Relational Databases and Fuzzy Sets Background
In this chapter we will provide an overview of relational databases and fuzzy set theory as will be needed when we describe the various fuzzy relational extensions in following chapters. The relational model has been highly influential based both on its sound mathematical foundations and highly successful implementations. First the formal definition of the relational model will be presented and then the design process will be discussed in more detail. In chapter 1 we have seen how entity-relationship modeling led to a relational data base design. Also we will describe the design approach using functional dependencies to develop the relations of the database and then briefly describe the querying of relational models by relational algebra, relational calculus and the higher level SQL language.
KeywordsRelational Database Relational Algebra Membership Grade Company Speciality Select Operation
Unable to display preview. Download preview PDF.
- 4.I. Hawryszkiewycz, Database Design and Analysis, Science Research Associates, Chicago, IL 1984.Google Scholar
- 8.A. Dutka and H. Hanson, Fundamentals of Data Normalization, Addison-Wesley, Reading MA, 1989.Google Scholar
- 9.W. Armstrong, “Dependency Structures of Data Base Relationships”, Proc. of 1974 Int. Fed. of Information Processing, 580–583, North Holland Amsterdam, 1974.Google Scholar
- 10.E. Codd, “Further Normalization of the Data Base Relational Model”, DataBase Systems, (ed. R. Rustin), Prentice-Hall, NY 1972.Google Scholar
- 11.A. Makinouchi, “A Consideration on Normal Form of Not Necessarily Normalized Relations in the Relational Data Model,” Proc. of the Third Int. Conf. on Very Large Databases, 447–453, 1977.Google Scholar
- 12.G. Jaeschke and H. Schek, “Remarks on the Algebra of Non First Normal Form Relations,” Proc. of the ACM SIGACT-SIGMOD Symp. on Principles of Database Systems, 124–138, 1982.Google Scholar
- 14.D. Van Gucht “On the Expressive Power of the Extended Relational Algebra”, Proc. 6th Princip. of Database Systems, 302–312, 1987.Google Scholar
- 17.S. Thomas and P. Fischer, “Nested Relational Structures,” Advances in Computing Research, 3, 269–307, JAI Press, Greenwich CT, 1989.Google Scholar
- 19.C. Date, A Guide to the SQL Standard (SQL/89) 2nd ed., Addison-Wesley, Reading MA, 1989.Google Scholar
- 20.E. Codd, “Relational Completeness of Data Bases Sublanguages”, DataBase Systems, (ed. R. Rustin), Prentice-Hall, NY 1972.Google Scholar
- 24.H. Zimmerman, Fuzzy Set Theory — and Its Applications, Kluwer, Norwell, MA 1985.Google Scholar
- 26.T. Terano, K. Asai and M. Sugeno, Fuzzy Systems Theory and Its Applications, Academic Press, NY, 1991.Google Scholar