The relative useful information measure: Some comments

Abstract

A quantitative-qualitative measure of relative information, also called the relative “useful” information measure, has recently been proposed and characterized by Taneja and Tuteja. However, in spite of their claim to the contrary, their measure is shown to be not necessarily nonnegative and, in fact, unbounded below as well as above. Since nonnegativity is one of the basic requirements of any information measure, Taneja and Tuteja's measure is not a true information measure. However, related measures of weighted entropy and weighted inaccuracy are both nonnegative.