utilities; entropies with branching property; entropies with sum property
Belis and Guiasu studied a generalization of Shannon entropy as weighted or useful entropy. In this paper, the weighted entropy of type $(\alpha, \beta)$ is defined and characterized and some if its properties are studied. Further generalizations involving more parameters of weighted entropy are also specified.
 M. Belis S. Guiasu: A quantitative-qualitative measure of information in cybernetics. IEEE Trans. Infor. Theory, H-14 (1968) 593-594.
 B. D. Sharma I. J. Taneja: Three Generalized Additive Measures of Entropy
. - Elektro. Inform. Kyber., 13 (1977), 7/8, 419-433. MR 0530208
 I. J. Taneja: On Axiomatic Characterization of Entropy of Type ($\alpha$, $\beta$)
. Apl. mat. 22 (1977), 409-417. MR 0469524
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