• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.277-280
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• 2002

In this paper, we characterize the Borel $\sigma$-field generated by the Hausdorff-Skorokhod metric on the space of normal and upper-semicontinuous fuzzy sets with compact support in the Ecleadean space R$\^$n/. As a result. we give a characterization of measurable fuzzy mappings .

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.333-352
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• 2017

In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.39-48
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• 2000

In this paper we define T-fuzzy integrals of set-valued mappings, which are extensions of fuzzy integrals of the single-valued functions defined by Sugeno. And we discuss their properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.380-386
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• 1998

In this paper we introduce the concept of fuzzy integrals for set-valued mappings, which is an extension of fuzzy integrals for single-valued functions defined by Sugeno. And we give some properties including convergence theorems on fuzzy integrals for set-valued mappings.

• East Asian mathematical journal
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• v.32 no.5
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• pp.685-700
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• 2016

The main object of this work to introduced and studied a new class of fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces. By using the random B-restricted accretive mapping with measurable mappings ${\alpha},{\alpha}^{\prime}:{\Omega}{\rightarrow}(0,1)$, an existence of random solutions for this class of fuzzy general nonlinear ordered random variational inequality (equation) with fuzzy mappings is established, a random approximation algorithm is suggested for fuzzy mappings, and the relation between the first value $x_0(t)$ and the random solutions of fuzzy general nonlinear ordered random variational inequality is discussed.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.425-434
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• 2007

We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.647-653
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• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.439-455
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• 2019

Let ${\Sigma}_k(p)$ be the class of univalent meromorphic functions defined on the unit disc ${\mathbb{D}}$ with k-quasiconformal extension to the extended complex plane ${\hat{\mathbb{C}}}$, where $0{\leq}k<1$. Let ${\Sigma}^0_k(p)$ be the class of functions $f{\in}{\Sigma}_k(p)$ having expansion of the form $f(z)=1/(z-p)+{\sum_{n=1}^{\infty}}\;b_nz^n$ on ${\mathbb{D}}$. In this article, we obtain sharp area distortion and weighted area distortion inequalities for functions in ${\sum_{k}^{0}}(p)$. As a consequence of the obtained results, we present a sharp upper bound for the Hilbert transform of characteristic function of a Lebesgue measurable subset of ${\mathbb{D}}$.