An Overview of Fuzzy Object-Oriented Database Models (FOOB-

We call this type of attributes crisp attributes.

 Complex attribute: can contain collections and/or references. For example, the attribute academicDegrees is a collection of academic degrees that the object the student has; since each academic degree is described by level and year. A reference of an attribute represents the relationship between objects and contains a value, or collection of values (which are themselves objects). Complex Object: is an object that contains one or more complex attributes.

2.3.2 Classes

Any collection of objects that have the same attribute values, and using the same operations is called a class (or object type). The notion of a class is the basis for instantiation. In another word, a class can be dened as a model, that specifying structure (the set of instance attributes) and behaviour (the set of instance operations). Figure 2.2 shows class instance shared attributes and methods

2.4 An Overview of Fuzzy Object-Oriented Database

Models (FOOBDMs)

Fuzzy set-theory is basically the theory of graded concepts; a theory where ev- erything is a matter of degree (Zimmermann, 2001). Since fuzzy theory was introduced by Zaheh (Zadeh,1965) till now, many researchers have devoted their eort in this eld.

2.4 An Overview of Fuzzy Object-Oriented Database Models (FOOBDMs)

Figure 2.2: Class Instances.

Fuzzy set-theory has been proven to be a good tool to deal with a kind of uncertainty called fuzziness, where it shows that the boundary between true and false is ambiguous, and appears in the natural language when interpreting the meaning of words or is included in the recognition of human beings' common sense reasoning. Fuzzy set-theory is applicable to many systems  from con- sumer products like washing machines or refrigerators to big systems like trains or subways. Recently, fuzzy theory has been a strong tool for combining new theories (called soft computing) such as genetic algorithms or neural networks to get knowledge from real data. The theory has matured into many concepts and techniques for handling complex phenomena that can not be analysed by classical methods. Chapter 3 will study and discuss in detail the basic concepts

2.4 An Overview of Fuzzy Object-Oriented Database Models (FOOBDMs) and denitions of fuzzy set-theory and fuzzy logic.

Fuzzy set-theory and logic techniques have been applied to database and in- formation retrieval areas for years. However, one of the rst proposals was pre- sented by Codd (Codd, 1979) for dealing with vague, imprecise and uncertain information occurred in databases and then further developed in (Codd, 1986) and (Codd, 1987), but the model did not use fuzzy logic. The use of the value NULL is proposed to indicate that an attribute can be any value of the domain. Later, the model presented by Buckles and Petry (Buckles & Petry,1982), (Buck- les & Petry, 1984) used the similarity measure dened by Zadeh (Zadeh, 1971). The proposal of Prade and Testemale (Prade & Testemale, 1984) went further, allowing attributes to have fuzzy values.

Attributes of precise and partial (imprecise and unknown) values were repre- sented by the possibility distribution proposed by Zadeh (Zadeh, 1971). Some research work based on this representation is presented in (Galindo & Galindo, 2008; Ma, 2005).

The integration of fuzzy techniques in databases allows these systems to model human activities more closely. Fuzzy set theory as an uncertainty management technique can increase the modeling capability of ODBMSs by eectively repre- senting imprecise data and performing exible queries on both crisp and fuzzy data (Shukla et al.,2011).

Fuzzy databases usually store information and its associated meta-information in order to add context to these databases.However,the fuzzy database systems became very complex and dicult to maintain because fuzzy concepts are very dicult to represent using traditional database representation forms.

2.4 An Overview of Fuzzy Object-Oriented Database Models (FOOBDMs) data that match it precisely, whereas, a vague query establishes a target qual- ication and is concerned also with data that are close to this target. Most conventional database systems cannot handle vague queries directly, forcing their users to retry specic queries again and again with some corrections until they match data that are suitable or satisfactory.

Precise (or exact) information has become a critical facet of the modern database applications and next generation information systems to make them more accessible by humans. In order to manage inexact information, fuzzy tech- niques have been widely included with dierent database models and theories. However, object oriented database systems are highly capable of representing and manipulating the complex objects as well as complicated and uncertain re- lationships existing among them. They are also appropriate for engineering and scientic applications, dealing with large data intensive applications(Shukla et al., 2011).

Petry (Petry,1997) presents the results many years of work from researchers around the world on the use of fuzzy set theory to represent imprecision in databases. It is comprehensive covering all of the major approaches and mod- els of fuzzy databases that have been developed including coverage of commer- cial/industrial systems and applications.

A proposal of describing dierent types of fuzziness at dierent levels in tradi- tional ODBMS has been introduced in (Blanco et al., 2001). Imprecise attribute domains, uncertainty in attribute values, uncertain object relationship, fuzzy sub- classes, fuzzy categories, uncertain object denition, uncertain class denition and fuzzy types are discussed in this proposal.

2.5 Similarity Measure Approaches