Abstract

The concept of a set-valued measure is introduced and illustrated by examples. Its significance for a new non-standard approach in artificial intelligence is explained. Then, the construction of factorization of these measures is mentioned, a special class of sigma-quasiatomic set-valued measures is defined and the corresponding characterization theorem is proved. This class involves set-valued measures ranging in a countable set which were used in modelling uncertainty in artificial intelligence. It enables to answer one question arising in connection with this application.

AMS classification 28B20 (68T30)

Keywords

set-valued measure

null-set

quasiatom

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The paper has a connection to the following work:

• I. Kramosil: Uncertainty processing under non-standard interpretation of probability values. Research report n. 1707, Institute of Information Theory and Automation, Prague, 1991.