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A sufficient and necessary condition of uncertainty distribution. (English) Zbl 1229.28029
There are many different uncertainty theories: The well-founded probability theory, the very flexible fuzzy set theory, Shafer’s evidence theory, Pawlak’s rough set theory a.s.o. B. Liu [Uncertainty theory. 2nd ed., Berlin: Springer (2007; Zbl 1141.28001)] has introduced a kind of uncertainty theory which is relatively close to probability theory. The present paper contributes to Liu’s theory and shows that a function on $$[0,1]$$ is an uncertainty distribution if and only if it is an increasing function (except the constants $$0$$ and $$1$$).

##### MSC:
 2.8e+11 Fuzzy measure theory
##### Keywords:
uncertainty measure; uncertainty distribution
Full Text:
##### References:
 [1] Gao X., International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems [2] Li X., Journal of Uncertain Systems 3 (2) pp 83– (2009) [3] Liu B., Uncertainty Theory (2004) [4] Liu B., Uncertainty Theory, 2. ed. (2007) [5] Liu B., Journal of Uncertain Systems 2 (1) pp 3– (2008) [6] Liu B., Uncertainty Theory, 3. ed. [7] Liu B., Theory and Practice of Uncertain Programming, 2. ed. (2009) · Zbl 1158.90010 · doi:10.1007/978-3-540-89484-1 [8] Liu B., Journal of Uncertain Systems 3 (1) (2009) [9] Liu Y., Proceedings of 10th National Youth Conference on Information and Management Sciences pp 23– (2008) [10] You C., Mathematical and Computer Modelling 49 (3) pp 482– (2009) · Zbl 1165.28310 · doi:10.1016/j.mcm.2008.07.007
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