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		Hongsheng QI,Daizhan CHENG.[en_title][J].Control Theory and Technology,2008,6(1):26~36.[Copy]

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HongshengQI,DaizhanCHENG
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Received:September 14, 2007

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Logic and logic-based control

Hongsheng QI, Daizhan CHENG

(Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China)

Abstract:

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.

Key words: Semi-tensor product Matrix expression of logic Mix-valued logic Logic-based fuzzy control