This is an author's version of the paper. Original version in: In proceeding of: IASTED International Conference on Computational Intelligence, Calgary, Alberta, Canada, Computational Intelligence, IASTED/ACTA Press, 2005, pp. 36–41, 2005. The final publication is available at www.actapress.com 36 PROCESSING FUZZY SQL QUERIES WITH FLAT, CONTEXT-DEPENDENT AND MULTIDIMENSIONAL MEMBERSHIP FUNCTIONS Bożena Malysiak, Dariusz Mrozek, Stanislaw Kozielski Institute of Informatics, Silesian University of Technology ul. Akademicka 16, 44-100 Gliwice, Poland malysiak@polsl.pl, mrozek@polsl.pl ABSTRACT Analysis of new trends in databases development shows that promising solution in databases gathering a huge quantities of information is approximate retrieval. This work presents the fuzzy queries processing with a special attention to context-dependent and multidimensional membership functions. In the first part, the analysis of occurrence of fuzzy values in SQL queries directed to the databases is shown. Next, the process of interpretation of filtering conditions in SQL queries is discussed and condition on compatibility degree is introduced to SQL queries notation. The main part of the paper describes application of con- text-dependent and multidimensional membership fun- ctions in fuzzy SQL queries as two different approaches, and a whole process of their usage interpretation. All issues considered in this work are illustrated by appropria- te examples. KEY WORDS Fuzzy Databases, Fuzzy SQL Queries, Membership Fun- ctions 1. Introduction In outward things, there are many domains where informa- tics systems collecting huge quantities of various data are applied. Efficient retrieval of needed information can be a critical problem in that systems. In traditional databases, classical retrieval algorithms assure searching only these objects which attributes are precisely consistent with con- ditions in a given query. Objects which are not precisely consistent with the given conditions are not located. Ana- lysis of new trends in database development shows that promising solution in database gathering a huge quantities of information is approximate retrieval [1, 2]. The main assumption of approximate retrieval methods is that the answer on the given query may contain set of the objects from database which are consistent with criteria defined in the query with the given degree. Queries of this type re- quire defining characteristic function, which determines in what degree searched object is consistent with criteria defined in the query and threshold value, which allows qualify objects that ought to occur in the resultant answer. For the fuzzy queries a membership function is the charac- teristic function. Its value defines matching degree of sear- ched object in database with criteria specified in the query [1, 2]. This work presents the fuzzy queries processing that point to the context-dependent and multidimensional member- ship functions. In the first part, the analysis of occurrence of fuzzy values in SQL queries directed to the databases is shown. Next, the process of interpretation of filtering conditions in SQL queries is discussed and condition on compatibility degree is introduced to SQL queries nota- tion. The main part of the paper describes application of context-dependent and multidimensional membership fun- ctions in fuzzy SQL queries as two different approaches, and a whole process of their usage interpretation. All issues considered in this work are illustrated by appropria- te examples. All of the presented queries will be directed to the database called DEPARTMENTS which structure is presented in Fig.1. Institutes InsNo : Integer InsNam e : String Employees EmpNo : Integer FirstName : String LastName : String Age : Integer Gender : String Seniority : Integer Requirement Paper : Trapezium Toner : Trapezium CDs : Trapezium DepNo : Integer Year : Date Departments DepNo : Integer DepName : String NOStaffRooms : Integer NOEmployees : Integer InsNo : Integer 0..n 1 0..n +is part of 1 0..n 1 0..n +employs 1 0..n 1 0..n +order 1 Consumption Paper : Integer Toner : Integer CDs : Integer DepNo : Integer Year : Date 0..n 1 0..n +use up Figure 1. The structure of the Departments database. 2. Fuzzy Values in SQL Queries Queries, the user directs to the database are often first for- mulated in the natural language. In these queries impre- cise, fuzzy terms may appear [3]. The conditions in such