广义粗糙近似算子的拓扑性质

粗糙集理论是一种处理不确定性问题的数学工具.粗糙近似算子是粗糙集理论中的核心概念,基于等价关系的Paw-lak粗糙近似算子可以推广为基于一般二元关系的广义粗糙近似算子.近似算子的拓扑结构是粗糙集理论的重点研究方向.文中主要研究基于一般二元关系的广义粗糙近似算子诱导拓扑的性质,给出了基于粒和基于子系统的广义粗糙近似算子诱...     

基于对象的广义粗糙近似算子的拓扑性质

粗糙集理论是一种处理不确定性问题的数学工具。近似算子是粗糙集理论中的核心概念，基于等价关系的Pawlak近似算子可以推广为基于一般二元关系的广义粗糙近似算子。近似算子的拓扑结构是粗糙集理论的重点研究方向。文中主要研究基于对象的广义粗糙近似算子诱导拓扑的性质，证明了广义近似空间中所有可定义集形成拓扑的充分条件也是其必要条件，研究了该拓扑的正则、正规性等拓扑性质；给出了串行二元关系与其传递闭包可以生成相同拓扑的等价条件；讨论了该拓扑与任意二元关系下基于对象的广义粗糙近似算子所诱导拓扑之间的相互关系。     

集族等价与基于粒的下近似算子研究

基于覆盖的粗集是推广经典粗集理论的方法之一,有基于元素、基于粒和基于子系统的3类定义上下近似的途径,以往大多数的文献往往从基于元素的角度出发进行定义。为了研究基于粒的近似算子特别是下近似算子的性质,借鉴格论中既约元、可约元等概念,提出了集族约简的概念。从集族约简出发,探讨了集族等价的概念与性质,并设计了集族约简的算法,得到了两个集族等价是两个集族生成相同的下近似运算的充要条件这一结果,为进一步开展一般二元关系下基于粒的近似算子的公理化方法的研究做了初步的理论方面的准备工作。     

区间值Fuzzy集分解定理上的近似算子研究

将广义粗糙模糊下、上近似算子拓展到区间上,并利用区间值模糊集分解定理给出一组新的广义区间值粗糙模糊下、上近似算子,证明二者在由任意二元经典关系构成的广义近似空间中是等价的,最后讨论了在一般二元关系下,两组近似算子的性质。     

信息系统中近似本体获取的粒计算方法

研究近似概念以及由此而生成的近似本体不仅是必要,而且其重要性日益增加.本文基于粒计算理论,以信息表作为领域本体的语境,给出获取近似概念和生成近似本体的数据模型,并提出基于粒计算的获取近似概念和生成近似本体的生成算法.实例表明该算法是有效的.     

多粒度空间与知识推理

旨在建立起多粒度空间中粗糙近似算子与知识推理中认知算子之间的一一对应关系,从而给出多粒度空间中粗糙近似算子更为合理的语义解释。对于任意逻辑公式,通过分析其语义集与加了认知算子后的语义集之间的关系,证明了全知算子EG对应于多粒度空间中模型AIU中的下近似算子,公共知识认知算子CG对应于模型RU中的下近似算子,分配知识认知算子DG对应于模型RI中的下近似算子,所得结论是模态逻辑与Pawlak粗糙集之间对应关系在多当事人环境下的推广。     

基于分子格及其类闭包子系统的粗近似

粗糙集的代数研究方法一直吸引着众多的研究人员,其中一个重要的研究方法是用算子的观点来看到粗糙集中的近似,并基于一般抽象代数结构来定义相应的粗糙近似算子。论文将分子格引入到粗糙集理论中作为基本代数系统,在分子格中构造了一个类似于闭包的子系统,并基于它们定义了更为一般和抽象的近似算子。文中还研究了相关粗近似结构的性质。     

二元关系的复合与近似算子的合成

定义了各种类型的经典二元关系和模糊二元关系,讨论了二元关系的合成及其性质.给出了两个近似空间合成的概念,并讨论合成前的近似空间所导出的近似算子与合成后的近似空间所导出的近似算子之间的关系.证明了合成后的近似空间所导出的近似算子恰好是两个近似空间所导出的近似算子的合成.     

粒计算的集合论描述

粒计算的形式化研究一直没有被仔细讨论.文中在集合论框架下,对粒计算做了系统研究,给出了粒度空间的三层模型(论域,基,粒结构).借用逻辑语言L判定粒的可定义性,将经典粗糙集通过此模型重新解释.根据模型中从基到粒结构不同的构造规则,引出并可约和交可约粒度空间的定义,分别讨论了不同粒度空间下覆盖、基和粒结构的关系,从而给出从覆盖求基的方法;进一步,利用子系统表示方法对扩展粗糙集以及一般的交可约与并可约空间的上下近似进行了研究,分析了现有的4种基于覆盖的粗糙集模型的合理性;研究了形式概念分析以及知识空间的粒度空间模型,给出这两种理论中上下近似的概念.     

广义区间值模糊粗糙近似算子的构造研究

构造了一组新的广义模糊粗糙近似算子,将其拓展到区间上.在由任意的二元区间值模糊关系构成的广义近似空间中,证明了该组近似算子与区间化的广义Dubois模糊粗糙近似算子是等价的,最后在一般二元区间值模糊关系下对该组近似算子的性质进行了讨论.     

An axiomatic characterization of a fuzzy generalization of rough sets

In rough set theory, the lower and upper approximation operators defined by a fixed binary relation satisfy many interesting properties. Several authors have proposed various fuzzy generalizations of rough approximations. In this paper, we introduce the definitions for generalized fuzzy lower and upper approximation operators determined by a residual implication. Then we find the assumptions which permit a given fuzzy set-theoretic operator to represent a upper (or lower) approximation derived from a special fuzzy relation. Different classes of fuzzy rough set algebras are obtained from different types of fuzzy relations. And different sets of axioms of fuzzy set-theoretic operator guarantee the existence of different types of fuzzy relations which produce the same operator. Finally, we study the composition of two approximation spaces. It is proved that the approximation operators in the composition space are just the composition of the approximation operators in the two fuzzy approximation spaces.     

Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory

The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfying many interesting properties. Many types of generalized rough set models have been proposed in the literature. This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used. In the constructive approach, concepts of rough intuitionistic fuzzy sets and intuitionistic fuzzy rough sets are defined, properties of rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are examined. Different classes of rough intuitionistic fuzzy set algebras and intuitionistic fuzzy rough set algebras are obtained from different types of fuzzy relations. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of crisp/fuzzy relations which produce the same operators.     

Topological properties of generalized approximation spaces

Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper concerns generalized approximation spaces via topological methods and studies topological properties of rough sets. Classical separation axioms, compactness and connectedness for topological spaces are extended to generalized approximation spaces. Relationships among separation axioms for generalized approximation spaces and relationships between topological spaces and their induced generalized approximation spaces are investigated. An example is given to illustrate a new approach to recover missing values for incomplete information systems by regularity of generalized approximation spaces.     

On intuitionistic fuzzy rough sets and their topological structures

In this paper, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of intuitionistic fuzzy approximation operators are examined. Relationships between intuitionistic fuzzy rough set approximations and intuitionistic fuzzy topologies are then discussed. It is proved that the set of all lower approximation sets based on an intuitionistic fuzzy reflexive and transitive approximation space forms an intuitionistic fuzzy topology; and conversely, for an intuitionistic fuzzy rough topological space, there exists an intuitionistic fuzzy reflexive and transitive approximation space such that the topology in the intuitionistic fuzzy rough topological space is just the set of all lower approximation sets in the intuitionistic fuzzy reflexive and transitive approximation space. That is to say, there exists an one-to-one correspondence between the set of all intuitionistic fuzzy reflexive and transitive approximation spaces and the set of all intuitionistic fuzzy rough topological spaces. Finally, intuitionistic fuzzy pseudo-closure operators in the framework of intuitionistic fuzzy rough approximations are investigated.     

基于决策规则的形式背景属性约简*

在经典形式背景中,利用对象和属性间的二元关系定义一对粗糙模糊上、下近似算子,讨论算子的基本性质,指出算子与已有粗糙近似算子的关系.利用定义的粗糙模糊上、下近似算子,得到两类决策规则,即确定性决策规则和可能性决策规则.针对两类决策规则,提出下近似约简和上近似约简的概念,关于上近似约简,得到可约属性和属性协调集的判别条件,给出属性约简方法,并举例说明方法的可行性.     

A review of: “ANTICIPATORY SYSTEMS”, by Robert Rosen,Pergamon Press,Oxford, 1985, X + 436pp.

In rough set theory there exists a pair of approximation operators, the upper and lower approximations, whereas in Dempster-Shafer theory of evidence there exists a dual pair of uncertainty measures, the plausibility and belief functions. It seems that there is some kind of natural connection between the two theories. The purpose of this paper is to establish the relationship between rough set theory and Dempster-Shafer theory of evidence. Various generalizations of the Dempster-Shafer belief structure and their induced uncertainty measures, the plausibility and belief functions, are first reviewed and examined. Generalizations of Pawlak approximation space and their induced approximation operators, the upper and lower approximations, are then summarized. Concepts of random rough sets, which include the mechanisms of numeric and non-numeric aspects of uncertain knowledge, are then proposed. Notions of the Dempster-Shafer theory of evidence within the framework of rough set theory are subsequently formed and interpreted. It is demonstrated that various belief structures are associated with various rough approximation spaces such that different dual pairs of upper and lower approximation operators induced by the rough approximation spaces may be used to interpret the corresponding dual pairs of plausibility and belief functions induced by the belief structures.     

覆盖粗糙近似的一致性研究

经典粗糙集理论知识的表现形式为论域上的划分,覆盖是比划分更一般的知识表现形式。为了扩展粗糙集理论的应用领域,有必要将粗糙集理论扩展到覆盖近似空间。覆盖近似空间下的概念近似是基于覆盖近似空间知识获取的关键。针对精确概念和模糊概念,研究者定义了不同的近似方法。通过对当前的近似算子进行研究,发现了它们的不一致,并从两个角度对近似算子的定义进行了修正,从而使得它们分别与原有的算子保持一致。所得结论为覆盖近似空间下的概念近似提供了新的研究途径。