This paper addresses the teachability/controllability of high order mix-valued logical control networks by using the semi-tensor product method, and presents some necessary and sufficient conditions for the reachabili...This paper addresses the teachability/controllability of high order mix-valued logical control networks by using the semi-tensor product method, and presents some necessary and sufficient conditions for the reachability/controllability. The high order mix-valued logical network is converted into an algebraic form first, baaed on which the reachability/controllability of the system is then investigated, and several necessary and sufficient conditions are established. The study of several illustrative examples shows that our new method is very effective in dealing with the reachability/controllability of high order mix-valued logical control networks.展开更多
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, im...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.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61074068,61034007,61174036the Research Fund for the Taishan Scholar Project of Shandong Province of Chinathe Natural Science Foundation of Shandong Province under Grant No.ZR2010FM013
文摘This paper addresses the teachability/controllability of high order mix-valued logical control networks by using the semi-tensor product method, and presents some necessary and sufficient conditions for the reachability/controllability. The high order mix-valued logical network is converted into an algebraic form first, baaed on which the reachability/controllability of the system is then investigated, and several necessary and sufficient conditions are established. The study of several illustrative examples shows that our new method is very effective in dealing with the reachability/controllability of high order mix-valued logical control networks.
基金the National Natural Science Foundation of China (No.60274010, 60343001, 60221301, 60334040)
文摘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.
