Article
Full entry |
PDF
(2.0 MB)
Feedback
PDF
(2.0 MB)
Feedback
Keywords:
Dempster-Shafer theory; possibilistic approach; belief function
Dempster-Shafer theory; possibilistic approach; belief function
Summary:
The elementary notions and relations of the so called Dempster–Shafer theory, introducing belief functions as the basic numerical characteristic of uncertainty, are modified to the case when probabilistic measures and basic probability assignments are substituted by possibilistic measures and basic possibilistic assignments. It is shown that there exists a high degree of formal similarity between the probabilistic and the possibilistic approaches including the role of the possibilistic Dempster combination rule and the relations concerning the possibilistic nonspecificity degrees.
References:
[1] Cooman G. De: Possibility theory I – III. Internat. J. Gen. Systems 25 (1997), 291–323, 325–351, 353–371 DOI 10.1080/03081079708945160
[2] Dubois D., Prade H.: Théorie des Possibilités – Applications à la Représentation des Connaissances en Informatique. Mason, Paris 1985 Zbl 0674.68059
[3] Dubois D., Prade, H., Sabbadin R.: Qualitative decision theory with Sugeno integrals. In: Uncertainty in Artificial Intelligence – Proceedings of the 14th Conference (G. T. Cooper and S. Morales, eds.), Madison, Wisconsin, pp. 121–128 MR 1806517 | Zbl 0984.91023
[4] Dubois D., Godo L., Prade, H., Zapico A.: Possibilistic representation of qualitative utility – an improved characterization. In: Proc. 6th International Conference on Information Processing and Management of Uncertainty (IPMU), Paris 1998, Vol. I, pp. 180–187
[5] Hisdal E.: Conditional possibilities, independence and noninteraction. Fuzzy Sets and Systems 1 (1978), 283–297 DOI 10.1016/0165-0114(78)90019-2 | Zbl 0393.94050
[6] Kramosil I.: A probabilistic analysis of the Dempster combination rule. In: The Logica Yearbook 1997 (T. Childers, ed.), Filosofia, Prague 1998, pp. 175–187 MR 1614001
[7] Kramosil I.: Alternative definitions of conditional possibilistic measures. Kybernetika 34 (1998), 2, 137–147 MR 1621506
[8] Kramosil I.: On stochastic and possibilistic independence. Neural Network World 4 (1999), 275–296
[9] Kramosil I.: Boolean–like interpretation of Sugeno integral. In: Proc. European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU 99), (A. Hunter and S. Parsons, eds., Lecture Notes in Artificial Intelligence 1638), Springer Verlag, Berlin 2000, pp. 245–255 MR 1773322 | Zbl 0930.28015
[10] Kramosil I.: Nonspecificity degrees of basic probability assignments in Dempster–Shafer theory. Computers and Artificial Intelligence 18 (1999), 6, 559–574 MR 1742716 | Zbl 0989.60009
[11] Vejnarová J.: Composition of possibility measures on finite spaces – preliminary results. In: Proc. 7th International Conference on Information Processing and Management of Uncertainty (IPMU), Paris 1998, Vol. I, 25–30
[12] Zadeh L. A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978), 3–28 DOI 10.1016/0165-0114(78)90029-5 | MR 0480045
Search
Partner of
