Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint
Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint
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DOI：
10.1016/j.ins.2010.10.024
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发表时间：
2011-02
期刊：
影响因子：
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通讯作者：
B. Shieh
中科院分区：
文献类型：
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作者：
B. Shieh
这项工作探讨了最小化线性目标函数的最大-t模糊关系方程约束，其中t是一个连续/阿基米德t-范数的可行性。传统的方法来解决这个问题显着改善，首先分离的问题分为两个子问题，根据可用的正系数。因此，这种分解比以前的文献更容易处理。其次，利用约束方程的最大解，求解非正系数的子问题，并减小正系数子问题的规模。这一步骤在传统方法中是独一无二的，因为它能够确定尽可能多的最佳变量。此外，几个规则被开发用于简化剩余的问题。最后，这些待定的最优变量是使用覆盖问题，而不是分支定界方法。三个示例表明，所提出的方法优于传统的计划。并对其潜在的应用进行了讨论。
The work examines the feasibility of minimizing a linear objective function subject to a max-t fuzzy relation equation constraint, where t is a continuous/Archimedean t-norm. Conventional methods for solving this problem are significantly improved by, first separating the problem into two sub-problems according to the availability of positive coefficients. This decomposition is thus more easily handled than in previous literature. Next, based on use of the maximum solution of the constraint equation, the sub-problem with non-positive coefficients is solved and the size of the sub-problem with positive coefficients reduced as well. This step is unique among conventional methods, owing to its ability to determine as many optimal variables as possible. Additionally, several rules are developed for simplifying the remaining problem. Finally, those undecided optimal variables are obtained using the covering problem rather than the branch-and-bound methods. Three illustrative examples demonstrate that the proposed approach outperforms conventional schemes. Its potential applications are discussed as well.