• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.121-124
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• 2005

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, we define a distance measure on interval-valued fuzzy numbers using Choquet integral with respect to a classical measure and investigate their properties.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.227-234
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• 2007

At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.71-75
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• 2009

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; $$\Phi((C)\;{\int}\;fd{\mu})\;{\leq}\;(C)\;\int\;\Phi(f)d{\mu},$$ where f is Choquet integrable, ${\Phi}\;:\;[0,\;\infty)\;\rightarrow\;[0,\;\infty)$ is convex, $\Phi(\alpha)\;\leq\;\alpha$ for all $\alpha\;{\in}\;[0,\;{\infty})$ and ${\mu}_f(\alpha)\;{\leq}\;{\mu}_{\Phi(f)}(\alpha)$ for all ${\alpha}\;{\in}\;[0,\;{\infty})$. Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.

• Proceedings of KOSOMES biannual meeting
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• 2004.11a
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• pp.69-75
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• 2004

The prevention of marine accidents has been a major topic in marine society and various policies and countermeasures have been developed, applied to the industries. The coastal VIS and navigational aids are considered as one of the effective methods to promote marine safety but they need relatively huge amount of budgets to build Thus prior to establishing these coastal VIS and navigational aids, it should be evaluated the navigational risk level in the coastal waterways from the Environmental Stress. So far as human beings are concerned, there are many types of fuzziness in the evaluation of navigational safety level. In order to reflect these fuzziness on this evaluation, this paper introduces the fuzzy integral suggested by Choquet to represent the fuzziness in the evaluation process. This paper aims to develop the method for this evaluation from the viewpoint of mariner's operational stress using the fuzzy logic and Choquet integral. In this paper, Korean coastal area is divided into 8 sectors and evaluated the priority for the needs of coastal VIS and navigational aids.

• Journal of Navigation and Port Research
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• v.28 no.5
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• pp.395-403
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• 2004

The prevention of marine accidents has been a major topic in marine society and various policies and countermeasures have been developed, applied to the industries. The coastal VTS and navigational aids are considered as one of the effective methods to promote marine safety but they need relatively huge amount of budgets to build Thus prior to establishing these coastal VTS and navigational aids, it should be evaluated the navigational safety level in the coastal waterways from the Environmental Stress. So far as human beings are concerned, there are many types of fuzziness in the evaluation of navigational safety level. In order to reflect these fuzziness on this evaluation, this paper introduces the fuzzy integral suggested by Choquet to represent the fuzziness in the evaluation process. This paper aims to develop the method for this evaluation from the viewpoint of mariner's operational stress using the fuzzy measure and Choquet integral. In this paper, Korean coastal area is divided into 8 sectors and evaluated the priority for the needs of coastal VTS and navigational aids.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1041-1044
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• 2005

Recently, Zhang et al.(Fuzzy Sets and Systems 147(2004) 475-485) proved Fatou's lemma and Lebesgue dominated convergence theorem under some conditions of fuzzy measure. In this note, we show that these conditions of fuzzy measure is essential to prove Fatou's lemma and Lebesgue dominated convergence theorem by examples

• Smart Structures and Systems
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• v.19 no.3
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• pp.323-333
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• 2017

Waste materials in concrete have been considered as one of the most important issues by the authorities, policy makers and researchers to maintain engineering serviceability in terms of economy, durability and sustainability. Therefore, evaluation and selection of waste materials with respect to multi criteria decision making (MCDM) for the construction industry has been gained importance for recovery and reuse. In this paper, Choquet integral based fuzzy approach is proposed for evaluating the most suitable waste materials with respect to compressive strength, tensile strength, flexural strength, compactness, toughness (resistivity for dynamic loads), water absorption and accessibility. On conclusion, waste tyre and silica fume were determined as the most suitable waste materials for concrete production. The obtained results are recommended to assist the authorities on configuring well designed strategies for construction industry with disposal materials.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.195-198
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• 2007

In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval-valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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• pp.749-753
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• 2007

In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

• Journal of the Korean Society of Marine Environment & Safety
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• v.9 no.1
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• pp.65-72
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• 2003

The prevention of marine accidents has been a major topic in marine society and various policies and countermeasures have been developed, applied to the industries. In order to improve the navigational safety level in the coastal waterways, the navigational safety level must be evaluated from the mariner's perception of safety. So far as human beings are concerned, there are many types of fuzziness in the evaluation of navigational safety level. In order to reflect these fuzziness on this evaluation, this paper introduces the fuzzy integral suggested by Choquet to represent the fuzziness in the evaluation process. This paper aims to develop the method for this evaluation from the viewpoint of mariner's operational stress using the fuzzy measure and Choquet integral. In this paper, Korean coastal area is divided into 8 sectors and evaluated the priority for the needs of coastal VTS and navigational aids. The results are found in the order named Mokpo, Yosu, Pohang, Inchon, Busan, Geoje, Gunsan, Donghae coastal area.