Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is m...Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is more robust than all other implication inferences for noise data and that CFS has better robustness than conventional fuzzy systems, which provide the solid foundation for CFS's potential application in fuzzy control and modeling and so on.展开更多
Based on the technique of integral within an ordered product of nonlinear bosonic operators we construct a kind of tripartite nonlinear entangled states, which can make up a complete set. As its application, we also d...Based on the technique of integral within an ordered product of nonlinear bosonic operators we construct a kind of tripartite nonlinear entangled states, which can make up a complete set. As its application, we also derive nonlinear 3-mode charge-related entangled state. The essential point for constructing these states lies in choosing the appropriate charge operator.展开更多
Vladimir Markin proposes a certain construction---a generalisation of syllogistic--in which he uses the constant @ with indef＇mite arity. The atomic formulae are of the following sort： S1S2 ...Sm@P1P2...Pn, where re...Vladimir Markin proposes a certain construction---a generalisation of syllogistic--in which he uses the constant @ with indef＇mite arity. The atomic formulae are of the following sort： S1S2 ...Sm@P1P2...Pn, where re＋n〉0. The standard syllogistic functors are here interpreted as follows： SAP=： S@P SeP=： SP@ SIP=： -SP@ SOP=： ~S@P Markin constructs a system of Fundamental Syllogistic （FS） with constant @ in an axiomatic way. Based on Markin＇s idea, we propose two constructions, which are formulations of the system of sequential predication built upon the quantifier-less calculus of names. The first one includes the FS system. The second one is enriched with individual variables and, among other things, allows including sequences of individual names in which one has to do with enumerative functors. The counterpart of Hao Wang＇s algorithm holds in the first system extended with negative terms.展开更多
A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degen...A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.展开更多
文摘Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is more robust than all other implication inferences for noise data and that CFS has better robustness than conventional fuzzy systems, which provide the solid foundation for CFS's potential application in fuzzy control and modeling and so on.
基金The project supported by National Natural Science Foundation of China and the President Foundation of the Chinese Academy of Sciences
文摘Based on the technique of integral within an ordered product of nonlinear bosonic operators we construct a kind of tripartite nonlinear entangled states, which can make up a complete set. As its application, we also derive nonlinear 3-mode charge-related entangled state. The essential point for constructing these states lies in choosing the appropriate charge operator.
文摘Vladimir Markin proposes a certain construction---a generalisation of syllogistic--in which he uses the constant @ with indef＇mite arity. The atomic formulae are of the following sort： S1S2 ...Sm@P1P2...Pn, where re＋n〉0. The standard syllogistic functors are here interpreted as follows： SAP=： S@P SeP=： SP@ SIP=： -SP@ SOP=： ~S@P Markin constructs a system of Fundamental Syllogistic （FS） with constant @ in an axiomatic way. Based on Markin＇s idea, we propose two constructions, which are formulations of the system of sequential predication built upon the quantifier-less calculus of names. The first one includes the FS system. The second one is enriched with individual variables and, among other things, allows including sequences of individual names in which one has to do with enumerative functors. The counterpart of Hao Wang＇s algorithm holds in the first system extended with negative terms.
文摘A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.
