• 경영과학
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• 제10권2호
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• pp.1-9
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• 1993

This paper shows the application of fuzzy set and nonlinear membership function to linear programming problems in a fuzzy environment. In contrast to typical linear programming problems, the objectives and constraints of the problem in a fuzzy environment are defined imprecisely. This paper describes that fuzzy linear programming models can be formulated using the basic concepts of membership functions and fuzzy sets, and that they can be solved by quadratic programming methods. In a numerical example, a linear programming problem with two constraints and two decision variables is provided to illustrate the solution procedure.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.337-349
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• 2011

This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tucker conditions for a crisp linear programming problem.

• 품질경영학회지
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• 제20권1호
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• pp.101-106
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• 1992

In this paper fuzzy goal programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraints set are considered. Because of fuzzy coefficients in both members of each constraint ranking methods for fuzzy numbers are considered. An additive model to solve fuzzy goal programming problems is formulated. The diversity of each methods provides a lot of different models of auxiliary linear programming problems from which fuzzy solutions to the fuzzy goal programming problem can be obtained.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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• pp.232-239
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• 2006

This paper is for applying interactive fuzzy linear programming for the problem of product mix planning, which is one of the aggregate planning problem. We developed a modified algorithm, which has two-phase approach for interactive fuzzy linear programming to get a better solution. Adding two-phase method, we expect to obtain not only the highest membership degree, but also a better utilization of each constrained resource.

• 한국경영과학회지
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• 제11권1호
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• pp.36-43
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• 1986

In this study, the fuzzy programming is extended to handle various types of membership functions by transformation of the complicated fuzzy programming problems into the equivalent crisp linear programming problems with single objective. It is well-known that the fuzzy programming problem with linear membership functions (i.e., ramp type) can be easily transformed into a linear programming problem by introducing one dummy variable to minimize the worst unwanted deviation. However, until recently not many researches have been done to handle various general types of complicated linear membership functions which might be more realistic than ramp-or triangular-type functions. In order to handle these complicated membership functions, the goal dividing concept, which is based on the fuzzy set operation (i. e., intersection and union operations), has been prepared. The linear model obtained using the goal dividing concept is more efficient and single than the previous models [4, 8]. In addition, this result can be easily applied to any nonlinear membership functions by piecewise approximation since the membership function is continuous and monotone increasing or decreasing.

• 한국산림과학회지
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• 제83권3호
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• pp.271-279
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• 1994

본(本) 논문(論文)에서는 인공조림임분경영계획(人工造林林分經營計劃) 문제를 해결하기 위하여 임업(林業)에서 최근 새롭게 적용되고 있는 퍼지 다목표(多目標) 선형계획법(線型計劃法)을 소개한다. 우선 퍼지 집합이론(集合理論)이 간략하게 설명되고 퍼지 선형계획법(線型計劃法) 및 퍼지 다목표 선형계획법이 개념적으로 소개된다. 그 다음 연구대상지역의 자료를 분석하여 표준적(標準的) 선형계획(線型計劃)모델이 구성되고 이 모델의 컴퓨터 계산에 의해 4개의 목재가격(木材價格) 범위에 대한 최적해(最適解)(순현재가(純現在價))가 각각 계산된다. 이 선형계획모델은 불확실한 4개의 목재가격정보를 조정하기 위해서 퍼지 다목표(多目標) 선형계획(線型計劃)모델로 재구성된다. 그리고 이 퍼지 모델의 계산에 의해 절충최적해(折衷最適解)가 얻어지게 된다. 4개의 목재가격 범위에 대해 얻어진 4개의 최적해와 하나의 절충최적해가 비교(比較)되고 논의(論議)된다.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.345-354
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• 2006

In this paper first, we find a canonical symmetrical trapezoidal(triangular) for the solution of the fuzzy linear system $A\tilde{x}=\tilde{b}$, where the elements in A and $\tilde{b}$ are crisp and arbitrary fuzzy numbers, respectively. Then, a model for fuzzy linear programming problem with fuzzy variables (FLPFV), in which, the right hand side of constraints are arbitrary numbers, and coefficients of the objective function and constraint matrix are regarded as crisp numbers, is discussed. A numerical procedure for calculating a canonical symmetrical trapezoidal representation for the solution of fuzzy linear system and the optimal solution of FLPFV, (if there exist) is proposed. Several examples illustrate these ideas.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.307-312
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• 1994

The authors have been devoted to researches on fuzzy theories and their applications, especially control theory and application problems, for recent years. In this paper, the authors present results on a comparison of optimal solutions between ones of an ordinary-typed mathematical linear programming problem(O.M.I.P. problem) and ones of a Zimmerman-typed fuzzy mathematical linear programming problem (F.M.L.P. problem), and comment about the sensitivity (differences and fuzziness on between O.M.L.P. problem and F.M.L.P. problem) on optimal solutions of these mathematical linear programming problems.

• 한국산림과학회지
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• 제85권2호
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• pp.172-179
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• 1996

본 연구는 산림자원(山林資源)의 다목적(多目的) 이용(利用) 문제에 합리적으로 접근하기 위하여 퍼지 다목표(多目標) 선형계획법(線型計劃法)을 삼림경영계획에 응용하고자 시도되었다. 산림이 가지고 있는 두 가지 기능 즉, 목재생산기능(木材生産機能)과 공익기능(公益機熊)이 지역별로 적절히 발휘되면서 조화를 이룰때 산림자원의 다목적 이용문제가 해결될 수 있다. 여기에서는 공익기능 중에서 휴양기능(休養機能)이 발휘되고 있는 자연휴양림(自然休養林)을 대상으로 목재생산기능과 휴양기능이 합목적적(合目的的)으로 조합을 이룰 수 있는 모델을 개발하였다. 우리나라에서 최초로 조성된 유명산 자연휴양림 지역을 대상으로 자료를 수집하여 퍼지 다목표(多目標) 선형계획(線型計劃)모델을 구성하였다. 그리고 이 모델의 계산을 통해 얻어진 결과가 기존의 휴양림 경영계획서상의 자료와 비교 검토되었다. 이때 유명산 자연휴양림 면적 829ha를 대상으로 퍼지 다목표(多目標) 선형계획(線型計劃)모델을 적용한 결과 4분기(分期) 동안 수확경신(收穫更新) 가능한 면적이 410.8ha로 나타났고 이 때의 수확재적은 $57,904m^3$ 였으며, 이 휴양림(休養林)을 찾는 방문객수는 약 860만명 정도로 추정되었다. 퍼지 목표(多目標) 선형계획(線型計劃)모델에 의해서 목재생산계획(木材生産計劃)과 휴양계획(休養計劃)이 동시에 최적화(最適化) 될때의 최대구성함수(最大構成函數)값 ${\lambda}$는 0.29로 나타났다.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.439-448
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• 2001

In this paper a fuzzy linear programming problem is presented. Then using the concept of comparison of fuzzy numbers, by the aid of the Mellin transform, we introduce a method for solving this problem.