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首页> 外文期刊>International Journal of Operational Research >Preferable Pareto optimal solutions for specified key objective functions to multiple objective linear programming problems using trade-off ratios under fuzzy environment: an iterative process
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Preferable Pareto optimal solutions for specified key objective functions to multiple objective linear programming problems using trade-off ratios under fuzzy environment: an iterative process

机译：优选的Pareto用于指定关键目标功能的最佳解决方案，在模糊环境下使用权衡差值进行多个客观线性规划问题：一个迭代过程

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摘要

In this paper, one general iterative process is proposed for obtaining preferable Pareto optimal solutions, based on specified key objective functions, to multiple objective linear programming problems under fuzzy environment. In reality, decision maker usually specifies one key objective function to such problems. But there are known disadvantages in applying existing fuzzy optimisation techniques, in which weights, utility functions etc. are used; whereas in other techniques, none of the objective functions can be specified effectively as key objective function. Moreover, correlation between key objective function and other objective functions may not be exactly known to the decision maker. In existing interactive fuzzy optimisation techniques, initially developed by Sakawa et al. (1984), all such reference levels of fuzzy objective functions are taken as unity. But we may find it unrealistic to expect each of conflicting objective functions to attain individual goals simultaneously. In this paper, we propose to employ trade-off ratios of membership functions of fuzzy objective functions to determine corresponding reference membership levels analytically and develop one iterative process to find preferable Pareto optimal solutions under fuzzy environment. Numerical examples further illustrate our proposed iterative process. Finally conclusions are drawn.
机译：在本文中，提出了一种基于指定的关键目标函数获得优选的Paroto最佳解决方案，以在模糊环境下对多目标线性规划问题获得优选的帕累托最优解。实际上，决策者通常会指定这种问题的一个关键目标函数。但是，在应用现有的模糊优化技术方面存在已知的缺点，其中使用权重，公用事业功能等;虽然在其他技术中，无客观函数可以有效地指定为关键目标函数。此外，决策者可能无法恰恰知道关键目标函数和其他客观函数之间的相关性。在现有的交互式模糊优化技术中，最初由Sakawa等人开发。 （1984），所有这些参考水平的模糊客观函数被视为统一。但是，我们可能会发现每个相互冲突的客观职能同时获得个别目标的情况不切实际。在本文中，我们建议采用模糊目标职能的会员职能的权衡比率，以便分析确定相应的参考会员级别，并开发一个迭代过程，以在模糊环境下找到优选的帕累托最佳解决方案。数值例子进一步说明了我们所提出的迭代过程。最后得出结论。

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