Results 71 to 80 of about 665 (108)

Extension and representation of comonotonically additive functionals

Fuzzy Sets and Systems, 2001
Two real functions \(f\), \(g\) are comonotonic, if \(f(x_1)< f(x_2)\) implies \(g(x_1)\leq g(x_2)\) for any \(x_1\), \(x_2\). The set \(K\) of all functions with compact support in a locally compact Hausdorff space is considered. A real-valued functional \(I\) on \(K\) is called comonotonically additive if \(I(f+ g)= I(f)+ I(g)\) whenever \(f,g\in K\)
Y. Narukawa, T. Murofushi, M. Sugeno
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Boundedness and symmetry of comonotonically additive functionals

Fuzzy Sets and Systems, 2001
A relationship between the Choquet integral and comonotically additive and monotone functionals \(I\) is reexamined. First, some necessary and sufficient conditions are given for the boundedness of \(I\) in terms of Narukawa's fuzzy measures. Then there is proved that \(I\) is symmetric if and only if it can be represented by the Šipoš integral.
Yasuo Narukawa, Toshiaki Murofushi, Michio Sugeno   +2 more
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Comonotone approximation of periodic functions

Journal of Approximation Theory
Denote by \(\widetilde{C}\) the space of continuous \(2\pi\)-periodic functions \(f\) endowed with the uniform norm \(\|f\| := \max\limits_{x\in \mathbb{R}} |f(x)|\) and by \(\omega_m (f,t)\) the \(m\)-th modulus of smoothness of \(f\). Furthermore, denote by \(\widetilde{C}^r\) the subspace of \(r\)-times continuously differentiable functions \(f\in ...
D. Leviatan, M.V. Shchehlov, I.O. Shevchuk   +2 more
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On comonotonic functions of uncertain variables

Fuzzy Optimization and Decision Making, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Comonotone approximation and interpolation by entire functions

Journal of Mathematical Analysis and Applications, 2019
The author examines variations of a theorem of \textit{L. Hoischen} [J. Approx. Theory 15, 116--123 (1975; Zbl 0318.30034)] in which the functions to be approximated are piecewise monotone, and the approximating entire functions (which are automatically piecewise monotone) are comonotone with the functions to be approximated, i.e., increasing and ...
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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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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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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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Comonotone approximation of twice differentiable periodic functions

Ukrainian Mathematical Journal, 2009
In the case where a 2π-periodic function f is twice continuously differentiable on the real axis ℝ and changes its monotonicity at different fixed points y i ∈ [− π, π), i = 1,…, 2s, s ∈ ℕ (i.e., on ℝ, there exists a set Y := {y i }
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A representation of a comonotone--additive and monotone functional by two Sugeno integrals

Fuzzy Sets and Systems, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pap, Endre, Mihailović, Biljana P.
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