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Uncertainty generating functions. (English) Zbl 0926.94013
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).
In 1966 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 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].
Reviewer: L.Paditz (Dresden)
MSC:
94A17 Measures of information, entropy
68T30 Knowledge representation
62B10 Statistical aspects of information-theoretic topics
28E10 Fuzzy measure theory
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03B48 Probability and inductive logic
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