Picard, Claude-François Weighted probabilistic information measures. (English) Zbl 0447.94011 J. Comb. Inf. Syst. Sci. 4, 343-356 (1979). 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. Reviewer: Pl. Kannappan (Waterloo) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 4 Documents MSC: 94A17 Measures of information, entropy Keywords:weighted probabilistic information measures; normalized preference × Cite Format Result Cite Review PDF