• Journal of Korean Society for Quality Management
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• v.20 no.1
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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 Reliability and Applications
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• v.12 no.2
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• pp.79-94
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• 2011

Redundancy-reliability allocation problems in multi-stage series-parallel systems are addressed in this study. Fuzzy programming techniques are proposed for finding satisfactory solutions. First, a multi-objective programming model is formulated for simultaneously maximizing system reliability and minimizing system total cost. Due to the nature of uncertainty in the problem, the fuzzy set theory and technique are used to convert the deterministic multi-objective programming model into a fuzzy nonlinear programming problem. A heuristic method is developed to get satisfactory solutions for the fuzzy nonlinear programming problem. A Pareto optimal solution is found with maximal degree of satisfaction from the interception area of fuzzy sets. A case study that is related to the electronic control unit installed on aircraft engine over-speed protection system is used to implement the developed approach. Results suggest that the developed fuzzy multi-objective programming model can effectively resolve the fuzzy and uncertain problem when design goals and constraints are not clearly confirmed at the initial conceptual design phase.

• Korean Management Science Review
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• v.10 no.2
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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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• v.29 no.1_2
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.63-68
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• 1998

This paper proposes fuzzy regression analysis with non-symmetric fuzzy coefficients. By assuming non-symmetric triangular fuzzy coefficients and applying the quadratic programming fomulation, the center of the obtained fuzzy regression model attains more central tendency compared to the one with symmetric triangular fuzzy coefficients. For a data set composed of crisp inputs-fuzzy outputs, two approximation models called an upper approximation model and a lower approximation model are considered as the regression models. Thus, we also propose an integrated quadratic programming problem by which the upper approximation model always includes the lower approximation model at any threshold level under the assumption of the same centers in the two approximation models. Sensitivities of Weight coefficients in the proposed quadratic programming approaches are investigated through real data.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.449-460
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• 2007

Several fuzzy approaches can be considered for solving multi-objective transportation problem. This paper presents a fuzzy goal programming approach to determine an optimal compromise solution for the multiobjective transportation problem. We assume that each objective function has a fuzzy goal. Also we assign a special type of nonlinear (hyperbolic) membership function to each objective function to describe each fuzzy goal. The approach focuses on minimizing the negative deviation variables from 1 to obtain a compromise solution of the multiobjective transportation problem. We show that the proposed method and the fuzzy programming method are equivalent. In addition, the proposed approach can be applied to solve other multiobjective mathematical programming problems. A numerical example is given to illustrate the efficiency of the proposed approach.

• Journal of Mechanical Science and Technology
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• v.20 no.6
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• pp.731-737
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• 2006

Interactive Fuzzy Physical Programming (IFPP) developed in this paper is a new efficient multi-objective optimization method, which retains the advantages of physical programming while considering the fuzziness of the designer's preferences. The fuzzy preference function is introduced based on the model of linear physical programming, which is used to guide the search for improved solutions by interactive decision analysis. The example of multi-objective optimization design of the spindle of internal grinder demonstrates that the improved preference conforms to the subjective desires of the designer.

• Journal of the Korean Institute of Navigation
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• v.20 no.4
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• pp.59-70
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• 1996

A berth assignment problem has a direct impact on assessment of charges made to ships and goods. In this paper, we concerned with of fuzzy mathematical programming models for a berth assignment problem to achieved an efficient berth operation in a fuzzy environment. In this paper, we focus on the berth assignment programming with fuzzy parameters which are based on personal opinions or subjective judgement. From the above point of view, assume that a goal and a constraint are given by fuzzy sets, respectively, which are characterized by membership functions. Let a fuzzy decision be defined as the fuzzy set resulting from the intersection of a goal and constraint. This paper deals with fuzziness in all parameters which are expressed by fuzzy numbers. A fuzzy parameter defined by a fuzzy number means a possibility distribution of the parameters. These fuzzy 0-1 integer programming problems are formulated by fuzzy functions whose concept is also called the extension principle. We deal with a berth assignment problem with triangular fuzzy coefficients and propose a branch and bound algorithm for solving the problem. We suggest three models of berth assignment to minimizing the objective functions such as total port time, total berthing time and maximum berthing time by using a revised Maximum Position Shift(MPS) concept. The berth assignment problem is formulated by min-max and fuzzy 0-1 integer programming. Finally, we gave the numerical solutions of the illustrative examples.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.457-465
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• 2004

Ramik[7] introduced a fuzzy goal programming (FGP)problem that generalizes a standard goal programming (GP) problem with fuzzy alternatives, fuzzy objective functions and fuzzy deviation functions for measuring the deviation between attained and desired goals being fuzzy. However, it is known that this FGP tends to produce an approximate solution since it uses an approximate fuzzy multiplication operation to solve the resultant fuzzy model. In this paper, we show that this FGP sometimes leads to the wrong decision. We also propose a procedure that gets the exact solution to overcome these problems. The method is based on $T_M$ (min norm)-based fuzzy operations using $\alpha-cut$ representations. We consider the same example as used in Ramik and investigate how our procedures are compared to Ramik's.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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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.