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ISIPTA'07 -
FIFTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Charles University, Faculty of Mathematicsand Physics

Prague, Czech Republic

16-19 July 2007

## ELECTRONIC PROCEEDINGS

## Andrew Bronevich, Alexander Lepskiy

# Measuring Uncertainty with Imprecision Indices

### Abstract

The paper is devoted to investigation of imprecision indices, which are used for evaluating uncertainty (namely imprecision), which is contained in information, described by fuzzy (non-additive) measures, in particular, by lower and upper probabilities. We argue that there exist various types of uncertainty, for example, randomness, investigated in probability theory, imprecision, described by interval calculi, inconsistency, incompleteness, fuzziness and so on. In general these types of uncertainty have very complex behavior, caused by their interaction. Therefore, the choice of uncertainty measures is not unique, and depends on the problems addressed. The classical uncertainty measures are Shannon’s entropy and Hartley’s measure. In the paper imprecision indices and also linear ones are introduced axiomatically. The system of axioms allows us to define various imprecision indices. So we investigate the algebraic structure of all imprecision indices and study their families with best properties.

** Keywords. ** Imprecision indices, lower and upper probabilities, uncertainty based information

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** Authors addresses: **

Andrew Bronevich

Nekrasovsky street 44, 347928, Taganrog, Russia

Alexander Lepskiy

Department of Mathematics, Taganrog State University of Radio Engineering, Nekrasovskij, 44, GSP-17A, Taganrog, 347928, Russia

** E-mail addresses: **

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