Fuzzy And Uncertain Object-Oriented Databases

The following sections are included:

• CONTENTS

• FOREWORD

• PREFACE

The field of databases is a very vast field which has been studied by many researchers for many years. Countless books and papers have been published that reflect the increasing importance of this field.

The present book contributes to this research by focusing on the integration of the object-oriented database theory with the theory of uncertainty modelling, which is another rapidly developing field. Combining the advantages of both theories permits the design of databases which are semantically far more powerful and user-friendly than the traditional ones. This chapter of the book explains the reasons for this and introduces the basic concepts an terminology of the underlying theories.

The chapter presents an object-centered representation, where both a range of allowed values and a range of typical values can be specified for the attributes describing a class. These ranges may be fuzzy. Then various kinds of (graded) inclusion relations can be defined between classes. Inheritance mechanisms are discussed in this framework, as well as other kinds of reasoning tasks such as classification. Updating is also discussed.

In this chapter, we extend the Object-Oriented Data Model to facilitate the enhanced representation of different types of imprecision. The modeling capability is derived by utilizing the similarity relation to generalize equality to similarity. Similarity permits the impreciseness in data to be represented. Imprecision in data results in uncertainty in classification. Both these mechanisms are explicitly accomodated in this model, which uses well defined semantics to differentiate between multi-valued objects with OR, XOR and AND connectives. It is shown that the addition of these semantics lead to a richer and more accurate representation of Object-Class relationships. A primitive operator, the merge, that preserves non-redundancy in the data model is defined. An object algebra for the model is defined and implementation details are discussed. A typical next-generation application for the model is described.

In this contribution a fuzzy object oriented data model is defined to manage crisp and imperfect information. This model is based on a visual paradigm that supports the representation of the data semantics and the direct browsing of the information. The model is defined as an extension of a graph-based object model, in which both the database schema and instances are represented as directed labelled graphs. This model allows to deal the requisites of many current applications involving data of different nature and with complex interrelationships.

The ultimate goal of the research discussed in this paper, is the design of a database model with a true flavour of reality. Because the real world is not always perfect and, moreover, because the world of the application model is not an ideal reflection of the real world, the “ideal” database model should be able to process imperfect information about the database application in a convenient and flexible way. This paper describes an effort to reach this goal with the UFO database model. UFO extends an object-oriented database model, which defines flexible modelling concepts, with capabilities to handle major forms of imperfection in information. The extended concepts cover all layers of the model and are explained here in detail. A practical implementation via an interface to an extended relational database model is also outlined.

The complexity of real world applications in the fields of intelligent information systems has required fuzzy data models for the representation and the processing of uncertain and imprecise data. In this paper, we propose a new Fuzzy Object Oriented Data model (F-model) and a Fuzzy Association algebra (FA-algebra) for the F-model as a query algebra. The F-model is investigated as a fuzzy extension of an Object Oriented data model which allows fuzzy classes and fuzzy associations. Databases are represented by a fuzzy schema graph at schema level and a fuzzy object graph at object instance level. The FA-algebra operators can operate on the fuzzy association patterns of homogeneous and heterogeneous structures. As the results of fuzzy association operations, the truth values of patterns are returned with the patterns. The completeness of the FA-algebra is shown. In the F-model, we describe the management of fuzzy objects with fuzzy attribute values. Objects representing linguistic terms are proposed for the representation of fuzzy attribute values. The fuzzy objects and the linguistic term objects are uniformly represented by the fuzzy association patterns which are manipulated by the FA-algebra operators. By the FA-algebra, the fuzzy queries involving fuzzy values can be processed easily.