D., Suppes P., and Tversky A. Foundations of measurement. Additive and Polynomial Representations vol. 1 (1971), Academic Press, New York-London
39. Lehmann D. Generalized qualitative probability: Savage revisited. Proc. UAI ' 96 (1996) 381-388
40. Popper K.R. The Logic of Scientific Discovery (1959), Routledge, London
41. Rényi A. On conditional probability spaces generated by a dimensionally ordered set of measures. Theor. Probab. Appl. 1 (1956) 61-71
42. R. Scozzafava, B. Vantaggi, Fuzzy relations in a coherent conditional probability setting, in: Proc. 7th International Conference on Information and Management Sciences (IMS), Chengdu (China), 2006, pp. 496-500.
43. P. Smets, Belief function and transferable belief model, Documentation of SIPTA, 2000, www.sipta.org/documentation/belief/belief.ps.
44. Walley P. Belief function representations of statistical evidence. Ann. Stat. 4 (1987) 1439-1465
45. Wong S.K.M., Yao Y.Y., Bollmann P., and Burger H.C. Axiomatization of qualitative belief structure. IEEE Trans. Systems Man Cybernet. 21 (1991) 726-734