• 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.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.33-39
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• 2005

In this paper, we prove the existence of a common random fixed point of two random multivalued generalized contractions by using functional expressions.

• Journal of Korea Water Resources Association
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• v.56 no.3
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• pp.195-210
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• 2023

Additional deposition and erosion in large rivers in South Korea have continued to occur toward morphological stabilization after massive dredging through the four major river restoration project, subsequently requiring precise bathymetry monitoring. Hyperspectral bathymetry method has increasingly been highlighted as an alternative way to estimate bathymetry with high spatial resolution in shallow depth for replacing classical intrusive direct measurement techniques. This study introduced the conventional Optimal Band Ratio Analysis (OBRA) of hyperspectral bathymetry method, and evaluated the performance in a domestic large river in normal turbid and flow condition. Maximum measurable depth was estimated by applying correlation coefficient and root mean square error (RMSE) produced during OBRA with cascadedly applying cut-off depth, where the consequent hyperspectral bathymetry map excluded the region over the derived maximum measurable depth. Also non-linearity was considered in building relation between optimal band and depth. We applied the method to the Nakdong and Hwang River confluence as a large river case and obtained the following features. First, the hyperspectal method showed acceptable performance in morphological mapping for shallow regions, where the maximum measurable depth was 2.5 m and 1.25 m in the Nakdong and Hwang river, respectively. Second, RMSE was more feasible to derive the maximum measurable depth rather than the conventional correlation coefficient whereby considering various scenario of excluding range of in situ depths for OBRA. Third, highly turbid region in Hwang River did not allow hyperspectral bathymetry mapping compared with the case of adjacent Nakdong River, where maximum measurable depth was down to half in Hwang River.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.729-737
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• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.17 no.4
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• pp.29-41
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• 2014

The Korean government has purchased land properties alongside any significant water bodies before setting up the buffers to secure water qualities. Since the annual budgets are limited, however, there has always been the issue of which land parcels ought to be given the priority. Therefore, this study aims to develop efficient mechanism for land acquisition priorities in stream corridors that would ultimately be vegetated for riparian buffer zones. The criteria of land acquisition priority were driven through literary review along with experts' advice. The relative weights of their value and priorities for each criterion were computed using the Analytical Hierarchy Process(AHP) method. Major findings of the study are as follows: 1. The decision-making structural model for land acquisition priority focuses mainly on the reduction of non-point source pollutants(NSPs). This fact is highly associated with natural and physical conditions and land use types of surrounding areas. The criteria were classified into two categories-NSPs runoff areas and potential NSPs runoff areas. 2. Land acquisition priority weights derived for NSPs runoff areas and potential NSPs runoff areas were 0.862 and 0.138, respectively. This implicates that much higher priority should be given to the land parcels with NSPs runoff areas. 3. Weights and priorities of sub-criteria suggested from this study include: proximity to the streams(0.460), land cover(0.189), soil permeability(0.117), topographical slope(0.096), proximity to the roads(0.058), land-use types(0.036), visibility to the streams(0.032), and the land price(0.012). This order of importance suggests, as one can expect, that it is better to purchase land parcels that are adjacent to the streams. 4. A standard scoring system including the criteria and weights for land acquisition priority was developed which would likely to allow expedited decision making and easy quantification for priority evaluation due to the utilization of measurable spatial data. Further studies focusing on both point and non-point pollutants and GIS-based spatial analysis and mapping of land acquisition priority are needed.