信息系统同态的性质及上下近似的不变性

作为研究信息系统之间关系的一种有力工具,信息系统同态的概念首先由J.W.Grzyrnala-Busse引入。本文研究了信息系统同态的一些性质,揭示了构成信息系统同态的对象映射、属性映射与值域映射之间的相互依赖性。由给定的论域上的划分,导出了一个新的信息系统同态,该同态对论域的划分与给定划分相同。同时,讨论了信息系统在同态的意义下,上近似与下近似的不变性,为粗糙集理论的进一步研究奠定了理论基础。     

合成信息系统与子信息系统的属性特征

数据库的合成和分解在实际应用中是一个很重要的问题,它所对应的数学模型就是信息系统的合成与分解,该文给出了对象合成信息系统、属性合成信息系统、对象子信息系统及属性子信息系统的定义,讨论了合成信息系统、子信息系统与原信息系统等属性特征之间的关系。     

优势关系下不协调目标信息系统的上近似约简

针对基于优势关系下不协调目标信息系统中属性约简的复杂问题,提出基于优势关系下不协调目标信息系统上近似约简的概念,得到上近似约简的判定定理以及辨识矩阵,建立不协调目标信息系统的上近似约简的具体方法,同时通过实例验证该方法的有效性,从而为优势关系下信息系统的知识发现提供理论基础。     

优势关系下不协调目标信息系统的下近似约简

在基于优势关系下的不协调目标信息系统中引入了下近似约简的概念,并得到了下近似约简的判定定理以及辨识矩阵,建立了不协调目标信息系统的下近似约简的具体方法,同时通过实例验证了该方法的有效性,从而为优势关系下信息系统的知识发现提供了理论基础。     

基于矩阵的粗糙集上下近似的计算方法

借助于论域子集的布尔列矩阵表示的思想,引入等价关系矩阵的诱导矩阵和矩阵的λ-截矩阵等概念,提出Pawlak粗糙集模型中概念上、下近似计算的矩阵方法,即利用论域子集的布尔列矩阵、论域上的等价关系矩阵和诱导矩阵三个矩阵间的运算来计算该子集的上、下近似集,并从理论上证明该方法的正确性.然后给出运用该方法计算论域子集上、下近似...     

不协调优势目标信息系统的启发式下近似约简

基于不协调优势目标信息系统,给出刻画属性重要性的新指标,以该指标为启发式信息,提出一种新的下近似约简算法。该算法具有较大的灵活性,能从搜索空间逐次删除不重要属性,避免重复计算属性的重要性,从而提高搜索的效率,且时间复杂度较低。通过实例说明了该算法的有效性。     

基于优势关系的粗糙集扩展研究

为了从多视角研究不完备信息系统中的粗糙集方法,论文分析了完备信息系统中的优势关系粗糙集和不完备信息系统中的扩展优势关系粗糙集,并以此为基础在不完备信息系统中提出了另一种扩展优势关系粗糙集。通过对新提出的粗糙集的性质进行分析,证明了其可以获得比扩展优势关系粗糙集更大的下近似和更小的上近似。     

序信息系统中基于粗糙集的证据获取与合成

通过在决策序信息系统中引入证据理论,提出一种基于粗糙集的证据获取与合成方法.利用证据信任度计算近似条件概率分配,根据属性重要度和证据支持度计算权重,然后用合成公式对近似条件概率分配进行合成,得到决策.     

模糊关系下的粗集粗糙度

本文研究粗糙集的粗糙度问题。首先仔细分析了Pawlak粗糙集的粗糙度,得到了粗糙集粗糙度包容相斥原理;然后将结果推广到模糊集理论领域,对研究模糊关系下模糊粗糙集理论有一定的作用。     

变精度相容粗糙集模型

将变精度粗糙集的思想引入相容粗糙集,提出了两种变精度相容粗糙集模型,在模型I中,目标概念的下近似和边界域的交集非空;在模型II中,目标概念的下近似和边界域的交集为空。研究了两种模型中上、下近似算子的基本性质、两种模型之间的关系,以及与其他粗糙集模型之间的关系。     

On Characteristics of Information System Homomorphisms

The notion of information system homomorphism as a powerful tool to study the relation between two information systems was introduced by J.W. Grzymala-Busse. In this work, we will present some characteristics of information system homomorphism, which reveal the interdependence of the three mappings, namely, object mapping, attribute mapping and value domain mapping. Besides, given a partition on universe, we can derive a new information system homomorphism defining a partition on universe identical with the partition given. In the mean time, some invariant characteristics of upper approximation and lower approximation under information system homomorphism are investigated. At last, we establish a surjection between rough sets of information systems under an information system homomorphism.     

一种改进的图像增强算法及其应用

为改进图像增强算法,使之更适合医学领域图片的处理,采用了粗糙集的上逼近和下逼近思想,将图像分为物体区和背景区,使用不同的函数进行增强,进而提出了一种改进的基于粗糙集的增强算法,并首次应用于医学图像处理领域.实验结果显示改进的基于粗糙集的增强效果优于直方图均衡化方法.     

The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets

This paper provides a continuation of ideas presented by Davvaz and Mahdavipour [B. Davvaz, M. Mahdavipour, Roughness in modules, Inform. Sci. 176 (2006) 3658-3674]. The notion of hypermodule is a generalization of the notion of module. In this paper, we consider the quotient hypermodule M/A and interpret the lower and upper approximations as subsets of the quotient hypermodule M/A. Then, we introduce the concept of quotient rough sub-hypermodule. Also, using the concept of fuzzy sets, we introduce and discuss the concept of fuzzy rough hypermodules and then we obtain the relation between fuzzy rough sub-hypermodules and level rough sets. This relation is characterized as a necessary and sufficient condition.     

粗糙模糊集的格论性质

Let U denote a finite and nonempty set called the universe, and P(U) a power set. Suppose R is an equiva-lence relation on U. Consider the equivalence relation ≈ (X≈Y←→^-RX=^-R and RX=RY, X,Y, ∈ F(U)) on F(U),the quotient set denoted by F(U)/≈. In this paper we show that F(U)/≈ is a distributive lattice.     

粗糙集的粗糙度

设U是全集,R是U上的等价关系,(U,R)是相应的近似空间,则粗相等关系≈是幂集P(U)上的等价关系,其商集为P(U)／≈,而商集P(U)／≈是一个分配格,本文考虑两种特殊情况,使得在这两种特殊情况下粗糙度有类似于集合论的包容排斥原理,同时我们还把此结论推广到粗糙模糊集上。     

Roughness in MV-algebras

In this paper, by considering the notion of an MV-algebra, we consider a relationship between rough sets and MV-algebra theory. We introduce the notion of rough ideal with respect to an ideal of an MV-algebra, which is an extended notion of ideal in an MV-algebra, and we give some properties of the lower and the upper approximations in an MV-algebra.     

Generalized rough sets based on relations

Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations. This paper studies arbitrary binary relation based generalized rough sets. In this setting, a binary relation can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a relation under which these properties hold for the relation based lower and upper approximation operations.This paper also explores the relationships between the lower or the upper approximation operation generated by the intersection of two binary relations and those generated by these two binary relations, respectively. Through these relationships, we prove that two different binary relations will certainly generate two different lower approximation operations and two different upper approximation operations.     

Roughness based on fuzzy ideals

The theory of rough set, proposed by Pawlak and the theory of fuzzy set, proposed by Zadeh are complementary generalizations of classical set theory. Many sets are naturally endowed with two binary operations: addition and multiplication. One concept which does this is a ring. This paper concerns a relationship between rough sets, fuzzy sets and ring theory. It is a continuation of ideas presented by Kuroki and Wang [N. Kuroki, P.P. Wang, The lower and upper approximations in a fuzzy group, Inform. Sci. 90 (1996) 203-220]. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by a fuzzy ideal. In fact, we apply the notion of fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some characterizations of the above approximations are made and some examples are presented.     

改进的粗糙描述逻辑框架

已有的粗糙描述逻辑(RDLs)都是基于经典的粗糙集理论,也就是在讨论可以处理不确定信息的粗糙描述逻辑前首先要定义出论域中元素间的某种等价关系。事实上,人们经常会遇到用形式概念表示的对象域,这种情况下一个自然的问题就是:如何处理可能出现的不确定性概念?把形式概念分析与粗糙集理论联系起来作为基础,建立了两种新的粗糙描述逻辑。把文献[14]中Y.Y.Yao等提出的方法应用于新的RDLs,其中的上(下)近似算子分别用格论算子和集合论算子来定义。这里的近似的定义虽然不同于传统的粗糙近似算子形式,但是有很好的实用性。基于这个新颖的上(下)近似的定义,把这两组近似算子引入到描述逻辑的结构中形成两种粗糙描述逻辑FlALC和FsALC。给出了相应的语法和语义,最后还给出了扩展的Tableaux算法,其可以用来解决相应的推理问题。