In this paper, we deal with a real problem on production and transportation in a housing material manufacturer, and consider a production and transportation planning under the assumption that the manufacturer makes mu...
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In this paper, we deal with a real problem on production and transportation in a housing material manufacturer, and consider a production and transportation planning under the assumption that the manufacturer makes multiple products at factories in multiple regions and the products are in demand in each of the regions. First, we formulate mixed zero-one programming problems such that the cost of production and transportation is minimized subject to capacities of factories and demands of regions. Second, to realize stable production and satisfactory supply of the products in fuzzy environments, fuzzy programming for the production and transportation problem is incorporated. Finally, under the optimal planning of production and transportation, we show a profit and cost allocation by applying a solution concept from game theory. Using actual data, we show usefulness of the fuzzy programming and a rational allocation scheme of the profit and cost. (C) 2001 Elsevier Science B.V. All rights reserved.
This paper provides a spectrum of chance-constrained programming as well as chance-constrained multiobjective programming and chance-constrained goal programming with fuzzy rather than crisp decisions, which will seek...
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This paper provides a spectrum of chance-constrained programming as well as chance-constrained multiobjective programming and chance-constrained goal programming with fuzzy rather than crisp decisions, which will seek a fuzzy set from the given reference collection as an optimal solution. The technique of fuzzy simulation is also presented to check fuzzy chance constraints and to handle fuzzy objective and goal constraints. Finally, a fuzzy simulation-based genetic algorithm for solving these models will be designed and illustrated by some numerical examples. (C) 2001 Elsevier Science B.V. All rights reserved.
Multi-level programming is characterized as mathematical programming to solve decentralized planning problems. We have considered a multi-level linear programming problem and applied fuzzy mathematical programming, (F...
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Multi-level programming is characterized as mathematical programming to solve decentralized planning problems. We have considered a multi-level linear programming problem and applied fuzzy mathematical programming, (FMP) approach to obtain the solution of the system. We have suggested FMP method for the minimization of the objectives using linear membership functions. FMP is a supervised search procedure (supervised by the higher level decision maker (DM)). The higher level DM provides the preferred values of decision variables under his control (to enable the lower level DM to search for his optimum in a wider feasible space) and the bounds of his objective function (to direct the lower level DM to search for his solutions in the right direction). (C) 2002 Elsevier Science B.V. All rights reserved.
This paper presents an application of fuzzy programming approach to the multi-objective stochastic linear programming problem. After converting the proposed stochastic programming problem into a deterministic problem ...
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This paper presents an application of fuzzy programming approach to the multi-objective stochastic linear programming problem. After converting the proposed stochastic programming problem into a deterministic problem (which may be linear or non-linear), fuzzy programming approach is applied to find the compromise solution. Assuming the coefficients of the decision variables in the objective functions and in the constraints, and the right-hand-side parameters in the constraints as normal random variables, a methodology is presented to convert the probabilistic problem into a deterministic problem. Then fuzzy programming is applied using linear as well as non-linear membership functions. The method leads to an efficient solution as well as an optimal compromise solution. Numerical example is also presented to illustrate the methodology. (C) 1997 Elsevier Science B.V.
作者：
Mikhailov, LUniv Manchester
Inst Sci & Technol Dept Computat Decis Technol Grp Manchester M60 1QD Lancs England
The estimation of the priorities from pairwise comparison matrices is the major constituent of the Analytic Hierarchy Process (AHP). The priority vector can be derived from these matrices using different techniques, a...
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The estimation of the priorities from pairwise comparison matrices is the major constituent of the Analytic Hierarchy Process (AHP). The priority vector can be derived from these matrices using different techniques, as the most commonly used are the Eigenvector Method (EVM) and the Logarithmic Least Squares Method (LLSM). In this paper a new fuzzy programming Method (FPM) is proposed, based on geometrical representation of the prioritisation process. This method transforms the prioritisation problem into a fuzzy programming problem that can easily be solved as a standard linear programme. The FPM is compared with the main existing prioritisation methods in order to evaluate its performance. It is shown that it possesses some attractive properties and could be used as an alternative to the known prioritisation methods, especially when the preferences of the decision-maker are strongly inconsistent.
In this paper, a multi-objective chance constrained programming problem has been considered when bi's are normal random variables and the constraints have a joint probability distribution. The probabilistic proble...
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In this paper, a multi-objective chance constrained programming problem has been considered when bi's are normal random variables and the constraints have a joint probability distribution. The probabilistic problem is converted into an equivalent deterministic non-linear programming problem. Then the fuzzy programming technique has been applied to obtain a compromise solution. A numerical example is also presented to illustrate the methodology. (C) 2000 Elsevier Science B.V. All rights reserved.
In this paper fuzzy programming technique is used to solve a multi-objective geometric programming problem as a vector minimum problem. A fuzzy membership function is defined for the multi-objective geometric programm...
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In this paper fuzzy programming technique is used to solve a multi-objective geometric programming problem as a vector minimum problem. A fuzzy membership function is defined for the multi-objective geometric programming problem. Two numerical examples are presented to illustrate the method.
Zimmermann's fuzzy approach to the compromise solution concept in the multi-objective linear programming problem is considered. It is shown that given a class of membership functions of fuzzy goals assigned to obj...
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Zimmermann's fuzzy approach to the compromise solution concept in the multi-objective linear programming problem is considered. It is shown that given a class of membership functions of fuzzy goals assigned to objective functions in the problem, wider than primarily proposed by Zimmermann, the use of classical linear programming methods to solve and analyse the problem is also possible. As a result of application of the method based on the parametric programming technique, one can obtain a fuzzy solution of the problem. This solution is a certain fuzzy subset of the set of weakly efficient solutions of the problem. The solution which belongs to this set to the highest degree is a maximizing one (in Bellman and Zadeh's terminology). It may also be obtained by use of the usual non-parametric simplex method.
It is shown how fuzzy programming, using either the min or product operator, may be used to generate the whole Pareto optimal set for nonlineár concave, or convex, multiobjective programming problems. Also, a new...
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It is shown how fuzzy programming, using either the min or product operator, may be used to generate the whole Pareto optimal set for nonlineár concave, or convex, multiobjective programming problems. Also, a new solution procedure for a fuzzy program, when the min operator is employed, is presented.
Mixed-integer optimization problems belong to the group of NP-hard combinatorial problems. Therefore, they are difficult to search for global optimal solutions. Mixed-integer optimization problems are always described...
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Mixed-integer optimization problems belong to the group of NP-hard combinatorial problems. Therefore, they are difficult to search for global optimal solutions. Mixed-integer optimization problems are always described by precise mathematical programming models. However, many practical mixed-integer optimization problems have inherited a more or less imprecise nature. Under these circumstances, if we take into account the flexibility of the constraints and the fuzziness of the objectives, the original mixed-integer optimization problems can be formulated as fuzzy mixed-integer optimization problems. Mixed-integer hybrid differential evolution (MIHDE) is an evolutionary search algorithm which has been successfully applied to many complex mixed-integer optimization problems. In this article, a fuzzy mixed-integer mathematical programming model is developed to formulate the fuzzy mixed-integer optimization problem. In addition the MIHDE is introduced to solve the fuzzy mixed-integer programming problem. Finally, the illustrative example shows that satisfactory results can be obtained by the proposed method. This demonstrates that MIHDE can effectively handle fuzzy mixed-integer optimization problems.
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