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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:
28E10 Fuzzy measure theory
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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)
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