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Reducing the search space of a linear fractional programming problem under fuzzy relational equations with max-Archimedean t-norm composition

机译:带有max-Archimedean t-范数的模糊关系方程下线性分数规划问题的搜索空间减少

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摘要

Prior studies have demonstrated that one of the minimal solutions of a fuzzy relational equation with the max-Archimedean t-norm composition is an optimal solution of a linear objective function with positive coefficients. However, this property cannot be adopted to optimize the problem of a linear fractional objective function. This study presents an efficient method to optimize such a linear fractional programming problem. First, some theoretical results are developed based on the properties of max-Archimedean t-norm composition. The result is used to reduce the feasible domain. The problem can thus be simplified and converted into a traditional linear fractional programming problem, and eventually optimized in a small search space. A numerical example is provided to illustrate the procedure.
机译:先前的研究表明,具有最大阿希米德t范数组成的模糊关系方程的最小解之一是具有正系数的线性目标函数的最优解。但是,不能采用此属性来优化线性分数目标函数的问题。这项研究提出了一种优化这种线性分数规划问题的有效方法。首先,基于max-Archimedean t-范数组成的性质,得出了一些理论结果。结果用于减少可行域。因此可以简化该问题并将其转换为传统的线性分数规划问题,并最终在较小的搜索空间中对其进行优化。提供了一个数值示例来说明该过程。

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