P. Lachout, M. Studeny and J. Sindelar:
On set-valued measures. Informatica
4 (1993), n. 1-2, pp. 21-44.
- 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)
- set-valued measure
scanned pdf copy (8967kB) is available.
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.