Imprecision index and its application to estimating the prior system information content

Abstract

In the paper, in the framework of the theory of monotone (fuzzy) measures, the so-called imprecision index given on these measures is defined and investigated. The imprecision index is a certain functional, which takes zero value on the probability measure (the most accurate) and satisfies the normalization and monotone conditions; i.e., for more inaccurate measures it takes greater values than for less inaccurate ones. The imprecision index is aimed at estimating the imprecision degree of the monotone measure and can be used for evaluating prior information content of non-deterministic systems. The set of linear imprecision indices is considered separately as a set of linear functionals of a certain form. Sufficient and necessary conditions for a linear functional to be a linear imprecision index are established. An example of applying the imprecision index to evaluating the information content of a contour for solving the problem of finding its minimal polygonal representation is presented.