Skip to main content

Fuzzy Functional Dependency and a Series of Design Issues of Fuzzy Relational Databases

  • Conference paper
Fuzziness in Database Management Systems

Part of the book series: Studies in Fuzziness ((STUDFUZZ,volume 5))

Abstract

Fuzzy functional dependencies (FFDs) reflect a kind of semantic knowledge about the real world and are considered as integrity constraints of fuzzy database models. This paper first reviews various efforts made on fuzzy extensions of classical databases with respect to different frameworks of fuzzy data representation. Primary attention is then paid to a series of fundamental issues towards building a theory of fuzzy relational database design. A general overview is provided to show our attempts that have been made to tackle these issues. These issues include FFD inference rules, the soundness and completeness of the FFD axiomatic system, the equivalence of FFD sets, lossless-join and dependency-preservation decompositions, θ-keys, and fuzzy normal forms. The elimination or reduction of data redundancy and update anomalies is the main concern of database design. A proper settlement of these issues enables us to tell what a “good” design is and how it can be obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Baldwin J.F., and Zhou S.C. (1984) A fuzzy relational inference language, Fuzzy sets and systems 14, 155–174.

    Article  Google Scholar 

  • Bosc P., and Pivert O. (1991) On the evaluation of simple fuzzy relational queries, Proceedings of IFSA’91 World Congress, July, Brussels.

    Google Scholar 

  • Bosc P., Pivert O., Farquhar K. (1992) Integrating fuzzy queries into a database management system: the example of DEC-VAX information warehouse, Proceedings of international conference on information processing and management of uncertainty (IPMU’92), pp. 259–262, July, Palma (Spain).

    Google Scholar 

  • Buckles B.P., and Petry F.E. (1982) A fuzzy representation of data for relational databases. Fuzzy sets and systems 7, 213–226.

    Article  Google Scholar 

  • Buckles B.P., and Petry F.E. (1984) Generalized databases and information systems. tech.report CSE,uni.of Texas at Arlinton.

    Google Scholar 

  • Buckles B.P., Petry F.E., and Sachar H.S. (1986) Design of similarity-based relational databases. In H.Prade and C.V.Negoita (eds.): Fuzzy logic in knowledge engineering, Verlag TUV Rheinland, pp. 3–7.

    Google Scholar 

  • Buckles B.P., Petry F.E., and Sachar H.S. (1989) A domain calculus for fuzzy relational databases, Fuzzy sets and systems, 29, 327–340.

    Article  Google Scholar 

  • Chen G.Q. (1989) Knowledge Representation with uncertainty and fuzzy data modeling (a survey), research paper No. 9005, ETEW, K.U.Leuven, Belgium.

    Google Scholar 

  • Chen G.Q. (1991a) A step towards the theory of fuzzy relational database design, Proceedings of IFSA’91 World Congress, pp44–47, July 7–12, Brussels.

    Google Scholar 

  • Chen G.Q. (1991b) Fuzzy data modeling: perspectives, problems and solutions, in E.E.Kerre (Ed.): Introduction to the basic principles of fuzzy set theory and some of its applications, Communication and Cognition, Gent, Belgium, pp. 294–343.

    Google Scholar 

  • Chen G.Q. (1992) Design of fuzzy relational databases based on fuzzy functional dependency, Ph.D. dissertation, ETEW, Nr. 84, K.U.Leuven, Belgium.

    Google Scholar 

  • Chen G.Q., Kerre E.E., and Vandenbulcke J. (1992) Fuzzy functional dependency and its axiomatic system, Proceedings of the Fourth International Conference on Information Processing and Management of Uncertainty (IPMU’92), pp. 313–316, July, Palma (Spain).

    Google Scholar 

  • Chen G.Q., Kerre E.E., and Vandenbulcke J. (1993a) A computational algorithm for the FFD closure and a complete axiomatization of fuzzy functional dependency (FF’ll). International Journal of Intelligent Systems (to appear).

    Google Scholar 

  • Chen G.Q., Kerre E.E., and Vandenbulcke J. (1993b) The dependency-preserving decomposition and a testing algorithm in a fuzzy relational data model. submitted to Fuzzy Sets and Systems.

    Google Scholar 

  • Chen G.Q., Vandenbulcke J., and Kerre E.E. (1992) A general treatment of data redundancy in a fuzzy relational data model, Journal of The American Society for Information Science, 43, 304–311.

    Article  Google Scholar 

  • Chen G.Q., Vandenbulcke J., and Kerre E.E. (1993) On the lossless-join decomposition in a fuzzy relational data model, Proceedings of the Second International Symposium on Uncertainty Modeling &Analysis (ISUMA’93), pp. 440–446, April, Maryland (USA).

    Google Scholar 

  • Codd E.F. (1970) A relational model for large shared data banks, Comm. ACM (13)6, 377–387.

    Google Scholar 

  • Dubois D., and Prade H. (1992) Generalized dependencies in fuzzy databases, Proceedings of the Fourth International Conference on Information Processing and Management of Uncertainty (IPMU’92), pp. 263–266, July, Palma (Spain).

    Google Scholar 

  • Kacprzyk J., and Ziolkowski A. (1986), Database queries with fuzzy linguistic quantifiers, IEEE Trans. on Sys. Man, and Cybern, SMC-16, pp. 474–479.

    Google Scholar 

  • Kacprzyk J., and Fedrizzi M., Eds. (1988) Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Springer-verlag.

    Book  Google Scholar 

  • Kerre E.E. (1988) Fuzzy sets and approximate reasoning. Lecture notes for the course (special topics in computer sciences), University of Nebraska, Lincoln, USA.

    Google Scholar 

  • Kiss A. (1990) X,-decomposition of fuzzy relational databases, Proceedings of international workshop on fuzzy sets and systems, December, Visegrad (Hungary).

    Google Scholar 

  • Prade H., and Testemale C. (1983) Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries. Proceedings of 2nd NAFIPS Workshop, Schenectady, NY.

    Google Scholar 

  • Raju K.V.S.V.N., and Majumdar A.K. (1987) The study of joins in fuzzy relational databases, Fuzzy Sets and Systems, 21, 19–34.

    Article  Google Scholar 

  • Rundensteiner E.A., Hawkes L.W., and Bandler W. (1989) On nearness measures in fuzzy relational data models. Int. J. of Approximate Reasoning, 3, 267–298.

    Google Scholar 

  • Shenoi S., and Melton A. (1989) Proximity relations in the fuzzy relational databases. Fuzzy Sets and Systems, 31, 285–296.

    Article  Google Scholar 

  • Shenoi S., Melton A., and Fan L.T. (1990) An equivalence classes model of fuzzy relational databases, Fuzzy Sets and Systems 38, 153–170.

    Article  Google Scholar 

  • Testemale C. (1986) A database system dealing with incomplete or uncertain information and vague queries. In H.Prade and C.V.Negoita (Eds.): Fuzzy logic in knowledge engineering. Verlag TUV Rheinland, pp. 29–45.

    Google Scholar 

  • Tripathy R.C., and Saxena P.C. (1990) Multivalued dependencies in fuzzy relational databases, Fuzzy Sets and Systems 38, 267–279.

    Article  Google Scholar 

  • Umano M. (1983) Retrieval from fuzzy databases by fuzzy relational algebra, in: Sanchez and Gupta (Eds.): Fuzzy Information Knowledge Representation and Decision Analysis, Pergamon Press, Oxford, England, pp. 1–6.

    Google Scholar 

  • Ullman J.D. (1982) Principles of Database Systems. Computer sciences press inc.

    Google Scholar 

  • Van Schooten A. (1988) Design and implementation of a model for the presentation and manipulation of uncertainty and imprecision in databases and expert systems. Ph.D thesis (in Dutch), University of Gent, Belgium.

    Google Scholar 

  • Zadeh L.A. (1965) Fuzzy sets. Information and Control, 8, 338–358.

    Article  Google Scholar 

  • Zadeh L.A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1 (1), 3–28.

    Article  Google Scholar 

  • Zadeh L.A. (1983) The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems, 11, 199–227.

    Article  Google Scholar 

  • Zemankova M., and Kandel A. (1984) Fuzzy Relational Database - a key to expert system. Verlag TUV Rheinland, Cologne.

    Google Scholar 

  • Zemankova M., and Kandel A. (1985) Implementing imprecision information systems, Information Sciences, 37, 107–141.

    Article  Google Scholar 

  • Zvieli A. (1986) A fuzzy relational calculus, In L. Kerschberg (Ed.): Expert database systems, Proceedings of 1st International Conference, April 1–4, South Carolina, USA.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, G. (1995). Fuzzy Functional Dependency and a Series of Design Issues of Fuzzy Relational Databases. In: Bosc, P., Kacprzyk, J. (eds) Fuzziness in Database Management Systems. Studies in Fuzziness, vol 5. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1897-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1897-0_8

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11805-4

  • Online ISBN: 978-3-7908-1897-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics