The concept of Rough sets was first introduced by Pawlak in 1981. Because this theory is very important and useful in many fields, e. g. in the information systems and the man-machine systems, many scholars both at ho...The concept of Rough sets was first introduced by Pawlak in 1981. Because this theory is very important and useful in many fields, e. g. in the information systems and the man-machine systems, many scholars both at home and abroad have studied it and obtained a lot of results. Now the theory of Rough sets is still progressing rapidly. However, when this theory is applied to describing an information system, the indiscernibility展开更多
Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyz...Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.展开更多
Covering-based rough sets,as a technique of granular computing,can be a useful tool for dealing with inexact,uncertain or vague knowledge in information systems.Matroids generalize linear independence in vector spaces...Covering-based rough sets,as a technique of granular computing,can be a useful tool for dealing with inexact,uncertain or vague knowledge in information systems.Matroids generalize linear independence in vector spaces,graph theory and provide well established platforms for greedy algorithm design.In this paper,we construct three types of matroidal structures of covering-based rough sets.Moreover,through these three types of matroids,we study the relationships among these matroids induced by six types of covering-based upper approximation operators.First,we construct three families of sets by indiscernible neighborhoods,neighborhoods and close friends,respectively.Moreover,we prove that they satisfy independent set axioms of matroids.In this way,three types of matroidal structures of covering-based rough sets are constructed.Secondly,we study some characteristics of the three types of matroid,such as dependent sets,circuits,rank function and closure.Finally,by comparing independent sets,we study relationships among these matroids induced by six types of covering-based upper approximation operators.展开更多
In this paper the auther begins with some known results about η_λ(=the least cardinal K such that K→(λ)~<∞), proving this theorem: If λ is not Ramsey cardinal and η_λ exists, then for every a<η_λ there...In this paper the auther begins with some known results about η_λ(=the least cardinal K such that K→(λ)~<∞), proving this theorem: If λ is not Ramsey cardinal and η_λ exists, then for every a<η_λ there is a weakly compact cardinal γ, such that λ<γ_α<η_λandγ_α<γ_βwhenever a<β<η_λ, therefore η_λ is the limit of the sequence(γ_α:a<η_λ), i.e. η_λ=limγ_α. The theorem is mainly based on the theory of models with indiscernibles.展开更多
The paper provides an interpretation of Leibniz＇s account of space that extends beyond the predominant interpretations in terms of the relativity of space, and the latter is mainly understood through the differential...The paper provides an interpretation of Leibniz＇s account of space that extends beyond the predominant interpretations in terms of the relativity of space, and the latter is mainly understood through the differential perspective of each monad＇s extrinsic denominators. This is attained by a thorough explication of the principle of indiscernibles, the abolition of the principle of locality, the advanced conception ofentelecheia in late Leibniz, and the character of the perception of each monad, which allow to discover in Leibniz＇s idea of space the notion of the hologram, and the holographic interconnectedness of things in the Universe.展开更多
文摘The concept of Rough sets was first introduced by Pawlak in 1981. Because this theory is very important and useful in many fields, e. g. in the information systems and the man-machine systems, many scholars both at home and abroad have studied it and obtained a lot of results. Now the theory of Rough sets is still progressing rapidly. However, when this theory is applied to describing an information system, the indiscernibility
基金the Scientific Research and Development Project of Shandong Provincial Education Department(J06P01)the Science and Technology Fundation of University of Jinan (XKY0703).
文摘Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.
基金Supported by the Research Foundation for Middle-aged and Young Scientist of Fujian Province(Grant No.JAT170731)
文摘Covering-based rough sets,as a technique of granular computing,can be a useful tool for dealing with inexact,uncertain or vague knowledge in information systems.Matroids generalize linear independence in vector spaces,graph theory and provide well established platforms for greedy algorithm design.In this paper,we construct three types of matroidal structures of covering-based rough sets.Moreover,through these three types of matroids,we study the relationships among these matroids induced by six types of covering-based upper approximation operators.First,we construct three families of sets by indiscernible neighborhoods,neighborhoods and close friends,respectively.Moreover,we prove that they satisfy independent set axioms of matroids.In this way,three types of matroidal structures of covering-based rough sets are constructed.Secondly,we study some characteristics of the three types of matroid,such as dependent sets,circuits,rank function and closure.Finally,by comparing independent sets,we study relationships among these matroids induced by six types of covering-based upper approximation operators.
文摘In this paper the auther begins with some known results about η_λ(=the least cardinal K such that K→(λ)~<∞), proving this theorem: If λ is not Ramsey cardinal and η_λ exists, then for every a<η_λ there is a weakly compact cardinal γ, such that λ<γ_α<η_λandγ_α<γ_βwhenever a<β<η_λ, therefore η_λ is the limit of the sequence(γ_α:a<η_λ), i.e. η_λ=limγ_α. The theorem is mainly based on the theory of models with indiscernibles.
文摘The paper provides an interpretation of Leibniz＇s account of space that extends beyond the predominant interpretations in terms of the relativity of space, and the latter is mainly understood through the differential perspective of each monad＇s extrinsic denominators. This is attained by a thorough explication of the principle of indiscernibles, the abolition of the principle of locality, the advanced conception ofentelecheia in late Leibniz, and the character of the perception of each monad, which allow to discover in Leibniz＇s idea of space the notion of the hologram, and the holographic interconnectedness of things in the Universe.
