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.
In this paper, a presented definition of type-2 fuzzy sets and type-2 fuzzy set operation on it was given. The aim of this work was to introduce the concept of general topological spaces were extended in type-2 fuzzy ...In this paper, a presented definition of type-2 fuzzy sets and type-2 fuzzy set operation on it was given. The aim of this work was to introduce the concept of general topological spaces were extended in type-2 fuzzy sets with the structural properties such as open sets, closed sets, interior, closure and neighborhoods in topological spaces were extended to general type-2 fuzzy topological spaces and many related theorems are proved.展开更多
In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existe...In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.展开更多
Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificati...Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.展开更多
In this paper,we give a fixed point theorem for multi-valued composite increasing operators,in partially ordered spaces,which generalizes the results of [1]-[3] and [5]- [8].
In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spac...In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.展开更多
In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure i...In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.展开更多
Cleverly using the relation of independence spaces and B-matroids, this paper firstly deals with the properties of the closure operator of an independence space, followed by presenting the definitions and solving some...Cleverly using the relation of independence spaces and B-matroids, this paper firstly deals with the properties of the closure operator of an independence space, followed by presenting the definitions and solving some relative properties for the sub-independence spaces of an independence space with the help of circuits.展开更多
The topological study of connectedness is heavily geometric or visual. Connectedness and connectedness-like properties play an important role in most topological characterization theorems, as well as in the study of o...The topological study of connectedness is heavily geometric or visual. Connectedness and connectedness-like properties play an important role in most topological characterization theorems, as well as in the study of obstructions to the extension of functions. In this paper, the behaviour of these properties in the realm of closure spaces is investigated using the class of perfect mappings. A perfect mapping is a type of map under which the image generally inherits the properties of the mapped space. It turns out that the general behaviour of connectedness properties in topological spaces extends to the class of isotone space.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
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In this paper, a presented definition of type-2 fuzzy sets and type-2 fuzzy set operation on it was given. The aim of this work was to introduce the concept of general topological spaces were extended in type-2 fuzzy sets with the structural properties such as open sets, closed sets, interior, closure and neighborhoods in topological spaces were extended to general type-2 fuzzy topological spaces and many related theorems are proved.
基金Supported by the National Natural Science Foundation of China (10761007)
文摘In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.
文摘Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.
文摘In this paper,we give a fixed point theorem for multi-valued composite increasing operators,in partially ordered spaces,which generalizes the results of [1]-[3] and [5]- [8].
文摘In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.
基金Supported by the National Natural Science Foundation of China(No.61173052)the Natural Science Foundation of Hunan Province(No.14JJ4007)
文摘In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.
基金Supported by NSF of Mathematical Special Foundation of Hebei Province(08M005)Supported by NSF of Educational Department of Hebei Province(2006105)
文摘Cleverly using the relation of independence spaces and B-matroids, this paper firstly deals with the properties of the closure operator of an independence space, followed by presenting the definitions and solving some relative properties for the sub-independence spaces of an independence space with the help of circuits.
文摘The topological study of connectedness is heavily geometric or visual. Connectedness and connectedness-like properties play an important role in most topological characterization theorems, as well as in the study of obstructions to the extension of functions. In this paper, the behaviour of these properties in the realm of closure spaces is investigated using the class of perfect mappings. A perfect mapping is a type of map under which the image generally inherits the properties of the mapped space. It turns out that the general behaviour of connectedness properties in topological spaces extends to the class of isotone space.
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.
