Compactness in Pavelka’s fuzzy logic for some compact lattices of truth values is shown, and the concept of gradual compactness is introduced to establish some corresponding results in a more general setting.
In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure op...In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.展开更多
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent ...The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.展开更多
It is no doubt that the researches on the N-compactness in[1] and [2] are a nice and important achievement in L-fuzzy topology. There is a natural and interesting question about the N-compactness——the sheaf structur...It is no doubt that the researches on the N-compactness in[1] and [2] are a nice and important achievement in L-fuzzy topology. There is a natural and interesting question about the N-compactness——the sheaf structures of N-compact sets. It is proved that, for weakly induced Hausdorff space, the N-compactness of L-fuzzy set A in the upper展开更多
文摘Compactness in Pavelka’s fuzzy logic for some compact lattices of truth values is shown, and the concept of gradual compactness is introduced to establish some corresponding results in a more general setting.
文摘In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.
文摘The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
基金Project supported partly by the National Natural Science Foundation of China
文摘It is no doubt that the researches on the N-compactness in[1] and [2] are a nice and important achievement in L-fuzzy topology. There is a natural and interesting question about the N-compactness——the sheaf structures of N-compact sets. It is proved that, for weakly induced Hausdorff space, the N-compactness of L-fuzzy set A in the upper
