Imprecision indices: axiomatic, properties and applications

Abstract

The paper is devoted to the investigation of imprecision indices. They are used for evaluating imprecision (or non-specificity) contained in information described by monotone (non-additive) measures. These indices can be considered as generalizations of the generalized Hartley measure. We argue that in some cases, for example in approximation problems, the application of imprecision indices is well justified comparing with well-known uncertainty measures because of their good sensitivity. In the paper, we investigate properties of so called linear imprecision indices; in particular, we introduce their various representations and describe connections to the theory of imprecise probabilities. We also study the algebraic structure of imprecision indices in the linear space and describe the extreme points of the convex set of all possible imprecision indices, in particular, of imprecision indices with symmetrical properties. We also show how to measure inconsistency in information by impression indices. At the end of the paper, we consider the application of imprecision indices in analysing the applicability of different aggregation rules in evidence theory.