Uncertainty in Multi-Source Databases
Database and database systems have become an essential part of everyday life, such as in banking activities, online shopping, or reservations of airline tickets and hotels. These trends place more demands on the capabilities of future database systems, wh
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In this chapter we introduce the ciset relational model, a collection of methods and techniques for organizing data centered on the notion of a ciset relation as the data structure. After we present the notion of a ciset relation, we present other fundamental concepts such as candidate key, primary key and foreign key in this model. Both entity integrity rule and the referential integrity rule are also explored. A ciset relational model is a blueprint of the database that can store conflicting information. In a ciset relational model, the data always is presented in the form of a table, which we call a ciset relation. Every piece of information is stored in one or more tables. Informally, a ciset relational database can be conceived as a collection of ciset relations. For example, data on all professors of a university can be organized in the form of a table FACULTY as shown in Table 3.1. TABLE 3.1 ciset relation: FACULTY
FACULTY F_ID 12312 31897 12674 56739
F_NAME John Smith Mary Lee Sandy Dewitt Bea Anthony
DEPT Marketing Mathematics Marketing Accounting
EVALUATION h0.5, 0.7i h0.4, 0.9i h0.1, 0.8i h0.7, 0.6i
As we contemplate the FACULTY table, we can identify several elements. P. S. Nair, Uncertainty in Multi-Source Databases © Springer-Verlag Berlin Heidelberg 2003
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3. THE CISET RELATIONAL MODEL
• The name of the table: FACULTY. • The column headings of the table: F_ID, F_NAME,DEPT and EVALUATION. • The set of rows of the table. • The column headings of table are known as ciset relational attributes. Thus the FACULTY table has four ciset relational attributes: F_ID, F_NAME, DEPT and EVALUATION. • Each row of the table is known as a ciset tuple. Thus the above table has four ciset tuples. From the user perspective, database model is still the classical relational model. The only conceptual di erence as far as the user is concerned can be summarized as follows. 1. As user inserts a new piece of data, user is asked to provide the confidence level. Similar is the situation when the user tries to delete a piece of information or modify a piece of information. 2. In addition to producing results of a query user can use the confidence index attribute to obtain the level of “trust” one can place on the result itself.
3.1 Formalization of Ciset Relation We now proceed to formalize the notion of a table. Let U be the set of all ciset relational attributes. For each attribute A 5 U , let DOM (A), called domain of A, denote the set of all possible values that can occur in that column. The domains are arbitrary, nonempty sets, nonempty fuzzy sets or nonempty cisets or nonempty subset of confidence indexes, finite or countably infinite. Note that if there is only one element in DOM(A), we need not include A as an attribute of the table. It is safe to assume that DOM (A) contains at least two di erent values. Let R = {A1 , . . . , An } be a finite set of ciset relational attributes. Then R is called a ciset relational scheme. A ciset relation r on a ciset relational scheme R is a finite set of mappings {t1 , . . . , tm }
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