D. Denneberg. Non-additive measure and integral. Kluwer Academic Publishers, 1994. Home/Search Document Not in Database Summary Related Articles Check |
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Fuzzy Measures and Integrals as Aggregation Operators.. - Modave, Kreinovich (2002) (Correct)
....decision making, this is necessary as we will see. 2. 1 Fuzzy integration theory In this section, Omega is a finite set and P( Omega Gamma is the set of subsets of Omega Gamma We briefly recall the definitions of fuzzy measures and Choquet integral (for more details see for example [2], 1] Definition 1 A fuzzy measure (or non additive measure) P( Omega Gamma5 is a set function : P( Omega Gamma [0; 1] such that (1) 0 , X) 1, 2) if A; B 2 P( Omega Gamma , A ae B, then (A) B) that is, is a non decreasing set function w.r.t inclusion. Remark: Fuzzy ....
D. Denneberg. Non-Additive Measure and Integral. Kluwer Academic Publisher, 1994.
Correlation And Dependence In Risk Management.. - Embrechts, McNeil.. (1999) (12 citations) (Correct)
....where they are comonotonic. The latter is computed by addition of the univariate quantiles since under comonotonicity VaR (X Y ) VaR (X) VaR (Y ) 10 The example shows that for a xed 10 This is also true when X or Y do not have continuous distributions. Using Proposition 4. 5 in Denneberg (1994) we deduce that for comonotonic random variables X Y = u v) Z) where u and v are continuous increasing functions and Z = X Y . Remark 1 then shows that VaR (X Y ) u v) VaR (Z) u(VaR (Z) v(VaR (Z) VaR (X) VaR (Y ) 28 PAUL EMBRECHTS, ALEXANDER MCNEIL, AND DANIEL ....
Denneberg, D. (1994): Non-additive Measure and Integral. Kluwer Academic Publishers, Dordrecht.
The construction of possibility measures from samples.. - De Baets, De Cooman.. (1996) (Correct)
.... function that is (finitely) additive and continuous from below on a field of sets S can be uniquely extended to a monotone set function fl on the closure from below S of S, and can be uniquely extended to a measure fl defined on the Caratheodory algebra of the outer set function fl of fl [18]. Similarly, in the context of possibility theory [13 15,20,26] it is very natural to ask whether a given set function defined on a particular class of subsets of a universe of discourse X, can be extended to a possibility measure defined on the power class (X) As we shall briefly explain ....
D. Denneberg. Non-additive measure and integral. Kluwer Academic Publishers, Dordrecht, 1994.
Study of the Probabilistic Information of a Random Set - Miranda, Couso, Gil (Correct)
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D. Denneberg. Non-additive measure and integral. Kluwer Academic Publishers, 1994.
Products of Capacities Derived from - Additive Measures Extended (Correct)
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D. Denneberg, Non-Additive Measure and Integral, Kluwer Academic Publishers, Dordrecht, 1997.
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