On Three Types of Covering-Based Rough Sets

Rough set theory is a useful tool for data mining. It is based on equivalence relations and has been extended to covering-based generalized rough set. This paper studies three kinds of covering generalized rough sets for dealing with the vagueness and granularity in information systems. First, we examine the properties of approximation operations generated by a covering in comparison with those of the Pawlak's rough sets. Then, we propose concepts and conditions for two coverings to generate an identical lower approximation operation and an identical upper approximation operation. After the discussion on the interdependency of covering lower and upper approximation operations, we address the axiomization issue of covering lower and upper approximation operations. In addition, we study the relationships between the covering lower approximation and the interior operator and also the relationships between the covering upper approximation and the closure operator. Finally, this paper explores the relationships among these three types of covering rough sets.     

Spatial data methods and vague regions: A rough set approach

Uncertainty management has been considered essential for real world applications, and spatial data and geographic information systems in particular require some means for managing uncertainty and vagueness. Rough sets have been shown to be an effective tool for data mining and uncertainty management in databases. The 9-intersection, region connection calculus (RCC) and egg–yolk methods have proven useful for modeling topological relations in spatial data. In this paper, we apply rough set definitions for topological relationships based on the 9-intersection, RCC and egg–yolk models for objects with broad boundaries. We show that rough sets can be used to express and improve on topological relationships and concepts defined with these models.     

Ontologies for agents

An ontology is a computational model of some portion of the world. It is often captured in some form of a semantic network-a graph whose nodes are concepts or individual objects and whose arcs represent relationships or associations among the concepts. This network is augmented by properties and attributes, constraints, functions, and rules that govern the behavior of the concepts. Formally, an ontology is an agreement about a shared conceptualization, which includes frameworks for modeling domain knowledge and agreements about the representation of particular domain theories. Definitions associate the names of entities in a universe of discourse (for example, classes, relations, functions, or other objects) with human readable text describing what the names mean, and formal axioms that constrain the interpretation and well formed use of these names. For information systems, or for the Internet, ontologies can be used to organize keywords and database concepts by capturing the semantic relationships among the keywords or among the tables and fields in a database. The semantic relationships give users an abstract view of an information space for their domain of interest     

Supporting User-Defined Granularities in a Spatiotemporal Conceptual Model

Granularities are integral to spatial and temporal data. A large number of applications require storage of facts along with their temporal and spatial context, which needs to be expressed in terms of appropriate granularities. For many real-world applications, a single granularity in the database is insufficient. In order to support any type of spatial or temporal reasoning, the semantics related to granularities needs to be embedded in the database. Specifying granularities related to facts is an important part of conceptual database design because under-specifying the granularity can restrict an application, affect the relative ordering of events and impact the topological relationships. Closely related to granularities is indeterminacy, i.e., an occurrence time or location associated with a fact that is not known exactly. In this paper, we present an ontology for spatial granularities that is a natural analog of temporal granularities. We propose an upward-compatible, annotation-based spatiotemporal conceptual model that can comprehensively capture the semantics related to spatial and temporal granularities, and indeterminacy without requiring new spatiotemporal constructs. We specify the formal semantics of this spatiotemporal conceptual model via translation to a conventional conceptual model. To underscore the practical focus of our approach, we describe an on-going case study. We apply our approach to a hydrogeologic application at the United States Geologic Survey and demonstrate that our proposed granularity-based spatiotemporal conceptual model is straightforward to use and is comprehensive.     

概念格与粗糙集的关系研究

概念格理论和粗糙集理论是两种不同的知识表示与知识发现的工具,都已被成功应用于许多领域.粗糙集理论的数据表现方式是信息系统,其研究基础是对象之间的等价关系;概念格理论的数据表现方式是形式背景,其研究基础是一种有序的层次结构--概念格.本文讨论了概念格理论与粗糙集理论之间的基本联系;重点分析了形式概念与等价类之间、概念格与分划之间的关系;证明了概念格与分划之间可以相互转换,给出了转换算法,并用例子加以说明.     

近似空间关系代数ASRA及应用

粗定位模型是一种基于粗集的近似区域表示模型 ,基于定性空间推理理论对其进行了代数形式化 .通过空间关系矩阵和 2 4 9种基本空间关系构造了近似空间关系代数 ASRA;讨论了 ASRA的公理和基本性质 ,研究了ASRA和 RCC5关系映射中存在的不确定性 ;把 ASRA应用于 GIS,提出了基于 ASRA的空间关系判定算法ASRA- RCC.与同类算法相比 ,ASRA- RCC能够同时支持确定和近似区域 ,并且具有较高的效率     

领域本体的一致性检查

针对领域本体中概念集的一致性检查问题,给出领域本体的形式化定义,阐述领域本体中的公理集,分析概念集的一致性检查方法,将OWL的本体表达方式转化为基于UML的表达方式,对UML进行适当的扩展,提供一种基于图形化的本体一致性检查机制。该方法基于图形化的形式,简洁直观、容易操作,克服了原有检查方法形式化程度高及复杂难操作的缺点。     

粗糙集理论中概念与运算的信息表示*

粗糙集理论对知识进行了形式化定义,为知识处理提供了一套严密的分析工具,但在代数表示下,粗糙集理论的本质不易被理解,并且,尚无高效的知识约简算法.该文首先建立了知识与信息之间的关系;然后,在此基础上给出了粗糙集理论中概念与运算的信息表示;最后,证明了知识约简在信息和代数两种不同表示下是等价的.这些结论有助于人们深刻理解粗糙集理论的本质,同时,为寻找高效的知识约简算法奠定了基础.     

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.     

Ontology and rule-based natural language processing approach for interpreting textual regulations on underground utility infrastructure

The nation’s massive underground utility infrastructure must comply with a multitude of regulations. The regulatory compliance checking of underground utilities requires an objective and consistent interpretation of the regulations. However, utility regulations contain a variety of domain-specific terms and numerous spatial constraints regarding the location and clearance of underground utilities. It is challenging for the interpreters to understand both the domain and spatial semantics in utility regulations. To address the challenge, this paper adopts an ontology and rule-based Natural Language Processing (NLP) framework to automate the interpretation of utility regulations – the extraction of regulatory information and the subsequent transformation into logic clauses. Two new ontologies have been developed. The urban product ontology (UPO) is domain-specific to model domain concepts and capture domain semantics on top of heterogeneous terminologies in utility regulations. The spatial ontology (SO) consists of two layers of semantics – linguistic spatial expressions and formal spatial relations – for better understanding the spatial language in utility regulations. Pattern-matching rules defined on syntactic features (captured using common NLP techniques) and semantic features (captured using ontologies) were encoded for information extraction. The extracted information elements were then mapped to their semantic correspondences via ontologies and finally transformed into deontic logic (DL) clauses to achieve the semantic and logical formalization. The approach was tested on the spatial configuration-related requirements in utility accommodation policies. Results show it achieves a 98.2% precision and a 94.7% recall in information extraction, a 94.4% precision and a 90.1% recall in semantic formalization, and an 83% accuracy in logical formalization.     

Learning fuzzy rules from fuzzy samples based on rough set technique

Although the traditional rough set theory has been a powerful mathematical tool for modeling incompleteness and vagueness, its performance in dealing with initial fuzzy data is usually poor. This paper makes an attempt to improve its performance by extending the traditional rough set approach to the fuzzy environment. The extension is twofold. One is knowledge representation and the other is knowledge reduction. First, we provide new definitions of fuzzy lower and upper approximations by considering the similarity between the two objects. Second, we extend a number of underlying concepts of knowledge reduction (such as the reduct and core) to the fuzzy environment and use these extensions to propose a heuristic algorithm to learn fuzzy rules from initial fuzzy data. Finally, we provide some numerical experiments to demonstrate the feasibility of the proposed algorithm. One of the main contributions of this paper is that the fundamental relationship between the reducts and core of rough sets is still pertinent after the proposed extension.     

Towards a digital library theory: a formal digital library ontology

Digital libraries (DLs) have eluded definitional consensus and lack agreement on common theories and frameworks. This makes comparison of DLs extremely difficult, promotes ad-hoc development, and impedes interoperability. In this paper we propose a formal ontology for DLs that defines the fundamental concepts, relationships, and axiomatic rules that govern the DL domain, therefore providing a frame of reference for the discussion of essential concepts of DL design and construction. The ontology is an axiomatic, formal treatment of DLs, which distinguishes it from other approaches that informally define a number of architectural variants. The process of construction of the ontology was guided by 5S, a formal framework for digital libraries. To test its expressibility we have used the ontology to create a taxonomy of DL services and to reason about issues of reusability, extensibility, and composability. Some practical applications of the ontology are also described including: the definition of a digital library services taxonomy, the proposal of a modeling language for digital libraries, and the specification of quality metrics to evaluate digital libraries. We also demonstrate how to use the ontology to formally describe DL architectures and to prove some properties about them, thus helping to further validate the ontology.     

基于混合推理的知识库的构建及其应用研究

该文提出了基于OWL本体与Prolog规则的平面几何知识库的构建方法,从而可形式化地表示平面几何中丰富的语义信息.一方面,用类型、定义域、值域、分类、属性、实例等本体描述来表达结构化的知识,为领域内概念与概念之间关系的描述提供形式化的语义;另一方面,用Prolog规则来解决本体不能有效表达的诸如属性之间的关系和操作等问题,从而支持复杂关系间的推理.在此基础上,用Protégé和Prolog构建了一个基于本体和规则的平面几何知识库.实验证明:此知识库可实现知识和语义层次上的信息查询,还可进行复杂问题求解,其丰富的语义描述和混合推理能力弥补了传统知识库的不足.     

VASA: An algebra for vague spatial data in databases

Many geographical applications deal with objects in space that cannot be adequately described by determinate, crisp spatial concepts because of their intrinsically indeterminate and vague nature. Geographical information systems and spatial database systems are currently unable to cope with this kind of data. To support the efficient representation, querying, and manipulation of vague spatial data in a database context, we present a formal data model called vague spatial algebra (VASA). This algebra comprises a set of vague spatial data types for vague points, vague lines, and vague regions together with a comprehensive collection of vague spatial operations and vague topological predicates. One of VASA's main benefits is that its formal framework is based on well known, general, and exact models of crisp spatial data types. This enables an exact definition of the vague spatial model since we can build upon an already existing theory of spatial data types. In particular, crisp spatial data types turn out to be a special case of their vague counterparts. In addition, our approach enables executable specifications for the operations, which can be immediately used as implementations. The article offers a precise and conceptually clean foundation for implementing a DBMS extension for vague spatial data and demonstrates the embedding of these new data types as attribute data types in a database schema as well as the incorporation of vague spatial operations and predicates into queries formulated in an SQL-like query language. All concepts have been verified in a prototype implementation.     

CAMO: A context-aware movie ontology generated from LOD and movie databases

Multimedia Tools and Applications - An ontology is a formal representation of domain knowledge as a set of concepts and their relationships in structured format. Besides various applications,...     

Approximate analysis of binary topological relations between geographic regions with indeterminate boundaries

 The development of formal models of spatial relations is a topic of great importance in spatial reasoning, geographic information systems (GIS) and computer vision, and has gained much attention from researchers across these research areas during the past two decades. In recent years significant achievements have been made on the development of models of spatial relations between spatial objects with precisely defined boundaries. However, these models cannot be directly applied to spatial objects with indeterminate boundaries which are found in many applications in geographic analysis and image understanding. This article develops a method for approximately analyzing binary topological relations between geographic regions with indeterminate boundaries based upon previous work on topological spatial relations and fuzzy sets. In addition, examples are given to demonstrate the method and related concepts. It is shown that the eight binary topological relations between regions in a two-dimensional space can be easily determined by the method.     

地理信息共享、地理数据标准化及地理信息的GIS描述

从地理信息共享、地理信息标准化研究的角度,着重分析了地理信息在GIS系统中的描述机制,讨论了地理目标、地理实体、地理现象的概念及其间的关系。认为GIS对地理现象的描述是以地理实体及其关系为基本单元的,而地理实体则由表示空间位置形状及空间关系的空间目标及描述物理属性的属性数据共同表示的。     

OCL for formal modelling of topological constraints involving regions with broad boundaries

Integrity constraints can control topological relations of objects in spatial databases. These constraints can be modelled using formal languages such as the spatial extension of the Object Constraint Language (Spatial OCL). This language allows the expression of topological integrity constraints involving crisp spatial objects but it does not support constraints involving spatial objects with vague shapes (e.g. forest stand, pollution zone, valley or lake). In this paper, we propose an extension of Spatial OCL based on (1) a geometric model for objects with vague shapes, and (2) an adverbial approach for modelling topological constraints involving regions with broad boundaries. This new language provides an easiness in the formal modelling of these complex constraints. Our approach has been implemented in a code generator. A case study is also presented in the paper in the field of agriculture spreading activities. AOCL _OVS takes account of the shape vagueness of spread parcel and improve spatial reasoning about them.     

A vocabulary for a multiscale process description for fast transmission and continuous visualization of spatial data

With the increasing availability of small mobile computers there is also an increasing demand for visualizing spatial data on those devices. Prominent applications are location based services in general, and car and pedestrian navigation in particular. In order to be able to offer both detail and overview of a spatial situation, the devices have to provide flexible zooming in and out in real-time. The same demands arise from the increasing amounts of data available and accessible by web services through limited bandwidth channels. The presentation of spatial data sets in different zoom levels or resolutions is usually achieved using generalization operations. When larger scale steps have to be overcome, the shape of individual objects typically changes dramatically; also objects may disappear or merge with others to form new objects. As these steps typically are discrete in nature, this leads to visual ‘popping effects’ when going from one level of detail to the other.In this paper, we will present an approach to decompose generalization into simple geometric and topologic operations that allow describing the complete generalization chain to generate a multiscale object representation. The goal is to generate a representation without redundancy and to transmit only that information which is needed when scale changes occur. This representation scheme ultimately enables a continuous visualization, where the changes between the representations are visually indistinguishable. We identify elementary generalization operations and apply these concepts for polyline simplification, the generalization of building ground plans and for displacement.     

随时间演化的不确定区域间拓扑关系判定

不确定性处理是时空数据库技术研究的新领域,现有研究成果集中在时空不确定性的表示模型方面,缺乏不确定性对象间时空关系特别是拓扑关系的分析.提出了利用3维拓扑分析模型来分析2维运动对象的时空关系,针对随时间演化的2维不确定性区域,将Egg/Yolk模型中的RCC（region connection calculus）区域扩充至3维,得到46种联合完备且互不相交的基本拓扑关系,根据各基本拓扑关系的时空特性,将46种基本关系归类为21类不确定性时空关系.