On measures of “useful” information

The quantitative-qualitative measure of information as given by Belis and Guiaşu is additive, the additivity being a modification of the additivity of Shannon's measure with due place for utilities of the scheme in this property. A characterization of Belis and Guiaşu's measure depending upon the additivity postulate has been provided. The additivity can be relaxed, and there can be several ways of choosing a nonadditive law in place of additivity. Starting from a particular type of nonadditivity relation we characterize a measure of nonadditive “useful” information, which may be considered as a quantitative-qualitative measure corresponding to the Havrda-Charvat-Vajda-Daróczy entropy of degree β