Basic Probability Assignments Representable via Belief Intervals for Singletons in Dempster-Shafer Theory

Serafı́n Moral Garcı́a, Joaquı́n Abellán
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:229-234, 2021.

Abstract

Dempster-Shafer Theory (DST) or Evidence theory has been commonly employed in the literature to deal with uncertainty-based information. The basis of this theory is the concept of basic probability assignment (BPA). The belief intervals for singletons obtained from a BPA have recently received considerable attention for quantifying uncertainty in DST. Indeed, they are easier to manage than the corresponding BPA to represent uncertainty-based information. Nonetheless, the set of probability distributions consistent with a BPA is smaller than the one compatible with the corresponding belief intervals for singletons. In this research, we give a new characterization of BPAs representable by belief intervals for singletons. Such a characterization might be easier to check than the one provided in previous works. In practical applications, this result allows efficiently knowing when uncertainty can be represented via belief intervals for singletons rather than the associated BPA without loss of information.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-moral-garci-a21b, title = {Basic Probability Assignments Representable via Belief Intervals for Singletons in Dempster-Shafer Theory}, author = {Moral Garc\'{\i}a, Seraf\'{\i}n and Abell\'an, Joaqu\'{\i}n}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {229--234}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/moral-garci-a21b/moral-garci-a21b.pdf}, url = {https://proceedings.mlr.press/v147/moral-garci-a21b.html}, abstract = {Dempster-Shafer Theory (DST) or Evidence theory has been commonly employed in the literature to deal with uncertainty-based information. The basis of this theory is the concept of basic probability assignment (BPA). The belief intervals for singletons obtained from a BPA have recently received considerable attention for quantifying uncertainty in DST. Indeed, they are easier to manage than the corresponding BPA to represent uncertainty-based information. Nonetheless, the set of probability distributions consistent with a BPA is smaller than the one compatible with the corresponding belief intervals for singletons. In this research, we give a new characterization of BPAs representable by belief intervals for singletons. Such a characterization might be easier to check than the one provided in previous works. In practical applications, this result allows efficiently knowing when uncertainty can be represented via belief intervals for singletons rather than the associated BPA without loss of information.} }
Endnote
%0 Conference Paper %T Basic Probability Assignments Representable via Belief Intervals for Singletons in Dempster-Shafer Theory %A Serafı́n Moral Garcı́a %A Joaquı́n Abellán %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-moral-garci-a21b %I PMLR %P 229--234 %U https://proceedings.mlr.press/v147/moral-garci-a21b.html %V 147 %X Dempster-Shafer Theory (DST) or Evidence theory has been commonly employed in the literature to deal with uncertainty-based information. The basis of this theory is the concept of basic probability assignment (BPA). The belief intervals for singletons obtained from a BPA have recently received considerable attention for quantifying uncertainty in DST. Indeed, they are easier to manage than the corresponding BPA to represent uncertainty-based information. Nonetheless, the set of probability distributions consistent with a BPA is smaller than the one compatible with the corresponding belief intervals for singletons. In this research, we give a new characterization of BPAs representable by belief intervals for singletons. Such a characterization might be easier to check than the one provided in previous works. In practical applications, this result allows efficiently knowing when uncertainty can be represented via belief intervals for singletons rather than the associated BPA without loss of information.
APA
Moral Garcı́a, S. & Abellán, J.. (2021). Basic Probability Assignments Representable via Belief Intervals for Singletons in Dempster-Shafer Theory. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:229-234 Available from https://proceedings.mlr.press/v147/moral-garci-a21b.html.

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