A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famo...A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famous experts working in artificial intelligence and fuzzy systems refuted the opinion. Elkan then gave another report entitled 'The Paradoxical Controversy over Fuzzy Logic' as a reply to the refutations mentioned above. Prof. Wu gave a detailed analysis on the controversy (see ref. [3]). This shows that there is no rigid logic foundation for fuzzy propositional calculus. In this note we first point out that it is impossible to keep all classical theorems as tautologies in the field of fuzzy propositional calculus. Then we introduce a formal deductive system in fuzzy propositional calculus by giving up certain classical axioms, and the corresponding soundness theorem is proved.展开更多
The concepts of metric R0-algebra and Hilbert cube of type RO are introduced. A unified approximate reasoning theory in propositional caculus system ? and predicate calculus system (?) is established semantically as w...The concepts of metric R0-algebra and Hilbert cube of type RO are introduced. A unified approximate reasoning theory in propositional caculus system ? and predicate calculus system (?) is established semantically as well as syntactically, and a unified complete theorem is obtained.展开更多
Since the formal deductive system (?) was built up in 1997, it has played important roles in the theoretical and applied research of fuzzy logic and fuzzy reasoning. But, up to now, the completeness problem of the sys...Since the formal deductive system (?) was built up in 1997, it has played important roles in the theoretical and applied research of fuzzy logic and fuzzy reasoning. But, up to now, the completeness problem of the system (?) is still an open problem. In this paper, the properties and structure of R0 algebras are further studied, and it is shown that every tautology on the R0 interval [0,1] is also a tautology on any R0 algebra. Furthermore, based on the particular structure of (?) -Lindenbaum algebra, the completeness and strong completeness of the system (?) are proved. Some applications of the system (?) in fuzzy reasoning are also discussed, and the obtained results and examples show that the system (?) is suprior to some other important fuzzy logic systems.展开更多
文摘A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famous experts working in artificial intelligence and fuzzy systems refuted the opinion. Elkan then gave another report entitled 'The Paradoxical Controversy over Fuzzy Logic' as a reply to the refutations mentioned above. Prof. Wu gave a detailed analysis on the controversy (see ref. [3]). This shows that there is no rigid logic foundation for fuzzy propositional calculus. In this note we first point out that it is impossible to keep all classical theorems as tautologies in the field of fuzzy propositional calculus. Then we introduce a formal deductive system in fuzzy propositional calculus by giving up certain classical axioms, and the corresponding soundness theorem is proved.
基金supported by the National Natural Science Foundation of China(Grant No.19331010).
文摘The concepts of metric R0-algebra and Hilbert cube of type RO are introduced. A unified approximate reasoning theory in propositional caculus system ? and predicate calculus system (?) is established semantically as well as syntactically, and a unified complete theorem is obtained.
文摘Since the formal deductive system (?) was built up in 1997, it has played important roles in the theoretical and applied research of fuzzy logic and fuzzy reasoning. But, up to now, the completeness problem of the system (?) is still an open problem. In this paper, the properties and structure of R0 algebras are further studied, and it is shown that every tautology on the R0 interval [0,1] is also a tautology on any R0 algebra. Furthermore, based on the particular structure of (?) -Lindenbaum algebra, the completeness and strong completeness of the system (?) are proved. Some applications of the system (?) in fuzzy reasoning are also discussed, and the obtained results and examples show that the system (?) is suprior to some other important fuzzy logic systems.
