A non-additive generalized measure of relative ”useful” information. (English) Zbl 0541.94009

Hooda, D. S.

Pure Appl. Math. Sci. 20, 143-151 (1984).

The author presents an axiomatic characterization of the following generalized measure \[ H^{\alpha}(P/Q;U/V)=(2^{\alpha -1}-1)^{- 1}\sum^{n}_{i=1}(u_ i/v_ i)p_ i[(p_ i/q_ i)^{\alpha -1}- 1],\quad \alpha \neq 1 \] of relative information, which is associated with the probability distribution P and the utility distribution U, having predicted probability distribution Q and utility distribution V, where \(P,Q\in \Delta_ n=\{P=(p_ 1,...,p_ n):\sum^{n}_{i=1}p_ i=1,\quad p_ i>0,\quad i=1,2,...,n\}\) and \(U,V\in U_ n=\{U=(u_ 1,...,u_ n):\quad u_ i>0,\quad i=1,2,...,n\}.\)

Reviewer: W.Sander

MSC:

94A17	Measures of information, entropy
39B99	Functional equations and inequalities

Keywords:

sum property; non-additivity; relative information; probability distribution; utility distribution