Fuzzy eqiu-join operator in type-1 and type-2 fuzzy relation databases

• Autorzy: Saxena, P. Ch. , Tayal, D. K.
• Języki publikacji: EN

Abstrakty

EN

The classical databases were designed primarily for the efficient storage and convenient retrieval of large amount of precise data as they focus on describing precise information and take care of only well defined and unambiguous data. However in real world applications, the data are often partially known (incomplete) or imprecise. Also many times, the information, the user of the database is interested in may not be precise for e.g. a college senior may be interested in finding a university that has a "good graduate Engineering program and low living costs". The meaning of "good" and "low" is imprecise and is based on subjective judgments. Consequently the concept of fuzzy relational database was proposed as an extension to classical databases to handle this type of data. To capture the impreciseness in data in a better way, two particular types of fuzzy relational data models viz. type-1 and type-2 fuzzy relational databases have been described in the literature. These databases contain each tuple partially which is specified by a membership grade of each tuple. A type-1 fuzzy relational database may have the domain of an attribute as a fuzzy set while a type-2 fuzzy relational database may have the domain of an attribute as a set of fuzzy subsets. The objective of this paper is to define a fuzzy equi-join operator in both the type-1 and type-2 fuzzy relational databases with the help of fuzzy equality which is defined using the concept of fuzzy functions. The various cases which occur while joining the fuzzy attribute values like the joining attributes have crisp values, values as elements of a fuzzy set or a fuzzy set etc are discussed. A methodology has been proposed to derive the membership value of the new (joined tuple). The usefulness of fuzzy join operator defined is shown in computing the join of the decomposed fuzzy relation schemas.

Słowa kluczowe

PL

relacyjne bazy danych

EN

type-1 fuzzy relational databases; type-2 fuzzy relational databases; projection; fuzzy join operator

• Czasopismo: Computing, Multimedia and Intelligent Techniques
• Rocznik: 2007
• Tom: Vol. 3, nr 1
• Strony: 7-19
• Opis fizyczny: Bibliogr. 19 poz., tab.

Twórcy

autor

Saxena, P. Ch.

autor

Tayal, D. K.

• Jawaharal Nehru University, New Mehrauli Road, Delhi, India,

Bibliografia

• [1] Raju K. V .S. V .N., Majumdar A. K., Fuzzy functional dependencies and lossless join decomposition of fuzzy relational databases, ACM Transactions on Database Systems, 1988, 2, 129-166.
• [2] Petry R. E., Fuzzy Databases Principles and Applications, Kluwer Academic Publishers, USA 1996.
• [3] Klir G. J., Yuan B., Fuzzy Sets & Fuzzy Logic, PHI, New York 1997.
• [4] Bhatttacharjee T. K., Majumdar A. K., Database Systems, McGraw Hill Publications, 2001.
• [5] Buckles B., Petry, F., Fuzzy databases and their applications, Fuzzy Information and Decision Processes, eds. M. Gupta, E. Sanchez, North Holland, Amsterdam, 2, 361-371.
• [6] Buckles B., Petry F., A fuzzy model for relational databases, Fuzzy Sets and Systems 1982, 7, 213-226.
• [7] Prade H., Dubois D., Generalised dependencies in fuzzy data bases, Journal of American Society for Information Science, 49(3), 219-235.
• [8] Prade H., Bosc P., Dubois D., Fuzzy functional dependencies - An overview and a critical discussion, In Proc: Third IEEE International Conference on fuzzy systems, Orlando, 1994, 325-330.
• [9] Jyoti S., Babu M. S., Multivalued dependencies in fuzzy relational databases and loss less join decomposition, Fuzzy Sets and Systems 1997, 88, 315-332.
• [10] Raju K. V. S. V. N., Mazumdar A. K., The study of joins in fuzzy relational databases, Fuzzy Sets and Systems 1987, 21, 19-34.
• [11] Casanova M. A., Fagin R., Papadimitriou C. H.: Inclusion dependencies and their interaction with the functional dependencies, In Proc: First ACM-SIGACT-SIGMOD principles of Database Systems Conference, 1982.
• [12] Ma Z. M., Zhang W. J., Ma W. Y, Mili F., Data Dependencies in Extended Possibility Based Fuzzy Relational Databases, International Journal of Intelligent Systems 2002, 17, 321-332.
• [13] Saxena P. C., Tyagi B. K., Fuzzy functional dependencies & independencies in extended fuzzy relational data models, Fuzzy Sets and Systems 1995, 69, 65-89.
• [14] Liu W. Y., Fuzzy data dependencies and implications of fuzzy data dependencies, Fuzzy Sets and Systems 1977, 92, 341-348.
• [15] Liao S. Y, Wang H. Q., Liu W. Y.: Functional dependencies with null values, fuzzy values & crisp values, IEEE Transactions on Fuzzy Systems 1999,7(1).
• [16] Chen G. Q., Kerre E. E., Vandenbulcke J., A computational algorithm for FFD closure and a complete axiomatization of fuzzy functional dependency (FFD), International Journal of Intelligent Systems 1994, 9, 421-439.
• [17] Chen G. Q., Kerre E. E., Vandenbulcke J., Normalization based on fuzzy functional dependency in a fuzzy relational data model, Journal of Information Systems 1996, 21(3), 299-310.
• [18] Sasaki M., Fuzzy functions, Fuzzy Sets and Systems 1993,55, 295-301.
• [19] Demirci M., Fuzzy functions and their fundamental properties, Fuzzy Sets and Systems 1999, 106, 239-246.