A set-theoretic view of belief functions: Logical operations and approximations by fuzzy sets

Studies in Fuzziness and Soft Computing

Volumn 219, Issue , 2008, Pages 375-410

  Dubois, Didier ^a   Prade, Henri ^a  

^a NONE

Author keywords

Fuzzy set; Knowledge representation; Possibility measure; Theory of evidence

Indexed keywords

EID: 38849184167     PISSN: 14349922     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-44792-4_14     Document Type: Article

References (44)

1. A. P. Dempster, "Upper and lower probabilities induced by a multivalued mapping." Annals of Mathematical Statistics, 38, 1967, pp. 325-339.
2. D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.
3. D. Dubois and H. Prade, "Additions of interactive fuzzy numbers," IEEE Trans. on Automatic Control, 26, 1981, 926-936.
4. D. Dubois and H. Prade, "On several representations of an uncertain body of evidence," Fuzzy Information and Decision Processes, edited by M. M. Gupta, E. Sanchez, North-Holland, Amsterdam, 1982, pp. 167-181.
5. D. Dubois and H. Prade, "Unfair coins and necessity measures. Towards a possibilistic interpretation of histograms." Fuzzy Sets and Systems 10, 1983, pp. 15-20.
6. D. Dubois and H. Prade, "Fuzzy sets and statistical data," European Journal of Operational Research, 25(3), 1986, 345-356.
7. D. Dubois and H. Prade, Théorie des Possibilités. Applications à la Représentation des Connaissances en Informatique, Masson, Paris, 1985.
8. D. Dubois and H. Prade, "A review of fuzzy set aggregation connectives," Information Sciences, 36, 1985, pp. 85-121.
9. D. Dubois and H. Prade, "Additivity and monotonicity of measures of information defined in the setting of Shafer's evidence theory." BUSEFAL (Université P. Sabatier, Toulouse), No. 24, 1985, pp. 64-76.
10. D. Dubois, R. Giles and H. Prade, "On the unicity of Dempster's rule of combination." International Journal of Intelligent Systems, 1 2), 1986, 133-142.
11. I. R. Ford, Jr., D. R. Fulkerson, Flows in Networks. Princeton University Press, Princeton, N.J., 1962.
12. R. Fortet and M. Kambouzia, "Ensembles aléatoires et ensembles flous," Publications Econométriques, IX, fascicule 1, 1976, pp. 1-23.
13. I. R. Goodman, "Fuzzy sets as equivalence classes of random sets." In: Fuzzy Set and Possibility Theory: Recent Developments, edited by R. R. Yager, Pergamon Press, Oxford, 1982, pp. 327-342.
14. I. R. Goodman, "Characterization of n-ary fuzzy set operations which induce homomorphic random set operations," In: Fuzzy Information and Decision Processes, edited by M. M. Gupta and E. Sanchez, North-Holland, Amsterdam, 1982, pp. 203-212.
15. M. Higashi and G. Klir, "Measures of uncertainty and information based on possibility distributions." International Journal of General Systems, 9, 1983, pp. 43-58.
16. U. Höhle, "Fuzzy filters: A generalization of credibility measures." Proc. IF AC Symposium on Fuzzy Information, Knowledge Representation, and Decision Analysis, Marseille, June 1983, pp. 111-114.
17. J.Kampé de Feriet, "Interpretation of membership functions of fuzzy sets in terms of plausibility and belief." In: Fuzzy Information and Decision Processes, edited by M. M. Gupta and E. Sanchez, North-Holland, Amsterdam, 1982, pp. 93-98.
18. D. H. Kranz, R. D. Luce, R. Suppes and A. Tversky, Foundations of Measurement. Vol. I, Academic Press, New York, 1971.
19. H. T. Nguyen, "On random sets and belief functions." Journal of Mathematical Analysis and Applications, 65, 1978, pp. 531-542.
20. E. M. Oblow, "A hybrid uncertainty theory," Proc. 5th International Workshop: "Expert Systems and their Applications," Avignon, May 13-15, 1985, pp. 1193-1201, published by ADI Paris.
21. H. Prade and C. Testemale, "Representation of soft constraints and fuzzy attribute values by means of possibility distributions in databases." In: The Analysis of Fuzzy Information, edited by J. C. Bezdek, CRC Press, Boca Raton, Fl., 1986, to appear, Vol. II.
22. T. Sales, "Fuzzy sets as set classes," Stochastica (Barcelona, Spain), VI, 1982, pp. 249-264.
23. B. Schweizer and A. Sklar, "Associative functions and abstract semi-groups." Publicationes Mathematicae Debrecen, 10, 1963, pp. 69-81.
24. G. Shafer, A Mathematical Theory of Evidence. Princeton University Press, Princeton, N.J., 1976.
25. G. Shafer, Belief Functions and Possibility Measures, Working Paper No. 163, School of Business, The University of Kansas, Lawrence, 1984.
26. P. Walley and T. Fine, "Towards a frequentist theory of upper and lower probability." The Annals of Statistics, 10, 1982, pp. 741-761.
27. Wang Pei-Zhuang, "From the fuzzy statistics to the falling random subsets." In: Advances in Fuzzy Sets, Possibility Theory and Applications, edited by P. P. Wang, Plenum Press, New York, 1983, pp. 81-96.
28. Wang Pei-Zhuang and E. Sanchez, "Treating a fuzzy subset as a projectable random subset." In: Fuzzy Information and Decision Processes, edited by M.M. Gupta and E. Sanchez, North-Holland, Amsterdam, 1982, pp. 213-220.
29. R. R. Yager, "Hedging in the combination of evidence." Journal of Information and Optimization Science, 4, No. 1, pp. 73-81, 1983.
30. R. R. Yager, "Entropy and specificity in a mathematical theory of evidence." Int. Journal of General Systems, 9, 1983, pp. 249-260.
31. R. R. Yager, "On different classes of linguistic variables defined via fuzzy subsets," Kybernetes, 13, 1984, pp. 103-110.
32. R. R. Yager, "Arithmetic and other operations on Dempster-Shafer structures," Tech. Report MII-508, Iona College, New Rochelle, N.Y., 1985.
33. R. R. Yager, The entailment principle for Dempster-Shafer granule," Tech. Report MII-512, Iona College, New Rochelle, N.Y., 1985.
34. R. R. Yager, Reasoning with uncertainty in expert systems." Proc. 9th Int. Joint Conf. on Artificial Intelligence, Los Angeles, 1985, pp. 1295-1297.
35. L. A. Zadeh, "Fuzzy sets," Information and Control, 8, 1965, pp. 338-353.
36. L. A. Zadeh, "Calculus of fuzzy restrictions." In: Fuzzy Sets and their Applications to Cognitive and Decision Processes, edited by L. A. Zadeh, K. S. Fu, K. Tanaka, M. Shimura, Academic Press, New York, 1975, pp. 1-39.
37. L. A. Zadeh, "PRUF: A meaning representation language for natural languages." Int. J. Man-Machine Studies, 10, 1978, pp. 395-460.
38. L. A. Zadeh, "Fuzzy sets as a basis for a theory of possibility." Fuzzy Sets and Systems, 1, 1978, pp. 3-28.
39. L.A. Zadeh, "A theory of approximate reasoning." In: Machine Intelligence, Vol. 9, edited by J. Hayes, D. Michie and L. I. Mikulich, John Wiley, New York, 1979, pp. 149-194.
40. L. A. Zadeh, "Fuzzy sets and information granularity." In: Advances in Fuzzy Set Theory and Applications, edited by M. M. Gupta, R. K. Ragade and R. R. Yager, North-Holland, Amsterdam, 1979, pp. 3-18.
41. L. A. Zadeh, "On the validity of Dempster's rule of combination of evidence." Memo UCB/ERL No. 79/24, University of California, Berkeley, 1979.
42. L. A. Zadeh, "A simple view of the Dempster-Shafer theory of evidence," Berkeley Cognitive Science Report No. 27, University of California, Berkeley, 1984.
43. Zhang Nan-Lun, "A preliminary study of the theoretical basis of the fuzzy set." BUSEFAL (Univ. P. Sabatier, Toulouse), No. 19, 1984, pp. 58-67.
44. Zhang Nan-Lun, "The membership and probability characteristics of random appearance," Journal of Wuhan Institute of Building Materials No. 1, 1981.