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Weighted probabilistic information measures. (English) Zbl 0447.94011

Through a set of five axioms (which are complicated to reproduce) the author obtains five continuous solutions of the axiom system, which includes (what the author calls) information of type Shannon-Guiasu with normalized preference, information of order \(\alpha\) with normalized preference etc. The author has not found all the solutions: for example on page 347, the author conveniently states that “if \(I_1(p,v)=0\) or if \(I_1(q,w)=0\), we put: \(f_1(p,v)=1\) or \(f_1(r,v)=1\)” without explanation (which are not part of the hypothesis) and ignores the corresponding solution.

MSC:

94A17 Measures of information, entropy