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A random set description of a possibility measure and its natural extension

Gert De Cooman (UGent) and Dirk Aeyels (UGent)
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Abstract
The relationship is studied between possibility and necessity measures defined on arbitrary spaces, the theory of imprecise probabilities, and elementary random set theory. It is shown how special random sets can be used to generate normal possibility and necessity measures, as well as their natural extensions. This leads to interesting alternative formulas for the calculation of these natural extensions.
Keywords
natural extension, coherence, possibility measure, random sets, upper prevision, upper probability, FUZZY

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Citation

Please use this url to cite or link to this publication:

Chicago
De Cooman, Gert, and Dirk Aeyels. 2000. “A Random Set Description of a Possibility Measure and Its Natural Extension.” Ieee Transactions on Systems Man and Cybernetics Part A-systems and Humans 30 (2): 124–130.
APA
De Cooman, Gert, & Aeyels, D. (2000). A random set description of a possibility measure and its natural extension. IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS, 30(2), 124–130.
Vancouver
1.
De Cooman G, Aeyels D. A random set description of a possibility measure and its natural extension. IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS. 2000;30(2):124–30.
MLA
De Cooman, Gert, and Dirk Aeyels. “A Random Set Description of a Possibility Measure and Its Natural Extension.” IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS 30.2 (2000): 124–130. Print.
@article{171034,
  abstract     = {The relationship is studied between possibility and necessity measures defined on arbitrary spaces, the theory of imprecise probabilities, and elementary random set theory. It is shown how special random sets can be used to generate normal possibility and necessity measures, as well as their natural extensions. This leads to interesting alternative formulas for the calculation of these natural extensions.},
  author       = {De Cooman, Gert and Aeyels, Dirk},
  issn         = {1083-4427},
  journal      = {IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS},
  keyword      = {natural extension,coherence,possibility measure,random sets,upper prevision,upper probability,FUZZY},
  language     = {eng},
  number       = {2},
  pages        = {124--130},
  title        = {A random set description of a possibility measure and its natural extension},
  url          = {http://dx.doi.org/10.1109/3468.833093},
  volume       = {30},
  year         = {2000},
}

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