• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.549-556
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• 2006

In this paper, we consider interval-valued Choquet integrals and fuzzy measures. Using these properties, we discuss some applications of them in multicriteria decision aid. In particular, we show how these interval-valued Choquet integrals can model behavioral analysis of aggregation in ulticriteria decision aid.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.411-421
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• 2007

The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.170-173
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• 2005

We note that Jang et at. studied closed set-valued Choquet integrals with respect to fuzzy measures. In this paper, we consider Choquet integrals of compact set-valued functions, and prove some properties of them. In particular, using compact set-valued functions, instead of interval valued we investigate characterization of compact set-valued Choquet integrals.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.251-272
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• 2003

Multidimensional integrals are expressed in terms of lower dimensional integrals and function evaluations. An iterative process is used where a trapezoidal and three point identities are used as generators for higher dimensional identities. Bounds are obtained utilising the resulting identities. It is demonstrated that earlier Ostrowski type results are obtained as particular instances of the current work.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.703-725
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• 2011

In this paper, we establish the vector-valued inequalities for the commutators of singular integrals with rough kernels. In particular, our results can essentially improve some well-known results.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.5
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• pp.588-592
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• 2005

We note that Jang et al. studied closed set-valued Choquet integrals with respect to fuzzy measures. In this paper, we consider Choquet integrals of compact set-valued functions, and prove some properties of them. In particular, using compact set-valued functions instead of interval valued, we investigate characterization of compact set-valued Choquet integrals.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.534-535
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• 2009

This paper deals with BEM analysis of transient elastodynamic problems using domain decomposition method and particular integrals. The particular method is used to approximate the acceleration term in the governing equation. The domain decomposition method is examined to consider multi-region problems. The domain of the original problem is subdivided into sub-regions, which are modeled by the particular integral BEM. The iterative coupling employing Schwarz algorithm is used for the successive update of the interface boundary conditions until convergence is achieved. The numerical results, compared with those by ABAQUS, demonstrate the validity of the present formulation.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.435-440
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• 2013

In this paper, we study the Henstock delta integral, which generalizes the Henstock integral. In particular, we study the relation between the Henstock and Henstock delta integrals.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.41-46
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• 2003

In this paper, we investigate the $SP_{\alpha}$-integral and the $M_{\alpha}$-integral defined on an interval of the n-dimensional Euclidean space $\mathbb{R}^n$. In particular, we show that these two integrals are equivalent.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.79-89
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• 2008

In this paper, we define the ap-Henstock integral and the ap-Denjoy integral of Banach-valued functions, and we investigate some properties of these two integrals. In particular, we show that the ap-Henstock integral is equivalent to the ap-Denjoy integral.