Results 1 to 10 of about 137 (97)
Aumann Type Set-valued Lebesgue Integral and Representation Theorem [PDF]
International Journal of Computational Intelligence Systems, 2009 n this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact ...
Jungang Li, Shoumei Li
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Mathematics, 2023 The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators that allow the classical theory of integrals to be ...
Muhammad Bilal Khan +4 more
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Mathematics, 2023 Convex bodies are naturally symmetrical. There is also a correlation between the two variables of symmetry and convexity. Their use, in either case, has been feasible in recent years because of their interchangeable and similar properties.
Muhammad Bilal Khan +4 more
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A Characterization Theorem for Aumann Integrals [PDF]
Set-Valued and Variational Analysis, 2014 A Daniell-Stone type characterization theorem for Aumann integrals of set-valued measurable functions will be proven. It is assumed that the values of these functions are closed convex upper sets, a structure that has been used in some recent developments in set-valued variational analysis and set optimization.
Cagin Ararat, Birgit Rudloff
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Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method [PDF]
Advances in Fuzzy Systems, 2018 We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with ...
Elhassan Eljaoui +2 more
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A Nonzero Set Problem with Aumann Stochastic Integral
Lecture Notes in Electrical Engineering, 2022 AbstractA nonzero set problem with Aumann set-valued random Lebesgue integral is discussed. This paper proves that the Aumann Lebesgue integral’s representation theorem. Finally, an important inequality is proved and other properties of Lebesgue integral are discussed.
Jungang Li
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On the Comparison of Aumann and Bochner Integrals
Journal of Mathematical Analysis and Applications, 2001 The Aumann and Bochner integrals of a multifunction taking on values in a separable Banach space with respect to a finitely additive measure are shown to be equivalent under certain conditions. Let \(\Sigma\) be a \(\sigma\)-algebra on a set \(\Omega\), let \(X\) be a separable Banach space and let \(ck(X)\) be the set of convex compact subsets of \(X\)
Anna Rita Sambucini
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On the upper and lower semicontinuity of the Aumann integral [PDF]
Journal of Mathematical Economics, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicholas C Yannelis
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On the properties of the Aumann integral with applications to differential inclusions and control systems [PDF]
Czechoslovak Mathematical Journal, 1989 The paper considers set-valued maps F(\(\omega)\) defined on a measure space \(\Omega\) with values being subsets of a Banach space X. The integral of F is defined, after Aumann, to be the set of integrals \(\int f(\omega)\), where f(\(\cdot)\) is a selection of F. Properties of the integral are established in this paper within the general framework of
Nikolaos S Papageorgiou +1 more
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Set valued Aumann–Pettis integrable martingale representation theorem and convergence
Annals of Functional Analysis, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M'Hamed El-Louh
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