Measuring Uncertainty with Imprecision Indices

The paper is devoted to the investigation of imprecision indices, introduced in [8]. They 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 investigate their families with best properties.