In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new...In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.展开更多
In this paper,the notion of local Sβ-compactness of L-topological spaces is introduced.It is proved that the local Sβ-compactness is an L-good extension,which is inherited by a closed subspace,multiplicative and inv...In this paper,the notion of local Sβ-compactness of L-topological spaces is introduced.It is proved that the local Sβ-compactness is an L-good extension,which is inherited by a closed subspace,multiplicative and invariable under the continuous open surjective L-valued Zadeh function.展开更多
Recent developments in mathematics have in a sense organized objects of study into categories, where properties of mathematical systems can be unified and simplified through presentation of diagrams with arrows. A cat...Recent developments in mathematics have in a sense organized objects of study into categories, where properties of mathematical systems can be unified and simplified through presentation of diagrams with arrows. A category is an algebraic structure made up of a collection of objects linked together by morphisms. Category theory has been advanced as a more concrete foundation of mathematics as opposed to set-theoretic language. In this paper, we define a pseudo-category on the class of isotonic spaces on which the idempotent axiom of the Kuratowski closure operator is assumed.展开更多
In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
Diverse concepts of space developed in history of natural philosophy,mathematics,physics,and other natural or cultural studies form theoretical models of spatial relations,given in human’s experience.Their diversity ...Diverse concepts of space developed in history of natural philosophy,mathematics,physics,and other natural or cultural studies form theoretical models of spatial relations,given in human’s experience.Their diversity is due not only to the multiplicity of philosophical and methodological approaches to the concept of space,but also to the variety of ways,in which spatial relationships can be organized.This variety gives a possibility to distinct autonomous spaces of different types with diverse sets of properties as well as separate spaces with their own ordinal,metrical,and sequential structures.Particularly,various ways of space semiotization in culture generate different types of autonomous and separate spaces:written texts,maps,pictures,chessboards,etc.In the same time,all particular notions of space are included in a general logical class.Its volume and content are covered by the philosophical category of space.Such general category cannot be reduced to mathematical,physical,or other concepts of space elaborated in particular sciences,however,it serves as a philosophical basis for their comparison.展开更多
Let L be a meet continuous lattice. It is proved that the category Top of topological spaces can be embedded in the category of strati?ed L-topological spaces as a concretely both re?ective and core?ective full subcat...Let L be a meet continuous lattice. It is proved that the category Top of topological spaces can be embedded in the category of strati?ed L-topological spaces as a concretely both re?ective and core?ective full subcategory if and only if L is a continuous lattice.展开更多
In this paper it is proved that for all completely distributive lattices L. the category of L-fuzzifying topological spaces can be wmbedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a...In this paper it is proved that for all completely distributive lattices L. the category of L-fuzzifying topological spaces can be wmbedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a simultaneously bireflective and bicoreflective full subcategory.展开更多
In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is al...In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.展开更多
In this paper,after discussing the prime implication filter of lattice implication algebra,we introduced the concept of prime space of lattice implication algebra,in which we analysised its topological property and di...In this paper,after discussing the prime implication filter of lattice implication algebra,we introduced the concept of prime space of lattice implication algebra,in which we analysised its topological property and discussed the relation between the category of topological space and the category of lattice implication algebras.展开更多
By contrasting the two British films, KesI and Billy Elliot2, which in different historical periods, the paper is a comparative cultural study to films. Aside from the similarities, the differences between the two fil...By contrasting the two British films, KesI and Billy Elliot2, which in different historical periods, the paper is a comparative cultural study to films. Aside from the similarities, the differences between the two films precisely show the cultural and social differences in reality. In Raymond Williams＇ s theory of cultural materialism, culture can be divided into three categories--the dominant, residual and emergent. In relation to this, the ＇cultural hybridity＇ can be shown clearly among the problems （eg. gender, class, sexuality, etc） that the two films involve. Then, I suggest that the relationships between Kes and the ＇emergent culture＇ is an important cultural aspect which Kes exceeds to Billy Elliot.展开更多
With the development of large scale text processing, the dimension of text feature space has become larger and larger, which has added a lot of difficulties to natural language processing. How to reduce the dimension...With the development of large scale text processing, the dimension of text feature space has become larger and larger, which has added a lot of difficulties to natural language processing. How to reduce the dimension has become a practical problem in the field. Here we present two clustering methods, i.e. concept association and concept abstract, to achieve the goal. The first refers to the keyword clustering based on the co occurrence of展开更多
The problem of embedding the Tsallis, Rényi and generalized Rényi entropies in the framework of category theory and their axiomatic foundation is studied. To this end, we construct a special category MES rel...The problem of embedding the Tsallis, Rényi and generalized Rényi entropies in the framework of category theory and their axiomatic foundation is studied. To this end, we construct a special category MES related to measured spaces. We prove that both of the Rényi and Tsallis entropies can be imbedded in the formalism of category theory by proving that the same basic partition functional that appears in their definitions, as well as in the associated Lebesgue space norms, has good algebraic compatibility properties. We prove that this functional is both additive and multiplicative with respect to the direct product and the disjoint sum (the coproduct) in the category MES, so it is a natural candidate for the measure of information or uncertainty. We prove that the category MES can be extended to monoidal category, both with respect to the direct product as well as to the coproduct. The basic axioms of the original Rényi entropy theory are generalized and reformulated in the framework of category MES and we prove that these axioms foresee the existence of an universal exponent having the same values for all the objects of the category MES. In addition, this universal exponent is the parameter, which appears in the definition of the Tsallis and Rényi entropies. It is proved that in a similar manner, the partition functional that appears in the definition of the Generalized Rényi entropy is a multiplicative functional with respect to direct product and additive with respect to the disjoint sum, but its symmetry group is reduced compared to the case of classical Rényi entropy.展开更多
文摘In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.
基金Supported by the Natural Science Foundation of Shandong Province（Y2003A01）
文摘In this paper,the notion of local Sβ-compactness of L-topological spaces is introduced.It is proved that the local Sβ-compactness is an L-good extension,which is inherited by a closed subspace,multiplicative and invariable under the continuous open surjective L-valued Zadeh function.
文摘Recent developments in mathematics have in a sense organized objects of study into categories, where properties of mathematical systems can be unified and simplified through presentation of diagrams with arrows. A category is an algebraic structure made up of a collection of objects linked together by morphisms. Category theory has been advanced as a more concrete foundation of mathematics as opposed to set-theoretic language. In this paper, we define a pseudo-category on the class of isotonic spaces on which the idempotent axiom of the Kuratowski closure operator is assumed.
文摘In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
文摘Diverse concepts of space developed in history of natural philosophy,mathematics,physics,and other natural or cultural studies form theoretical models of spatial relations,given in human’s experience.Their diversity is due not only to the multiplicity of philosophical and methodological approaches to the concept of space,but also to the variety of ways,in which spatial relationships can be organized.This variety gives a possibility to distinct autonomous spaces of different types with diverse sets of properties as well as separate spaces with their own ordinal,metrical,and sequential structures.Particularly,various ways of space semiotization in culture generate different types of autonomous and separate spaces:written texts,maps,pictures,chessboards,etc.In the same time,all particular notions of space are included in a general logical class.Its volume and content are covered by the philosophical category of space.Such general category cannot be reduced to mathematical,physical,or other concepts of space elaborated in particular sciences,however,it serves as a philosophical basis for their comparison.
基金Project supported by the 973 Project of the Ministry of Science and Technology of China(No.2002cb312200)the Excellent Young Teachers Program of the Ministry of Education of Chinaand Huo Yingdong Education Foundation.
文摘Let L be a meet continuous lattice. It is proved that the category Top of topological spaces can be embedded in the category of strati?ed L-topological spaces as a concretely both re?ective and core?ective full subcategory if and only if L is a continuous lattice.
基金This work is supported by the Natural Science Foundation of Chinathe Foundation for Fellows Returned from Abroadthe Mathematical Center of the Education Ministry of China
文摘In this paper it is proved that for all completely distributive lattices L. the category of L-fuzzifying topological spaces can be wmbedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a simultaneously bireflective and bicoreflective full subcategory.
文摘In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.
文摘In this paper,after discussing the prime implication filter of lattice implication algebra,we introduced the concept of prime space of lattice implication algebra,in which we analysised its topological property and discussed the relation between the category of topological space and the category of lattice implication algebras.
文摘By contrasting the two British films, KesI and Billy Elliot2, which in different historical periods, the paper is a comparative cultural study to films. Aside from the similarities, the differences between the two films precisely show the cultural and social differences in reality. In Raymond Williams＇ s theory of cultural materialism, culture can be divided into three categories--the dominant, residual and emergent. In relation to this, the ＇cultural hybridity＇ can be shown clearly among the problems （eg. gender, class, sexuality, etc） that the two films involve. Then, I suggest that the relationships between Kes and the ＇emergent culture＇ is an important cultural aspect which Kes exceeds to Billy Elliot.
文摘With the development of large scale text processing, the dimension of text feature space has become larger and larger, which has added a lot of difficulties to natural language processing. How to reduce the dimension has become a practical problem in the field. Here we present two clustering methods, i.e. concept association and concept abstract, to achieve the goal. The first refers to the keyword clustering based on the co occurrence of
文摘The problem of embedding the Tsallis, Rényi and generalized Rényi entropies in the framework of category theory and their axiomatic foundation is studied. To this end, we construct a special category MES related to measured spaces. We prove that both of the Rényi and Tsallis entropies can be imbedded in the formalism of category theory by proving that the same basic partition functional that appears in their definitions, as well as in the associated Lebesgue space norms, has good algebraic compatibility properties. We prove that this functional is both additive and multiplicative with respect to the direct product and the disjoint sum (the coproduct) in the category MES, so it is a natural candidate for the measure of information or uncertainty. We prove that the category MES can be extended to monoidal category, both with respect to the direct product as well as to the coproduct. The basic axioms of the original Rényi entropy theory are generalized and reformulated in the framework of category MES and we prove that these axioms foresee the existence of an universal exponent having the same values for all the objects of the category MES. In addition, this universal exponent is the parameter, which appears in the definition of the Tsallis and Rényi entropies. It is proved that in a similar manner, the partition functional that appears in the definition of the Generalized Rényi entropy is a multiplicative functional with respect to direct product and additive with respect to the disjoint sum, but its symmetry group is reduced compared to the case of classical Rényi entropy.
