Interval-Valued Intuitionistic Fuzzy-Rough Sets

This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.

Homomorphic Properties of Fuzzy Rough Groups

This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.

Fuzzy Rough Ring and Its Properties

This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.

Intuitionistic Fuzzy Rough Sets Based on Two Intuitionistic Fuzzy Implicators

This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.

On uniqueness of (fuzzy) relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.

L-Fuzzy Rough Set Based on Complete Residuated Lattice

Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.

一种新的L-fuzzy粗糙集的刻画方法

远域作为分子的邻近结构,在模糊拓扑中起着重要的作用.能否把远域应用到粗糙集理论中用于刻画近似算子?我们在这方面进行了有益的尝试,得到了较好的结论.基于远域系统,我们讨论了串行的、自反的、弱传递的、弱一元的和传递的等性质,得到了很好的结论.

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。

Dominance-based fuzzy rough approach to an interval-valued decision system

Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance principle in terms of pairs of objects. In this paper, a ranking method of interval-valued data is used to describe the degree of dominance in the interval-valued information system. Therefore, the fuzzy rough technique is employed to construct the rough approximations of upward and downward unions of decision classes, from which one can induce at least and at most decision rules with certainty factors from the interval-valued decision system. Some numerical examples are employed to substantiate the conceptual arguments.

Definability and Textural Rough Set Algebras

In this paper,a counterpart of definability is studied in texture spaces.The concept of textural complete field is defined and the relations with textural definable sets are investigated.If a texture is discrete,then textural definability coincides with definability.Using this fact,we obtain some basic results for definability in rough set algebras.Further,we discuss on definability for fuzzy rough sets considering textural fuzzy direlations.

双论域区间值直觉模糊vague粗糙集及其应用

区间值直觉模糊集可诱导出vague集和粗糙集,而后两者的结合具有不确定性深入分析的优势.立足双论域区间值直觉模糊粗糙集,引入vague集进行融合扩张,研究双论域区间值直觉模糊vague粗糙集.首先,定义区间值直觉模糊vague相容类,构建双论域区间值直觉模糊vague粗糙集模型,提出关于双逼近近似和三支决策区域的计算算法,并确立该模型的精确度、粗糙度、依赖度.然后,研究该模型的近似算子与不确定性度量的性质.最后,采用医疗例子进行模型计算、度量测量、性质验证,并得到关于患者临床诊断的患病分析与治疗决策.

粗糙模糊集的构造与公理化方法

用构造性方法和公理化研究了粗糙模糊集 .由一个一般的二元经典关系出发构造性地定义了一对对偶的粗糙模糊近似算子 ,讨论了粗糙模糊近似算子的性质 ,并且由各种类型的二元关系通过构造得到了各种类型的粗糙模糊集代数 .在公理化方法中 ,用公理形式定义了粗糙模糊近似算子 ,各种类型的粗糙模糊集代数可以被各种不同的公理集所刻画 .阐明了近似算子的公理集可以保证找到相应的二元经典关系 ,使得由关系通过构造性方法定义的粗糙模糊近似算子恰好就是用公理化定义的近似算子 .

粗糙集理论介绍和研究综述

介绍粗糙集理论的基本原理 ,粗糙集理论中的知识表示以及目前粗糙集理论的研究状况。

模糊粗糙集理论研究进展

介绍模糊粗糙集的概念及发展进程.提出了理论建立过程中,分别以推广到模糊集、引入模糊逻辑算子、拓展到两个论域为特点的三个发展阶段;分析、比较了各阶段代表性理论的特点,并对模糊粗糙集的未来发展作出了预期。

模糊空间中的直觉模糊粗糙近似

粗糙集和直觉模糊集的结合是一新的研究热点。在模糊近似空间中,结合模糊等价关系,构造直觉模糊粗糙近似算子,在γ算子和其余算子γ*的基础上,证明了这些近似算子的性质。在模糊近似空间中,给出λ上(下)近似以及αβ-截集的λ上(下)近似,证明了它们的性质;给出直觉模糊集的粗糙度ραβA和λ水平截集的粗糙度,并讨论了其性质。

基于覆盖的区间直觉模糊粗糙集

在经典的覆盖近似空间中,定义了区间直觉模糊概念的粗糙近似。通过区间直觉模糊覆盖概念,给出了一种基于区间直觉模糊覆盖的区间直觉模糊粗糙集模型。讨论了两种模型的一些相关性质。

基于覆盖的模糊粗糙集模型

讨论基于覆盖理论的模糊粗糙集模型。给出了模糊集的粗糙上、下近似算子,讨论了算子的基本性质,证明了覆盖粗糙集模型下所有模糊集的下近似构成一个模糊拓扑,并得到了覆盖模糊粗糙集模型的公理化描述。

区间直觉模糊粗糙集

将模糊粗糙集推广到区间直觉模糊粗糙集,基于区间直觉模糊等价关系和两个论域之间的一般区间直觉模糊关系,给出了区间直觉模糊粗糙集模型的不同形式,并讨论了一些相关性质。

双论域L模糊粗糙集

基于双论域粗糙集构造了定义在L模糊关系上的双论域L模糊粗糙集,并讨论了双论域L模糊粗糙集基本性质。

基于粗糙集的间接学习

粗糙集理论为处理不精确、不确定数据提供了一个新的数学方法,已被广泛应用于人工智能、模式识别与智能信息处理等计算机领域. 在Pawlak粗糙集模型[1,2]中,等价关系起着至关重要的作用.任意给定一个概念(论域的子集),人们不一定能用知识库中的知识(等价类)来精确地描述,这时就用关于这个概念构成的集合的一对上、下近似来描述.但是,对等价关系的严厉要求限制了粗糙集理论的应用,因此许多学者从各方面对Pawiak粗糙集模型作了推广[3～5].