Goal programming (GP) and fuzzy programming (FP) are two approaches for solving the vector optimization problem by reducing it to a single (or sequential) objective one. These two approaches have some similarities and...
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Goal programming (GP) and fuzzy programming (FP) are two approaches for solving the vector optimization problem by reducing it to a single (or sequential) objective one. These two approaches have some similarities and both of them have more than one form to handle the multiobjective problem. This paper highlights the similarities between GP and FP and answers the question how each one can lead to the other. However, we will consider in this paper the min-operator to transform the linear FP to a crisp program since this approach is more popular and applied than the others. In addition, some new forms of fuzzy programs are presented in this paper. These new forms use the concept of deviational variables of GP (and not the min-operator) to transform the FP to a crisp one. Finally, a numerical example to illustrate the relationship between the two approaches is given. (C) 1997 Elsevier Science B.V.
In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order ...
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In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper,. we focus on the solution procedure of the multiobjective transportation problem (MOTP) where the cost coefficients of the objective functions, and the source and destination parameters have been expres...
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In this paper,. we focus on the solution procedure of the multiobjective transportation problem (MOTP) where the cost coefficients of the objective functions, and the source and destination parameters have been expressed as interval values by the decision maker. This problem has been transformed into a classical MOTP where to minimize the interval objective function, the order relations that represent the decision maker's preference between interval profits have been defined by the right limit, left limit, centre, and half-width of an interval. The constraints with interval source and destination parameters have been converted into deterministic ones. Finally, the equivalent transformed problem has been solved by fuzzy programming technique. Numerical examples have been provided to illustrate the solution procedure for three possible cases of the original problem. (C) 1999 Elsevier Science B.V. All rights reserved.
In conventional multiobjective decision making problems, the estimation of the parameters of the model is often a problematic task. Normally they are either given by the decision maker (DM), who has imprecise informat...
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In conventional multiobjective decision making problems, the estimation of the parameters of the model is often a problematic task. Normally they are either given by the decision maker (DM), who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets for which a lot of fuzzy approaches to multiobjective programming have been developed. In this paper we propose a method to solve a multiobjective linear programming problem involving fuzzy parameters (FP-MOLP), whose possibility distributions are given by fuzzy numbers, estimated from the information provided by the DM. As the parameters, intervening in the model, are fuzzy the solutions will be also fuzzy. We propose a new Pareto Optimal Solution concept for fuzzy multiobjective programming problems. It is based on the extension principle and the joint possibility distribution of the fuzzy parameters of the problem. The method relies on cc-cuts of the fuzzy solution to generate its possibility distributions. These ideas are illustrated with a numerical example. (C) 1999 Elsevier Science B.V. All rights reserved.
The estimate of the parameters which define a conventional multiobjective decision making model is a difficult task. Normally they are either given by the Decision Maker who has imprecise information and/or expresses ...
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The estimate of the parameters which define a conventional multiobjective decision making model is a difficult task. Normally they are either given by the Decision Maker who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from the past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets and several fuzzy approaches to multiobjective programming have been developed [1,9-11]. The fuzziness of the parameters gives rise to a problem whose solution will also be fuzzy, see [2,3], and which is defined by its possibility distribution. Once the possibility distribution of the solution has been obtained, if the decision maker wants more precise information with respect to the decision vector, then we can pose and solve a new problem. In this case we try to find a decision vector, which approximates as much as possible the fuzzy objectives to the fuzzy solution previously obtained. In order to solve this problem we shall develop two different models from the initial solution and based on Goal programming: an Interval Goal programming Problem if we define the relation "as accurate as possible" based on the expected intervals of fuzzy numbers, as we showed in [4], and an ordinary Goal programming based on the expected values of the fuzzy numbers that defined the goals. Finally, we construct algorithms that implement the above mentioned solution method. Our approach will be illustrated by means of a numerical example. (C) 1999 Elsevier Science B.V. All rights reserved.
This paper attempts to model capital budgeting problems by chance constrained integer programming in a fuzzy environment (rather than a stochastic environment). Some examples are also provided to illustrate the potent...
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This paper attempts to model capital budgeting problems by chance constrained integer programming in a fuzzy environment (rather than a stochastic environment). Some examples are also provided to illustrate the potential applications of new models. Finally, a fuzzy simulation based genetic algorithm is designed for solving chance constrained integer programming models with fuzzy parameters.
This paper presents a new fuzzy preference programming method for deriving priorities from inconsistent interval pairwise comparison matrices in the Analytical Hierarchy Process (AHP). The preference programming metho...
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This paper extends chance constrained programming from stochastic to fuzzy environments. Analogous to stochastic programming, some crisp equivalents of chance constraints in fuzzy environments are presented. We also p...
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This paper extends chance constrained programming from stochastic to fuzzy environments. Analogous to stochastic programming, some crisp equivalents of chance constraints in fuzzy environments are presented. We also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents. Finally, a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed. (C) 1998 Published by Elsevier Science B.V.
The existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models (optimistic models) which maximize the maximum possible return. This paper presents a spectrum of minimax ...
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The existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models (optimistic models) which maximize the maximum possible return. This paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as-well as chance constrained multiobjective programming and chance constrained goal programming, in which the minimax models will select the alternative that provides the best of the worst possible return. Finally, a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples. (C) 1998 Elsevier Science Inc. All rights reserved.
This paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives. We also present a fuzzy...
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This paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives. We also present a fuzzy simulation technique for handling fuzzy objective constraints and fuzzy goal constraints. Finally, a fuzzy simulation based genetic algorithm is employed to solve a numerical example. (C) 1998 Elsevier Science B.V. All rights reserved.
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