Two generalized measures of “useful” information

The weighted additivity corresponding to additivity plays a very important role in study of useful information. By using the sum property, the equation satisfied by weighted additivity has been converted to a functional equation, which is further generalized in two ways. The real and continuous solutions of the generalized functional equations have been obtained. In terms of these real and continuous solutions, two new generalized measures of useful information have been characterized and their particular cases have been studied. Some bounds and comparison results have also been obtained.