An Object-Oriented Approach to Managing Fuzziness in Spatially Explicit Models Coupled to a Geographic Database

This chapter uses a spatially explicit, individual-based ecological modeling problem to illustrate an approach to managing fuzziness in spatial databases that accommodates the use of nonfuzzy as well as fuzzy representations of geographic databases. The approach taken here uses the Extensible Component Objects for Constructing Observable Simulation Models (ECO-COSM) system loosely coupled with geographic information systems. ECO-COSM Probe objects flexibly express the contents of a spatial database within the context of an individualized fuzzy schema. It affords the ability to transform traditional nonfuzzy spatial data into fuzzy sets that capture the uncertainty inherent in the data and model’s semantic structure. The ecological modeling problem was used to illustrate how combining Probes and ProbeWrappers with Agent objects affords a flexible means of handling semantic variation and is an effective approach to utilizing heterogeneous sources of spatial data.

A Constraint Based Fuzzy Object Oriented Database Model

The objective of this chapter is to define a fuzzy object-oriented formal database model that allows us to model and manipulate information in a (true to nature) natural way. Not all the elements (data) that occur in the real world are fully known or defined in a perfect way. Classical database models only allow the manipulation of accurately defined data in an adequate way. The presented model was built upon an object-oriented type system and an elaborated constraint system, which, respectively, support the definitions of types and constraints. Types and constraints are the basic building blocks of object schemes, which, in turn, are used for defining database schemes. Finally, the definition of the database model was obtained by providing adequate data definition operators and data manipulation operators. Novelties in the approach are the incorporation of generalized constraints and of extended possibilistic truth values, which allow for a better representation of data(base) semantics.

Object-Oriented Publish/Subscribe for Modeling and Processing Imperfect Information

In the publish/subscribe paradigm, information providers disseminate publications to all consumers who expressed interest by registering subscriptions with the publish/subscribe system. This paradigm has found widespread applications, ranging from selective information dissemination to network management. In all existing publish/subscribe systems, neither subscriptions nor publications can capture uncertainty inherent to the information underlying the application domain. However, in many situations, knowledge of either specific subscriptions or publications is not available. To address this problem, this chapter proposes a new object-oriented publish/subscribe model based on possibility theory and fuzzy set theory to process imperfect information for expressing subscriptions, publications, or both combined. Furthermore, the approximate publish/subscribe matching problem based on fuzzy measures is defined, and the real-world A-ToPSS™ system is described.

Fuzzy and Probabilistic Object Bases

Database systems have evolved from relational databases to those integrating different modeling and computing paradigms, in particular, object orientation and probabilistic reasoning. This chapter introduces an extension of the probabilistic object base model by Eiter et al. (2001), using fuzzy sets for representing and handling vague and imprecise values of object attributes. A probabilistic interpretation of relations on fuzzy set values is proposed to integrate them into that probability-based framework. Then, the definitions of fuzzy-probabilistic object base schemas, instances, and selection operation are presented. Other algebraic operations, namely, projection, renaming, Cartesian product, join, intersection, union, and difference of the probabilistic object base model are also adapted for its fuzzy extension.

A Framework to Build Fuzzy Object-Oriented Capabilities Over an Existing Database System

Fuzzy object-oriented database models allow the representation, storage, and retrieval of complex imperfect information according to the object-oriented data paradigm. This chapter describes both a framework and an architecture that can be used to develop fuzzy object-oriented capabilities using the conventional features of the object-oriented data paradigm. We present a framework composed of a set of classical classes, which gives support to fuzzily described complex objects. We also explain how to deal with fuzzy extensions of object-oriented features using as a basis, the conventional object-oriented features. This proposal can be used to build a fuzzy object-oriented database system, by taking as a base an existing database system and minimizing the development effort.

Fuzzy Information Modeling with the UML

Computer applications in nontraditional areas have put requirements on conceptual data modeling. Some conceptual data models, being the tool of design databases, were proposed. However, information in real-world applications is often vague or ambiguous. Currently, less research has been done in modeling imprecision and uncertainty in conceptual data models. The UML (Unified Modeling Language) is a set of object-oriented modeling notations and is a standard of the Object Data Management Group (ODMG). It can be applied in many areas of software engineering and knowledge engineering. Increasingly, the UML is being applied to data modeling. In this chapter, different levels of fuzziness are introduced into the class of the UML and the corresponding graphical representations are given. The class diagrams of the UML can hereby model fuzzy information.

Generalization Data Mining in Fuzzy Object-Oriented Databases

In this chapter, we consider the application of generalization-based data mining to fuzzy similarity-based object-oriented databases (OODBs). Attribute generalization algorithms have been most commonly applied to relational databases, and we extend these approaches. A key aspect of generalization data mining is the use of a concept hierarchy. The objects of the database are generalized by replacing specific attribute values by the next higher-level term in the hierarchy. This will then eventually result in generalizations that represent a summarization of the information in the database. We focus on the generalization of similarity-based simple fuzzy attributes for an OODB using approaches to the fuzzy concept hierarchy developed from the given similarity relation of the database. Then consideration is given to applying this approach to complex structure-valued data in the fuzzy OODB.

FRIL++ and Its Applications

We introduce a deductive probabilistic and fuzzy object-oriented database language, called FRIL++, which can deal with both probability and fuzziness. Its foundation is a logic-based probabilistic and fuzzy object-oriented model where a class property (i.e., an attribute or a method) can contain fuzzy set values, and uncertain class membership and property applicability are measured by lower and upper bounds on probability. Each uncertainly applicable property is interpreted as a default probabilistic logic rule, which is defeasible, and probabilistic default reasoning on fuzzy events is proposed for uncertain property inheritance and class recognition. The design, implementation, and basic features of FRIL++ are presented. FRIL++ can be used as both a modeling and a programming language, as demonstrated by its applications to machine learning, user modeling, and modeling with words herein.

Introducing Fuzziness in Existing Orthogonal Persistence Interfaces and Systems

Previous research has resulted in generalizations of the capabilities of OODB models and query languages to cope with imprecise and uncertain information in several ways, informed by previous research in fuzzy relational databases. As a result, a number of models and techniques to integrate fuzziness in its various facets in object data stores are available for researchers and practitioners, and even extensions to commercial systems have been implemented. Nonetheless, for those models and techniques to become widespread in industrial contexts, more attention should be paid to their integration with current database design and programming practices, so that the benefits of fuzzy extensions could be easily adopted and seamlessly integrated in current applications. This chapter attempts to provide some criteria to select the fuzzy extensions that more seamlessly integrate in the current object storage paradigm known as orthogonal persistence, in which programming-language object models are directly stored, so that database design becomes mainly a matter of object design. Concrete examples and case studies are provided as practical illustrations of the introduction of fuzziness both at the conceptual and the physical levels of this kind of persistent system.

Index Structures for Fuzzy Object-Oriented Database Systems

This chapter gives an overview of indexing techniques suitable for fuzzy object-oriented databases (FOODBSs). First, typical query patterns used in FOODBSs are identified, namely, single-valued, set-valued, navigational, and type hierarchy access. The description of the patterns does not follow a particular fuzzy object-oriented data model but is kept general enough to be used in different FOODBS contexts. Second, for each query pattern, index structures are presented that support the efficient evaluation of these queries. These range from standard index structures (like B-trees) to sophisticated access methods (like Join Index Hierarchies). Due to space constraints, an explanation of the basic techniques is given rather than an exhaustive description. However, the interested reader is supplied with a broad list of references for further reading. Finally, a summary and outlook conclude the chapter.