| 引用本文: | 范洪彪,冯俊娥,孟敏.模糊关系不等式 A o X o B ≤ C 的解[J].控制理论与应用,2016,33(5):694~700.[点击复制] |
| FAN Hong-biao,FENG Jun-e,MENG Min.Solutions to fuzzy relation inequality A o X o B ≤ C[J].Control Theory and Technology,2016,33(5):694~700.[点击复制] |
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| 模糊关系不等式 A o X o B ≤ C 的解 |
| Solutions to fuzzy relation inequality A o X o B ≤ C |
| 摘要点击 3086 全文点击 1806 投稿时间：2015-11-02 修订日期：2016-06-15 |
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| DOI编号 10.7641/CTA.2016.15016 |
| 2016,33(5):694-700 |
| 中文关键词 模糊关系不等式 全部解 半张量积 格化线性规划 |
| 英文关键词 fuzzy relation inequalities all solutions semi-tensor product latticized linear programming |
| 基金项目 国家自然科学基金项目(61374025)资助. |
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| 中文摘要 |
| 对于普通的矩阵乘积, 当一个方程或者不等式有解时, 有可能存在无数多个解, 而直接求解它们又是很困
难的. 同样, 对于有限论域上采用最大–最小合成算子的模糊关系方程或者不等式也存在着类似的问题. 不幸的是,
研究此类问题的文献相对较少. 本文致力于研究模糊关系不等式A o X o B ≤ C的一种新求解方法. 首先, 利用两
个重要的公式, 将所考虑的模糊关系不等式转化成较简单的形式. 对于模糊关系不等式的可解性给出一个充分必
要条件. 它表明模糊关系不等式A o X o B ≤ C的解可以由有限个节点解来刻画. 然后, 利用矩阵的半张量积, 给出
具体的求解算法. 最后, 介绍了具有模糊关系不等式限制的格化线性规划, 来说明本文所提出方法的有效性. |
| 英文摘要 |
| For traditional matrix product, there may exist infinite solutions, in a sense that some matrix equations or
inequalities can be solved. Furthermore, it is very difficult to solve them directly. Similarly, for max-min composition in
finite course, fuzzy relational equations or inequalities may also have the same trouble. Unfortunately, there are few papers
referring to the problem. This paper devotes to deriving a new method of solving fuzzy relation inequality (FRI) in terms
of A?X ?B 6 C. First of all, two important formulas are proved. Then, the considered FRIs are converted into simplified
ones taking use of the two transformations. While for solvability of FRIs, a necessary and sufficient condition is obtained.
It illustrates that the solutions of considered FRIs can be depicted by finite ones. Via semi-tensor product (STP) of matrices,
a concrete algorithm is derived. Finally, with FRIs constraints latticized linear programming is presented to demonstrate
effectiveness of the proposed methods. |
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