• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.79-88
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• 1999

This work aims to establish an algorithm for solving the problem of convex programming with several objective-functions with linear constraints. Starting from the idea of Rosen's algorithm for solving the problem of convex programming with linear con-straints and taking into account the solution concept from multi-dimensional programming represented by a program which reaches "the best compromise" we are extending this method in the case of multidimensional programming. The concept of direction of min-imization is introduced and a necessary and sufficient condition is given for a s∈Rn direction to be a direction is min-imal. The two numerical examples presented at the end validate the algorithm.

• 한국경영과학회지
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• 제17권3호
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• pp.67-78
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• 1992

MODM (multiobjective decision-making) problem is very complex system for the analyst. The problem is more complex if the goals of each of the objective functions are expressed imprecisely. It requires suitable MODM method to deal with imprecisions. Therefore, we present a new interactive fuzzy decision making method for solving multiobjective nonlinear programming problems by assuming that the decision maker (DM) has imprecise goals that assume fuzzy linguistic variable for each of the objective functions. The imprecise goals of the DM are quantified by eliciting corresponding membership functions through the interactive with the DM out of six membership functions. After determining membership functions, in order to generate the compromise or satisficing solution which is .lambda.-pareto optimal, .lambda.-max problem is solved. The higher degree of membership is chosen to satisfy imprecise goals of all objective functions by combining the membership functions. Then, the values are the compromise or satisficing solution. On the basis of the proposed method, and interactive computer programming is written to implement man-machine interactive procedures. Our programming is a revised version of sequential unconstrained minimization technique. Finally, a numerical example illustrates various aspects of the results developed in this paper.

• 대한기계학회논문집A
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• 제33권2호
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• pp.114-126
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• 2009

In this paper, a versatile multi-criteria optimization concept for fatigue life prediction is introduced. Multi-criteria decision making in engineering design refers to obtaining a preferred optimal solution in the context of conflicting design objectives. Compromise decision support problems are used to model engineering decisions involving multiple trade-offs. These methods typically rely on a summation of weighted attributes to accomplish trade-offs among competing objectives. This paper gives an interpretation of the decision parameters as governing both the relative importance of the attributes and the degree of compensation between them. The approach utilizes a response surface model, the compromise decision support problem, which is a multi-objective formulation based on goal programming. Examples illustrate the concepts and demonstrate their applicability.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회(1)
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• pp.68-69
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• 2005

• Structural Engineering and Mechanics
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• 제3권4호
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• pp.373-382
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• 1995

The weighting strategy has received a great attention and has been widely applied to multicriterion optimization. This gaper examines a global criterion method (GCM) with the weighting objectives strategy in fuzzy structural engineering problems. Fuzziness of those problems are in their design goals, constraints and variables. Most of the constraints are originated from analysis of engineering mechanics. The GCM is verified to be equivalent to fuzzy goal programming via a truss design. Continued and mixed discrete variable spaces are presented and examined using a fuzzy global criterion method (FGCM). In the design process a weighting parameter with fuzzy information is introduced into the design and decision making. We use a uniform machine-tool spindle as an illustrative example in continuous design space. Fuzzy multicriterion optimization in mixed design space is illustrated by the design of mechanical spring stacks. Results show that weighting strategy in FGCM can generate both the best compromise solution and a set of Pareto solutions in fuzzy environment. Weighting technique with fuzziness provides a more relaxed design domain, which increases the satisfying degree of a compromise solution or improves the final design.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2012년도 학술발표회
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• pp.227-227
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• 2012

본 연구는 수자원계획 문제에서 다기준 의사결정기법을 적용할 때 발생할 수 있는 두 가지 문제에 대해 분석하였다. 첫 번째는 다기준 의사결정기법 선택의 차이가 결과에 어느 정도 영향을 미칠 수 있는지를 제시하였고 두 번째는 평가기준에 대한 가중치와 대안들의 평가치에 대한 불확실성을 최소화하기 위해 민감도 분석을 수행하는 절차를 제시하였다. 첫 번째 문제를 위해 가중합계법, Compromise Programming, 계층화분석과정, 수정된 계층화 분석과정, 가중곱방법, TOPSIS, ELECTRE-2, Regime 방법을 사용하였다. 또한 최근 사용빈도가 높은 삼각형 Fuzzy 숫자와 다기준 의사결정기법을 결합한 기법에 대해서도 분석하였는데 Fuzzy WSM, Fuzzy 계층화분석과정, Fuzzy 수정 계층화분석과정, Fuzzy TOPSIS, Fuzzy Compromise Programming을 검토하였다. 분석결과 평가기준에 대한 가중치 조건과 표준화 방법이 동일한 상황에도 불구하고 조금씩 다른 순위를 제시하는 것으로 나타났다. 또한 다양한 MCDM 기법들을 적용해도 동일한 순위로 나타나는 대안들이 있었다. 따라서 다기준 의사결정기법을 사용한 수자원 관리계획을 수립할 때에는 다양한 분석기법을 활용해서 기법의 선택으로 인한 불확실성을 최소화해야 한다. 두 번째 문제는 평가기준에 대한 가중치와 대안의 효과 정량화 자료의 불확실성을 극복하기 위해 각각에 대한 민감도 분석을 수행하였다. 본 연구는 유량확보와 수질개선을 위한 수자원 계획 수립을 위해 가중합계법을 이용한 문제에 두 경우의 민감도 분석을 모두 수행하였다. 이 과정에서 결정계수와 민감도 계수를 산정하여 이용하였다. 본 연구는 향후 수자원 관리 및 계획 분야에서 다기준 의사결정기법을 적용할 때 사용될 수 있는 기초 가이드라인이 될 것이다.

• 한국수자원학회논문집
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• 제50권3호
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• pp.169-179
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• 2017

최근 우리나라는 온난화 현상 및 기후변화 등으로 인해 국지성 호우 발생 빈도가 잦아지고 있다. 특히 인구가 밀집되어 있는 도심지역이면서 지형적 지리적 여건, 우수배제능력 부족 등으로 인해 내수침수의 위험도가 높은 지역은 국지성 호우에 취약하다. 이에 본 연구에서는 집중호우에 취약한 장항읍을 시범유역으로 지정하고 대표적인 내수범람 해석모형인 XP-SWMM 모형을 이용한 침수해석을 실시하였다. 또한 해당지역에 알맞은 홍수방어 대책 을 수립하기 위해 다기준 의사결정기법(Multi-Criteria Decision Making)을 이용, 다양한 홍수방어 대안을 비교 및 평가하여 최적의 홍수방어대안을 제시하였다. 해당지역의 침수해소를 위해 구조적 침수방지대책(관로 개량, 우수저류지 설치, 우수펌프장 설치)을 선정하였으며, 대상지역을 3개의 소유역으로 분할하여 최적대안을 결정하였다. 2차원 내수침수 해석모형인 XP-SWMM을 이용하여 각 대안 설치 시 침수모의를 진행하였으며, 다기준 의사결정기법 Compromise Programming 기법을 이용하여 시범지역에 적합한 최적대안 우선순위를 결정하였으며, 그 결과 장항1지구의 경우 우수펌프장 설치, 장항2지구와 3지구의 경우 우수저류지 설치가 홍수방어를 위한 최적대안으로 선정되었다.

• Industrial Engineering and Management Systems
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• 제11권1호
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• pp.1-10
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• 2012

Supplier selection is an essential task within the purchasing function of supply chain management because it provides companies with opportunities to reduce various costs and realize stable and reliable production. However, many companies find it difficult to determine which suppliers should be targeted as each of them has varying strengths and weaknesses in performance which require careful screening by the purchaser. Moreover, information required to assess suppliers is not known precisely and typically fuzzy in nature. In this paper, therefore, fuzzy multi-objective linear programming (fuzzy MOLP) is presented under fuzzy goals: cost minimization, service level maximization and purchasing risk. To solve the problem, we introduce an enhanced two-phase approach of fuzzy linear programming for the supplier selection. In formulated problem, Analytical Hierarchy Process (AHP) is used to determine the weights of criteria, and Taguchi Loss Function is employed to quantify purchasing risk. Finally, we provide a set of alternative solution which enables decision maker (DM) to select the best compromise solution based on his/her preference. Numerical experiment is provided to demonstrate our approach.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2000년도 춘계학술발표대회 논문집
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• pp.143-148
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• 2000

In this article, we presents multi-objective design optimization of laminated composite beam using Fuzzy programming method. At first, the two design objectives are minimizing the structural weight and maximizing the buckling load respectively. Fuzzy multi-optimization problem can be formulated based on results of single optimizations. Due to different relative importance of design objectives, membership functions are constructed by adding exponential parameters for different objective's weights. Finite element analysis of composite beam for buckling behavior are carried by Natural mode method proposed by J.Argyris and computational time of analysis can be reduced. With this scheme, a designer can conveniently obtain a compromise optimal solution of a multi-objective optimization problem only by providing some exponential parameters corresponding to the importance of the objective functions.

• 국제학술발표논문집
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• The 2th International Conference on Construction Engineering and Project Management
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• pp.69-78
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• 2007

In real world, the project managers handle conflicting goals that govern the use of resources within the stipulated time and budget with required quality and safety. These conflicting goals are required to be optimized simultaneously by the project managers in the framework of fuzzy aspiration levels. The fuzzy linear programming model proposed herein helps project managers to minimize total project costs, completion time, and crashing costs considering indirect costs, contractual penalty costs etc by practically charging them in terms of direct cost of the project. A case study of bituminous pavement under construction is considered to demonstrate the feasibility of applying the proposed model for optimization of project parameters. Consequently, the proposed model yields an efficient compromise solution and the decision maker's overall degree of satisfaction with multiple fuzzy goal values. Additionally, the proposed model provides a systematic decision-making framework, enabling decision maker to interactively modify the fuzzy data and model parameters until a satisfactory solution is obtained. The significant characteristics that differentiate the proposed model with other models include, flexible decision-making process, multiple objective functions, and wide-ranging decision information.