自反、对称关系下近似算子的拓扑性质

研究一般论域下粗糙近似算子的基本性质,借助自反、对称关系下的近似算子构造了粗糙拓扑空间,并讨论了它与满足公理（clop）的拓扑空间的关系。     

The minimization of axiom sets characterizing generalized approximation operators

In the axiomatic approach of rough set theory, rough approximation operators are characterized by a set of axioms that guarantees the existence of certain types of binary relations reproducing the operators. Thus axiomatic characterization of rough approximation operators is an important aspect in the study of rough set theory. In this paper, the independence of axioms of generalized crisp approximation operators is investigated, and their minimal sets of axioms are presented.     

基于优势关系下的协调近似空间(续)

在基于优势关系下的不协调目标信息系统中引入了分布和最大分布协调近似空间的概念,并证明了在优势关系下不协调目标信息系统也可以转化为一个分布以及最大分布协调近似空间,这更加方便了基于优势关系下不协调目标信息系统的研究,从而进一步丰富了粗糙集理论。     

粗糙集构成的拓扑空间

在Pawlak近似空间意义下研究粗糙集构成的拓扑空间。讨论了当论域不受限于有限集时粗糙集可以构成一个拓扑空间,并从拓扑空间的分离性上证明了其粗糙拓扑空间是一个正规的拓扑空间。     

无限论域上粗糙集的拓扑结构

讨论了当论域不限制是有限集时满足自反、传递关系的广义近似空间中的近似算子的拓扑结构;证明了论域 上满足自反、传递关系的集合与其上所有的拓扑的集合是一一对应的;指出了该拓扑空间的拓扑基。     

Invertible approximation operators of generalized rough sets and fuzzy rough sets

This paper studies the classes of rough sets and fuzzy rough sets. We discuss the invertible lower and upper approximations and present the necessary and sufficient conditions for the lower approximation to coincide with the upper approximation in both rough sets and fuzzy rough sets. We also study the mathematical properties of a fuzzy rough set induced by a cyclic fuzzy relation.     

On generalized intuitionistic fuzzy rough approximation operators

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak’s rough approximations have been made in the literature over the years. This paper proposes a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper intuitionistic fuzzy rough approximation operators induced from an arbitrary intuitionistic fuzzy relation are defined. Basic properties of the intuitionistic fuzzy rough approximation operators are then examined. By introducing cut sets of intuitionistic fuzzy sets, classical representations of intuitionistic fuzzy rough approximation operators are presented. The connections between special intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are further established. Finally, an operator-oriented characterization of intuitionistic fuzzy rough sets is proposed, that is, intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of intuitionistic fuzzy relations which produce the same operators.     

一种基于粗糙集的近似质量求取属性约简的决策算法

提出一种基于粗糙集的近似质量求取属性约简的算法。该算法以集合近似的质量为迭代准则，以所有条件属性为初始约简集合，通过逐步缩减来求取约简，保证了所求取的约简对问题的分类量力不会减弱。同时给出了该算法的时间复杂度分析，并举例验证了所提出算法的有效性和实用性。     

Rough approximations on a complete completely distributive lattice with applications to generalized rough sets

The generalizations of rough sets considered with respect to similarity relation, covers and fuzzy relations, are main research topics of rough set theory. However, these generalizations have shown less connection among each other and have not been brought into a unified framework, which has limited the in-depth research and application of rough set theory. In this paper the complete completely distributive (CCD) lattice is selected as the mathematical foundation on which definitions of lower and upper approximations that form the basic concepts of rough set theory are proposed. These definitions result from the concept of cover introduced on a CCD lattice and improve the approximations of the existing crisp generalizations of rough sets with respect to similarity relation and covers. When T-similarity relation is considered, the existing fuzzy rough sets are the special cases of our proposed approximations on a CCD lattice. Thus these generalizations of rough sets are brought into a unified framework, and a wider mathematical foundation for rough set theory is established.     

基于优势关系下的协调近似空间

在基于优势关系下的信息系统中引入了协调近似空间的概念,并证明了在优势关系下不协调目标信息系统也可以转化为一个协调近似空间,这进一步方便了基于优势关系下不协调目标信息系统的研究,丰富了粗糙集理论.     

粗糙集属性约简算法研究

粗糙集理论是一个新的处理不确定性问题的数学工具，属性约简是粗糙集理论的核心问题之一。但求解最优约简已被证明是一个NP—hard问题。基于属性重要度的启发式算法在属性约简中应用的较多．文中分别介绍了基于区分矩阵、基于相关矩阵和基于信息量的属性约简算法。对其思想进行了剖析和总结。     

基于分子格的粗糙集模型推广

粗糙集模型的推广是粗糙集理论研究的重要方向之一。在分子格的框架下,定义了一个从分子到一般元素 的映射,基于该映射,分别构造了两种上近似算子和两种下近似算子,并讨论了这些算子的基本性质。     

On definable concepts of rough set models

In various generalized rough set models, definable concepts are used to approximate other concepts. Based on a unified abstract rough set theory, this paper investigates the mathematical structure of the set of definable concepts in several generalized rough set models such as relation based models, covering based models, and fuzzy based models. It is shown that there exist two kinds of interesting structures for the set of definable concepts, which are often used in rough set models: the complementary structure and the equational structure. In addition, relations between different rough set models are discussed.     

粗集理论中知识的粗糙性研究

粗集理论是处理知识不精确和不完善的一种归纳学习方法,其基本思想是在保持分类能力不变的前提下,通过知识约简,导出概念的分类规则。熵作为对不确定性的一种度量,可用于描述近似空间(U,R)中对象的分类情况。在文中,知识的粗糙性定义为近似空间中的粗糙熵,近似空间上基于等价关系的划分过程是其粗糙熵不断减小的过程。同时讨论了信息系统中的若干粗糙熵性质。     

Pawlak近似空间中软集的软上（下）近似

在Pawlak近似空间上首次引入了等效软集的软上下近似的概念,研究了软上下近似的交、并、补代数运算的若干性质。结果令人满意。     

粗糙集的拓扑结构

本文在Pawlak近似空间意义下研究粗糙集构成的拓扑空间。借助粗糙集的表示构造了粗糙拓扑空间,其中的开集为粗糙相等关系下的等价类;讨论了粗糙拓扑空间中的内部、闭包算子与近似空间中粗糙近似算子的关系,并给出了粗糙拓扑空间的拓扑基。     

一种基于粗集的值约简方法

针对Rough Set理论中的值约简问题进行了研究，对基于决策间不可区分关系的值约简算法进行了改进，使其能够处理信息系统出现的各种情况。     

一种粗糙模糊控制器的设计与仿真

研究了应用粗糙集理论上、下近似定义对模糊控制规则进行拓展设计粗糙模糊控制器的方法,完成了水箱水位粗糙模糊控制器的设计,并分别进行了模糊控制和粗糙模糊控制仿真研究,研究结果表明该粗糙模糊控制能有效改善模糊控制的性能。     

粒度聚类算法研究

信息粒度是对信息和知识细化的不同层次的度量。基于信息粒度的聚类分析方法,凭借能够灵活选择粒度结构,消除聚类结果和先验知识之间的不协调性,有效完成聚类任务等优点,成为国内外学者的研究热点之一。从粗糙集、模糊集、商空间3个理论角度与传统聚类算法相结合,阐述并分析了把粒度的思想引入到聚类中的有效算法及其优缺点,并对这样结合后处理高维复杂数据的可行性及有效性做了分析与展望。