Results 61 to 70 of about 101 (91)

Comonotone approximation of periodic functions

Mathematical Notes, 2008
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Dzyubenko, G. A., Pleshakov, M. G.
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On comonotonic functions of uncertain variables

Fuzzy Optimization and Decision Making, 2012
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Regular fuzzy measure and representation of comonotonically additive functional

Fuzzy Sets and Systems, 2000
Two real-valued functions \(f,g: X\to\mathbb{R}\) are called comonotonic if \(f(x)< f(x')\) implies \(g(x)\leq g(x')\) for all \(x,x'\in X\). A functional \(I: K\to\mathbb{R}\) on a space of real-valued functions is called comonotonically additive if \(I(f+g)= I(f)+ I(g)\) for any pair of comonotonic functions of \(K\). It is proved that a functional \(
Yasuo Narukawa, Toshiaki Murofushi, Michio Sugeno   +2 more
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A representation of a comonotone--additive and monotone functional by two Sugeno integrals

Fuzzy Sets and Systems, 2005
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Endre Pap, Biljana P. Mihailovic
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Distribution Functions, Measurability and Comonotonicity of Functions

1994
For a function we introduce the system of upper level sets. Together with a set function it gives rise to the decreasing distribution function and, in the next chapter, the integral. No measurability requirements have to be imposed on the function if the set function is defined on the whole power set.
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The comonotonically additive functional on the class of continuous functions with compact support

Proceedings of 6th International Fuzzy Systems Conference, 2002
This paper discusses the functional I defined on the class of continuous functions K, which is comonotonically additive and monotone. It is shown that the functional I can be represented by the difference of two Choquet integrals with respect to regular fuzzy measures when the universal set X is a locally compact Hausdorff space, and that the ...
Y. Narukawa, T. Murofushi, M. Sugeno
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A symmetric conjugate condition for the representation of comonotonically additive and monotone functionals

Fuzzy Sets and Systems, 2008
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Hashem Parvaneh Masiha, M. Rahmati
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Representation of Comonotonically Additive Functional by Choquet Integral

2000
This paper discusses the functional I defined on the class of continuous functions K, that is comonotonically additive and monotone. The extension of the domain of the functional and the extension I* of the functional are shown. It is discussed that the condition under which the functional I* can be represented by one Choquet integral.
Yasuo Narukawa, Toshiaki Murofushi, Michio Sugeno   +2 more
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Comonotone approximation of \(|X|\) by rational functions

1983
It is shown that the rational approximant r(x)\(\in {\mathcal R}^ n_ n[- 1,1]\) introduced by Newman satisfying \(| | x| -r(x)| \leq 3\bar e^{\sqrt{n}}\) is actually a comonotone approximation of \(| x|\) on [-1,1] in that r'(x)\(\leq 0\) for \(x\in [-1,0]\) and r'(x)\(\geq 0\) for \(x\in [0,1]\). Furthermore, it is shown that the result of Vyaceslavov
Iliev, G. L., Optiz, U.
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Shape Preserving Multi Approximation by Comonotone Functions

International Journal of Mathematics and Computer Science
We prove a multi direct comonotone theorem for the comonotone approximation of piecewise monotone functions via multi ...
Mayada Kareem, Rehab Kamel, Ahmed Hussain   +2 more
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