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Logic and logic-based control
  • 时间：0
  • 分类：TP13[自动化与计算机技术—控制科学与工程;自动化与计算机技术—控制理论与控制工程]
  • 作者机构：[1]Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China
  • 相关基金：This work was partly supported by the National Natural Science Foundation of China （No.60274010, 60343001, 60221301, 60334040）.
  • 相关项目：控制科学中若干关键基础问题的研究
关键词： 逻辑学, 模糊控制, 半张量积, 矩阵表达, Semi-tensor product, Matrix expression of logic, Mix-valued logic, Logic-based fuzzy control
中文摘要：

这篇论文给逻辑的矩阵表情。在矩阵表达式下面，对逻辑操作符的一般描述被建议。用矩阵的半张肌产品，逻辑等价的证明，含意，等等，能非常被简化。某些一般性质被揭示。基于矩阵表示，然后，逻辑操作员被扩大到多珍视的逻辑，它为模糊逻辑推理提供一个基础。最后，我们建议逻辑的一种新类型，叫的珍视混合的逻辑，；一种新设计技术，叫的基于逻辑的模糊控制。他们为模糊系统的控制为模糊逻辑的应用程序提供一个数字地可计算出来的框架。

英文摘要：

This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.

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