an:01164040
Zbl 0926.94013
Ramer, Arthur
Uncertainty generating functions
EN
de Cooman, Gert (ed.) et al., Foundations and applications of possibility theory. Proceedings of the 1st international conference, FAPT'95, Ghent, Belgium, December 13--15, 1995. Singapore: World Scientific. Adv. Fuzzy Syst., Appl. Theory. 8, 41-46 (1995).
1995
a
94A17 68T30 62B10 28E10 94D05 03B48
Dirichlet generating function; exponential generating function; information generating function; Renyi entropy; possibilistic measure; information distance; Shannon entropy; Dirichlet sums
In 1966 \textit{S. Golomb} [IEEE Trans. Inf. Theory IT-12, 75-77 (1966)] proposed defining generating functions, of Dirichlet type, associated with probability distributions, and termed them information generating. The latter because their derivatives at 1 correspond to Shannon entropy. Independently, in 1987 \textit{A. Ramer} [Fuzzy Sets Syst. 24, l83-196 (1987; Zbl 0638.94027)] used finite Dirichlet sums to obtain a characterization of certain information measures in evidence theory. Now the logarithmic derivative at 0 represented a variant of entropy. In this paper this approach is applied first to possibilistic uncertainty, and then to belief functions (evidence theory). The corresponding functions are termed (after Golomb) uncertainty generating. Their derivatives reproduce basic uncertainty measures, while their linear approximations give novel measures, serve to quantify numerically the effect of change of context, and provide several insights into questions about conditional objects. A list of basic references is given.
For the entire collection see [Zbl 0887.00012].
L.Paditz (Dresden)
0638.94027