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

  • Authors:
  • G. de Cooman;D. Aeyels

  • Affiliations:
  • SYSTeMS Res. Group, Ghent Univ.;-

  • Venue:
  • IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
  • Year:
  • 2000

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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