• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.380-383
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• 2003

In this paper, we propose a fuzzy group decision making method for multiple decision maker-multiple objective programming problems to obtain the agreeable solution. In the proposed method, considering the vague nature of human subjective judgement it is assumed that each of multiple decision makers has a fuzzy goal for each of his/her own objective functions. After eliciting the membership functions from the decision makers for their fuzzy goals, total M-Pareto optimal solution concept is defined in membership spaces in order to deal with multiple decision maker-multiple objective programming problems. For generating a candidate of the agreeable solution which is total M-Pareto optimal, the extended weighted minimax problem is formulated and solved for some weighting vector which is specified by the decision makers in their subjective manner, Given the total M-Pareto optimal solution, each of the derision makers must either be satisfied with the current values of the membership functions, or update his/her weighting vector, However, in general, it seems to be very difficult to find the agreeable solution with which all of the decision makers are satisfied perfectly because of the conflicts between their membership functions. In the proposed method, each of the decision makers is requested to estimate the degree of satisfaction for the candidate of the agreeable solution. Using the estimated values or satisfaction of each of the decision makers, the core concept is desnfied, which is a set of undominated candidates. The interactive algorithm is developed to obtain the agreeable solution which satisfies core conditions.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.33-44
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• 1998

This paper is concerned with the existence of mutiple positive solution of (equation omitted) with Dirichlet boundary condition.

• Journal of Korean Society for Atmospheric Environment
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• v.19 no.6
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• pp.733-743
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• 2003

The flow field in multiple fluid sphere systems was studied analytically. The expanded zero vorticity cell model based on Kuwabara's theory (1959) was applied and the effects of gas slippage at the collecting surface were considered. Also, the solid sphere system was extended to fluid sphere including the effects of the induced internal circulation inside the liquid droplet spheres or gas bubble systems. As a result, the obtained analytic solution was converged to the existing solutions for flow field around solid and bubble sphere systems with proper boundary conditions. Based on the resolved flow field, the terminal velocity around the collecting fluid spheres was obtained. Subsequently, this study evaluated the most general solution for flow field around the multiple fluid sphere systems. The obtained flow field in multiple fluid sphere could be used as a fundamental consideration of wet scrubber design and devices for removing particles by fluid-fluid interactions.

• Journal of Communications and Networks
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• v.8 no.3
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• pp.313-322
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• 2006

We consider a power controlled code division multiple access (CDMA) system with multiple flow types. At each of the N nodes, there are F flow types with different signal-to-interference-and-noise-ratio (SINR) requirements. To keep the complexity of the transmitter low, we assume that each node uses the same power level for all its flows. The single flow case has been fully solved and is well-understood. We concentrate on the multiple flow case, and use a novel and different approach. For the uplink problem with N = 2 and F arbitrary, the necessary and sufficient conditions to have a solution are found and proved. For the general N > 1 uplink problem, we provide a necessary condition for the problem to have a solution and an iterative algorithm to find the optimum solution. For the downlink case with F > 1 some properties of the optimal sequences are obtained.

• Journal of KSNVE
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• v.7 no.1
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• pp.55-60
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• 1997

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

• Research in Mathematical Education
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• v.16 no.3
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• pp.155-176
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• 2012

It is an important issue to explore classroom environments which are conducive to developing students' mathematical performance. This study explores the effects of different classroom environments (solution-demand and corresponding-time setting) on mathematical performances. Fourteen and eighteen prospective teachers were required to prove a task under different conditions respectively: a) Cognitive demand of multiple-solution corresponding time of three hours, and b) Cognitive demand of a right solution corresponding time of 20 minutes. We used SOLO as the assessment tool for mathematical performance from quality perspective. Significant differences were found in the quantity and quality of mathematical performance. The regular environment focusing on speed and accuracy were found to be directly linked to low levels of performance. The findings above provide implications to the cognitive benefits of multiple-solution demand and corresponding time setting.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.275-281
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• 1996

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

• IE interfaces
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• v.17 no.spc
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• pp.28-36
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• 2004

The main purpose of this study is to find out the optimal solution of the vehicle routing problem considering heterogeneous vehicle(s), double-trips, and multi depots. This study suggests a mathematical programming model with new numerical formula which considers the amount of delivery and sub-tour elimination and gives optimal solution by using OPL-STUDIO(ILOG). This study also suggests modified genetic algorithm which considers the improvement of the creation method for initial solution, application of demanding point, individual and last learning method in order to find excellent solution, survival probability of infeasible solution for allowance, and floating mutation rate for escaping from local solution. The suggested modified genetic algorithm is compared with optimal solution of the existing problems. We found the better solution rather than the existing genetic algorithm. The suggested modified genetic algorithm is tested by Eilon and Fisher data(Eilon 22, Eilon 23, Eilon 30, Eilon 33, and Fisher 10), respectively.

• Journal of the military operations research society of Korea
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• v.27 no.1
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• pp.28-38
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• 2001

A transportation problem amy have multiple optimal solutions, if an optimal solution to the problem is degenerate. This study derives a condition, under which multiple degenerate optimal solutions exist, fro ma current degenerate optimal transportation tableau by utilizing the homogeneous equation obtained from the closed loops connecting degenerate basic variable and non-basic variables, and discusses a method of generating alternative degenerate optimal solutions and their associated transportation tableaus. Each degenerate optimal solution may not have the same range of feasibility in sensitivity analysis on supply and demand quantity due to different set of shadow prices which multiple degenerate solution have.

• School Mathematics
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• v.16 no.1
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• pp.1-17
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• 2014

Mathematical creativity in school mathematics is connected with problem solving. The purpose of this study was to analyse elementary students' the mathematical creativity using multiple solution tasks which required to solve a mathematical problem in different ways. For this research, I examined and analyzed the response to four multiple solution tasks according to the evaluation system of mathematical creativity which consisted of the factors of creativity(fluency, flexibility, originality). The finding showed that mathematical creativity was different between students with greater clarity. And mathematical creativity in tasks was different. So I questioned the possibility of analysis of students' the mathematical creativity in mathematical areas. According to the evaluation system of mathematical creativity of this research, mathematical creativity was proportional to the fluency. But the high fluency and flexibility was decreasing originality because it was easy for students to solve multiple solution tasks in the same ways. So, finding of this research can be considered to make the criterion in both originality in rare and mathematical aspects.