On Interpretation of Non-atomic Values and Induction of Decision Rules in Fuzzy Relational Databases

  • Rafal A. Angryk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)


In this paper, we propose two new ways to interpret uncertain information reflected by non-atomic descriptors. We focus our research on data stored in a proximity-based fuzzy relational database as the database provides convenient mechanisms for recording and interpretation of uncertain information. In proximity-based fuzzy databases the lack of certainty about obtained information can be reflected via insertion of non-atomic attribute values. In addition, the database extends classical equivalence relations with fuzzy proximity relations, which provide users with interesting analytical capabilities. In this paper we concentrate on both of these properties when proposing new approaches to interpretation of non-atomic values for decision making purposes.


Decision Rule Wait Time Food Type Proximity Relation Partition Tree 


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  1. 1.
  2. 2.
    Buckles, B.P., Petry, F.E.: A fuzzy representation of data for relational databases. Fuzzy Sets and Systems 7(3), 213–226 (1982)MATHCrossRefGoogle Scholar
  3. 3.
    Petry, F.E.: Fuzzy Databases: Principles and Applications. Kluwer Academic Publishers, Boston (1996)MATHGoogle Scholar
  4. 4.
    Codd, F.E.: A relational model of data for large share data banks. Communications of the ACM 13(6), 377–387 (1970)MATHCrossRefGoogle Scholar
  5. 5.
    Zadeh, L.A.: Similarity relations and fuzzy orderings. Information Sciences 3(2), 177–200 (1970)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Shenoi, S., Melton, A.: Proximity Relations in the Fuzzy Relational Database Model. International Journal of Fuzzy Sets and Systems 31(3), 285–296 (1989)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Shenoi, S., Melton, A., Fan, L.T.: Functional Dependencies and Normal Forms in the Fuzzy Relational Database Model. Information Sciences 60(1-2), 1–28 (1992)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Tamura, S., Higuchi, S., Tanaka, K.: Pattern Classification Based on Fuzzy Relations. IEEE Transactions on Systems, Man, and Cybernetics SMC-1(1), 61–66 (1971)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kumar De, S., Biswas, R., Roy, A.R.: On extended fuzzy relational database model with proximity relations. Fuzzy Sets and Systems 117, 195–201 (2001)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Quinlan, J.: Induction of decision trees. Machine Learning 1(1), 81–106 (1986)Google Scholar
  11. 11.
    Han, J., Kamber, M.: Data Mining: Concepts and Techniques. Morgan Kaufmann, New York (2000)Google Scholar
  12. 12.
    Quinlan, J.: Simplifying decision trees. International Journal of Man-Machine Studies 27, 221–234 (1987)CrossRefGoogle Scholar
  13. 13.
    Quinlan, J.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)Google Scholar
  14. 14.
    Shannon, C.E.: A Mathematical Theory of Communication. Bell System Technical Journal 27, 379–423, 623-656 (1948)MATHMathSciNetGoogle Scholar
  15. 15.
    Angryk, R., Petry, F.: Discovery of Abstract Knowledge from Non-Atomic Attribute Values in Fuzzy Relational Databases. In: Modern Information Processing, From Theory to Applications, pp. 171–182. Elsevier, Amsterdam (2006)Google Scholar
  16. 16.
    Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques, June 2005. Morgan Kaufmann, San Francisco (2005)MATHGoogle Scholar
  17. 17.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach. Prentice-Hall, Englewood Cliffs (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rafal A. Angryk
    • 1
  1. 1.Department of Computer ScienceMontana State UniversityBozemanUSA

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