【作者】 阎瑞霞；

【导师】 郑建国；

【作者基本信息】 东华大学 ， 管理科学与工程， 2012， 博士

【摘要】 粗糙集建立在分类机制基础上,利用已知的知识库近似刻画不精确或不确定的研究对象。粗糙集已成功地应用到了社会生活中的很多方面,随着其应用广度和深度的不断拓展,粗糙集的扩展研究引起了学者们的重视。目前,粗糙集的扩展理论主要指粗糙集在等价关系、近似空间和论域三个方向的扩展。其中,粗糙集在关系扩展和近似空间扩展理论已经成功应用于多属性决策、故障诊断等领域。但是,粗糙集的论域扩展理论研究刚刚起步、定义还不统一、性质还不够完善；另一方面,现实问题大都涉及到两个论域的情况,比如：个性化营销中商品属性集与顾客特征集、企业经营诊断中企业出现的问题集和解决方案集、疾病诊断中疾病的症状集和药物集、机械故障诊断中故障集和解决方案集等都可以看作两个不同的论域,利用粗糙集的论域扩展理论对上述问题进行推理、分析和获取相关规则,可以为我们做决策提供帮助。因此,粗糙集的论域扩展研究在理论和应用两个方面均有重要的意义。已有的粗糙集的论域扩展理论是建立在相容关系基础上的,在一定程度上限制了其应用。本文通过比较分析已有粗糙集论域扩展理论的相关定义,将两个论域之间的相容关系扩展为无限制的二元关系：一般关系,构建基于一般关系的论域扩展粗糙集近似算子：双论域粗糙集近似算子,基于双论域粗糙集近似算子的粗糙集称为双论域粗糙集。具体来说,本文的主要工作如下：(1)丰富和发展粗糙集的论域扩展理论。在双论域粗糙集近似算子的基础上,定义了双论域粗糙集的属性重要度、属性约简、相对属性约简、信息熵和信息粒度等概念,研究双论域粗糙集的基本性质和不确定性度量。(2)在模糊信息系统中研究双论域粗糙集。利用模糊关系和水平截集构造模糊双论域粗糙集近似算子,定义基于模糊双论域粗糙集近似算子的粗糙集为模糊双论域粗糙集。从粗糙集和模糊关系两个角度研究模糊双论域粗糙集的性质和定义,研究模糊双论域粗糙集的属性重要度、属性约简、相对属性约简等基本概念和性质,并给出实例予以说明。(3)在概率近似空间中研究双论域粗糙集。利用包含度和阈值构造了变精度双论域粗糙集近似算子,定义基于变精度双论域粗糙集近似算子的粗糙集为变精度双论域粗糙集。从粗糙集和包含度两个角度研究变精度双论域粗糙集的性质,研究不同阂值下变精度双论域粗糙集的包含关系；定义并研究变精度双论域粗糙集的属性重要度、属性约简、相对属性约简等基本概念和性质,并给出实例予以说明。类似地,定义并研究双参数变精度双论域粗糙集近似算子的基本概念和性质。(4)设计基于双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集的专家系统。设计双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集上、下近似算子的求解算法；同时,提出研究对象的双论域、模糊双论域和变精度双论域正域、负域、可能域和边界域的计算方法。针对研究对象与专家系统中规则不完全匹配的问题,利用双论域、模糊双论域和变精度双论域正域、负域、可能域和边界域提取与研究对象匹配的确定性规则和可能性规则。本文利用构造性方法研究粗糙集的论域扩展理论及应用,通过比较分析已有的粗糙集的论域扩展定义,构造双论域粗糙集,深入研究双论域粗糙集的重要概念和性质；针对多决策问题中常见的不确定性信息,在模糊近似空间和概率近似空间中研究模糊双论域粗糙集和变精度双论域粗糙集；另外,将双论域粗糙集、模糊双论域粗糙集和变精度双论域粗糙集引入到专家系统中,促进了双论域粗糙集的理论和应用的发展。更多还原

【Abstract】 Rough set theory as a new mathematical tool is fit for data mining. Rough set theory has received a lot of attention on areas in both of real-life applications and the theory itself. Meanwhile, the real-life applications promote rough set theory research by means of extending structures of rough set. Pawlak rough set is discussed in approximation space, which is constituted by universe, equivalence relation, and approximation space. The promoted research of rough set is extension of universe, equivalence relation and approximation space. At the aspect of approximation space, many research communities have done much in rough set theory and application research on extension of equivalence relation and approximation space. However, the study on rough set on universe extension has just started internally. Definitions about rough set on universe extension are lack of unity. Properties of rough set on universe extension are not perfect. Applications from rough set on universe extension are few. On the other hand, practical problems are mostly related to two universes. For example, characteristics of customer and attributes of product in marketing, problems and solutions in the diagnosis of enterprise business, symptoms of disease and diagnosis in fault diagnosis and so on are problems with two different universes. Rough set on universe extension is especially applicable to solve these issues, which can help us make decisions. Thus, rough set on universe extension is significant in theory and applications.In this paper, rough set on universe extension is discussed by relax tolerance relation to general relation, which is named Rough Set over Dual-universe (RSDU for short). Approximation operators, basic concepts and uncertainty measures of RSDU are discussed. RSDU in fuzzy information system and probability space are also studied in this dissertation. Applications based on RSDU, FRSDU and VPRSDU are illustrated in expert system. Specifically, the main contributions can be formulated as follows:(1) This paper has made positive contributions to the enrichment and development of RSDU theory. In accordance with the limitation of research on traditional rough set on universe extension, we proposed RSDU by general relation in place of tolerance relation. Attribute significance, attribute reduction, information entropy and information granular of RSDU are presented. The relations between Pawlak rough set and RSDU are studied and uncertainty measures of RSDU are discussed.(2) For vague description of problems often comes up in our real life. RSDU are researched in fuzzy information system, which is named Fuzzy Rough Set over Dual-universes(FRSDU for short). FRSDU is introduced by discussing fuzzy relation and cut set. Approximation operators are derived. Attribute significance and attribute reduction of FRSDU are presented. Properties of FRSDU are discussed from the angles of rough set and fuzzy set and examples are advanced to illustrate FRSDU.(3) For dependency degree formula is accurately described in RSDU and noise data exerts a considerable influence when we deal with problems. Variable Precision Rough Set over Dual-universes (VPRSDU) is introduced by discussing inclusion degree. Approximation operators of VPRSDU are derived by using general relation and inclusion degree. Properties of VPRSDU are discussed from the angles of inclusion degree and threshold. Attribute significance, attribute reduction and relative attribute reduction of VPRSDU are presented. Then, two parametric variable precision rough set over Dual-universes is presented and examples are advanced to illustrate VPRSDU.(4) For research objects and expert system may be not perfectly matched, RSDU, FRSDU and VPRSDU are utilized to construct expert system. Algorithms for lower and upper approximation of RSDU, FRSDU and VPRSDU are advanced. Positive region, negative region, boundary region and possibility region are obtained. Expert knowledge and research objects draw certainty rules and possible rules.In this paper, constructive method is utilized to research rough set on universe extension:RSDU. New concepts of RSDU are presented by comparing with traditional concepts. RSDU in fuzzy and probability information system are researched for uncertainty in real life. Applications of rough set on universe extension are discussed in expert system.更多还原