Possibilistic alternatives of elementary notions and relations of the theory of belief functions

Ivan Kramosil

Kybernetika (2001)

  • Volume: 37, Issue: 2, page [109]-126
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Kramosil, Ivan. "Possibilistic alternatives of elementary notions and relations of the theory of belief functions." Kybernetika 37.2 (2001): [109]-126. <http://eudml.org/doc/33521>.

@article{Kramosil2001,
abstract = {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.},
author = {Kramosil, Ivan},
journal = {Kybernetika},
keywords = {Dempster-Shafer theory; possibilistic approach; belief function; Dempster-Shafer theory; possibilistic approach; belief function},
language = {eng},
number = {2},
pages = {[109]-126},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Possibilistic alternatives of elementary notions and relations of the theory of belief functions},
url = {http://eudml.org/doc/33521},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Kramosil, Ivan
TI - Possibilistic alternatives of elementary notions and relations of the theory of belief functions
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 2
SP - [109]
EP - 126
AB - 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.
LA - eng
KW - Dempster-Shafer theory; possibilistic approach; belief function; Dempster-Shafer theory; possibilistic approach; belief function
UR - http://eudml.org/doc/33521
ER -

References

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  2. Dubois D., Prade H., Théorie des Possibilités – Applications à la Représentation des Connaissances en Informatique, Mason, Paris 1985 Zbl0674.68059
  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 Zbl0984.91023MR1806517
  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 (1998) 
  5. Hisdal E., 10.1016/0165-0114(78)90019-2, Fuzzy Sets and Systems 1 (1978), 283–297 (1978) Zbl0393.94050DOI10.1016/0165-0114(78)90019-2
  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 (1997) MR1614001
  7. Kramosil I., Alternative definitions of conditional possibilistic measures, Kybernetika 34 (1998), 2, 137–147 (1998) MR1621506
  8. Kramosil I., On stochastic and possibilistic independence, Neural Network World 4 (1999), 275–296 (1999) 
  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 Zbl0930.28015MR1773322
  10. Kramosil I., Nonspecificity degrees of basic probability assignments in Dempster–Shafer theory, Computers and Artificial Intelligence 18 (1999), 6, 559–574 (1999) Zbl0989.60009MR1742716
  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 (1998) 
  12. Zadeh L. A., 10.1016/0165-0114(78)90029-5, Fuzzy Sets and Systems 1 (1978), 3–28 (1978) MR0480045DOI10.1016/0165-0114(78)90029-5

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