Extending object-oriented databases for fuzzy information modeling

Abstract

In this paper, based on possibility distribution and the semantic measure of fuzzy data, we introduce an extended object-oriented database model to handle imperfect as well as complex objects in the real world. Some major notions in object-oriented databases such as objects, classes, objects–classes relationships, subclass/superclass, and multiple inheritances are extended under fuzzy information environment. A generic model for fuzzy object-oriented databases and some operations are hereby developed in the paper.

Introduction

A major goal for database research has been the corporation of additional semantics into the data model. In real-world application, information is often vague or ambiguous. Therefore, different kinds of incomplete information have been extensively introduced into relational databases [1], [2], [3]. However, classical relational database model and its extension of imprecision and uncertainty do not satisfy the need of modeling complex objects with imprecision and uncertainty. So many researches have been concentrated on the development of some database models to deal with complex objects and uncertain data together. In [4], an extended nested relational data model (also known as an NF² data model) was introduced for representing and manipulating complex and uncertain data in databases and the extended algebra and the extended SQL-like query language were hereby defined. Also physical data representation of the model and the core operations that the model provides were also introduced in [4]. It should be pointed out that, being the extension of relational data model, NF² data model is able to handle complex-valued attributes and may be better suited to some complex applications such as office automation systems, information retrieval systems and expert database systems [4]. But it is difficult for NF² data model to represent complex relationships among objects and attributes. Some advanced abstracts in data modeling (e.g., class hierarchy, inheritance, superclass/subclass, and encapsulation) are not supported by NF² data model, which are needed by many real applications. Therefore, in order to model uncertain data and complex-valued attributes as well as complex relationships among objects, current efforts have been focused on conceptual data models and object-oriented databases (OODB) with imprecise and uncertain information.

Based on fuzzy set theory, Zvieli and Chen [5] introduced three levels of fuzziness in the ER model. At the first level, entity sets, relationships, and attribute sets may fuzzy, namely, they have degree of membership in the model. The second level is related with the fuzzy occurrences of entities and relationships. The third level concerns the fuzzy values of attributes of special entities and relationships. By using fuzzy set theory, the fuzzy extensions of several major EER concepts were introduced in [6], including superclass/subclass, generalization/specialization, category, and the subclass with multiple superclasses. In addition to the ER/EER model, IFO data model [7] is a mathematically defined conceptual data model that incorporates the fundamental principles of semantic database modeling within a graph-based representational framework. The extensions of IFO to deal with fuzzy information were proposed in [8]. In [8], several types of imprecision and uncertainty such as the values without semantic representation, the values with semantic representation and disjunctive meaning, the values with semantic representation and conjunctive meaning, and the representation of uncertain information were incorporated into the attribute domain of the object-based data model. In addition to the attribute-level uncertainty, the uncertainty was also considered to be at the object and class level. However, some major concepts in object-based modeling, including object–class relationship, superclass/subclass, and multiple inheritance, were not discussed in [8].

Regarding modeling imprecise and uncertain information in object-oriented databases, Zicari in [9] first introduced incomplete information, namely, null values, where incomplete schema and incomplete objects can be distinguished. From then on, the incorporation of imprecise and uncertain information in object-oriented databases has increasingly received the attentions, where fuzziness is witnessed at the levels of object instances and class hierarchies. Based on similarity relationship, in [10], the range of attribute values is used to represent the set of allowed values for an attribute of a given class. Depending on the inclusion of the actual attribute values of the given object into the range of the attributes for the class, the membership degrees of an object to a class can be calculated. The weak and strong class hierarchies were defined based on monotone increase or decrease of the membership of a subclass in its superclass. Based on the extension of a graphs-based model object model, a fuzzy object-oriented data model was defined in [11]. The notion of strength expressed by linguistic qualifiers was proposed, which can be associated with the instance relationship as well as an object with a class. Fuzzy classes and fuzzy class hierarchies were thus modeled in the OODB. An uncertainty and fuzziness (UFO) in an object-oriented databases model was proposed in [12] to model fuzziness and uncertainty by means of fuzzy set theory and generalized fuzzy set, respectively. That the behaviour and structure of the object are incompletely defined results in a gradual nature for the instantiation of an object. The partial inheritance, conditional inheritance, and multiple inheritances are permitted in fuzzy hierarchies. Based on possibility theory, vagueness and uncertainty were represented in class hierarchies in [13], where the fuzzy ranges of the subclass attributes defined restrictions on that of the superclass attributes and then the degree of inclusion of a subclass in the superclass was dependent on the inclusion between the fuzzy ranges of their attributes. Based on the concept of the semantic proximity, an evaluated method of the fuzzy association degree was given in semantic data models [14]. Full fuzzy extended entity-relationship model and the graphical representations were presented in [15], and the formal design methodology for fuzzy object-oriented databases from fuzzy entity-relationship model was also provided. Recent efforts have been paid on the establishment of consistent framework for a fuzzy object-oriented model based on the standard for the Object Data Management Group (ODMG) object data model [16], [17].

It can be seen that although there are some work in the literature for modelling fuzzy information in object-oriented databases, their focuses were mainly on fuzzy objects and fuzzy classes. It is not clear what are fuzzy object relationships and what are fuzzy inheritance hierarchies. In this paper, based on possibility distribution and the semantic measure of fuzzy data, we further investigate the issues of fuzzy object-oriented databases. Some major notions in object-oriented databases such as objects, classes, objects–classes relationships, subclass/superclass, and multiple inheritances are extended under fuzzy information environment. A generic model for fuzzy object-oriented databases is hereby introduced.

The remainder of this paper is organized as follows. Section 2 gives the basic knowledge about fuzzy data and semantic measure. The fuzzy objects, fuzzy classes and fuzzy object–class relationships are described in Section 3. Section 4 investigates fuzzy inheritance hierarchies. Section 5 gives a generic fuzzy object-oriented database model and some operations. Section 6 concludes this paper.