Multisets and Fuzzy Multisets as a Framework of Information Systems

  • Sadaaki Miyamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3131)


Multisets are now a common tool and a fundamental framework in information processing. Their generalization to fuzzy multisets has also been studied. In this paper the basics of multisets and fuzzy multisets are reviewed, fundamental properties of fuzzy multisets are proved, and advanced operations are defined. Applications to rough sets, fuzzy data retrieval, and automatic classification are moreover considered.


Information Retrieval Near Neighbor Extension Principle Cardinal Data Fuzzy Database 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)zbMATHGoogle Scholar
  2. 2.
    Blizard, W.D.: Multiset theory. Notre Dame Journal of Formal logic 30(1), 36–66 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. General Systems 17, 191–209 (1990)zbMATHCrossRefGoogle Scholar
  4. 4.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley, New York (2001)zbMATHGoogle Scholar
  5. 5.
    Calude, C.S., P˘aun, G., Rozenberg, G., Salomaa, A. (eds.): Multiset Processing. LNCS, vol. 2235, pp. 225–235. Springer, Heidelberg (2001)zbMATHCrossRefGoogle Scholar
  6. 6.
  7. 7.
    Li, B., Peizhang, W., Xihui, L.: Fuzzy bags with set-valued statistics. Comput. Math. Applic. 15, 811–818 (1988)CrossRefGoogle Scholar
  8. 8.
    Kim, K.S., Miyamoto, S.: Application of fuzzy multisets to fuzzy database systems. In: Proc. of 1996 Asian Fuzzy Systems Symposium, Kenting, Taiwan, R.O.C, December 11–14, pp. 115–120 (1996)Google Scholar
  9. 9.
    Knuth, D.E.: The Art of Computer Programming, Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1969)Google Scholar
  10. 10.
    Liu, Z.Q., Miyamoto, S. (eds.): Soft Computing and Human-Centered Machines. Springer, Heidelberg (2000)Google Scholar
  11. 11.
    Manna, Z., Waldinger, R.: The Logical Basis for Computer Programming, Deductive Reasoning, vol. 1. Addison-Wesley, Reading (1985)Google Scholar
  12. 12.
    Miyamoto, S.: Fuzzy Sets in Information Retrieval and Cluster Analysis. Kluwer Academic Publishers, Dordrecht (1990)Google Scholar
  13. 13.
    Miyamoto, S.: Information retrieval based on fuzzy associations. Fuzzy Sets and Systems 39, 191–205 (1990)CrossRefGoogle Scholar
  14. 14.
    Miyamoto, S.: Fuzzy multisets with infinite collections of memberships. In: Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA 1997), Prague, Chech, June 25-30, vol. 1, pp. 61–66 (1997)Google Scholar
  15. 15.
    Miyamoto, S., Kim, K.S.: An image of fuzzy multisets by one variable function and its application. J. of Japan Society for Fuzzy Theory and Systems 10(1), 157–167 (1998) (in Japanese)Google Scholar
  16. 16.
    Miyamoto, S., Kim, K.S.: Multiset-valued images of fuzzy sets. In: Proceedings of the Third Asian Fuzzy Systems Symposium, Masan, Korea, June 18-21, pp. 543–548 (1998)Google Scholar
  17. 17.
    Miyamoto, S.: Application of rough sets to information retrieval. Journal of the American Society for Information Science 47(3), 195–205 (1998)CrossRefGoogle Scholar
  18. 18.
    Miyamoto, S.: Fuzzy multisets and their generalizations. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 225–235. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Miyamoto, S.: Information clustering based on fuzzy multisets. Information Processing and Management 39(2), 195–213 (2003)zbMATHCrossRefGoogle Scholar
  20. 20.
    Mizutani, K., Miyamoto, S.: Fuzzy multiset model for information retrieval and clustering using a kernel function. In: Zhong, N., Raś, Z.W., Tsumoto, S., Suzuki, E. (eds.) ISMIS 2003. LNCS (LNAI), vol. 2871, pp. 417–421. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  21. 21.
    Pawlak, Z.: Rough Sets . Kluwer, Dordrecht (1991)Google Scholar
  22. 22.
    Petry, F.E.: Fuzzy Databases: Principles and Applications . Kluwer, Boston (1996)Google Scholar
  23. 23.
    Ramer, A., Wang, C.C.: Fuzzy multisets. In: Proc. of 1996 Asian Fuzzy Systems Symposium, Kenting, Taiwan, December 11-14, pp. 429–434 (1996)Google Scholar
  24. 24.
    Rebai, A.: Rebai, Canonical fuzzy bags and bag fuzzy measures as a basis for MADM with mixed non cardinal data. European J. of Operational Res. 78, 34–48 (1994)zbMATHCrossRefGoogle Scholar
  25. 25.
    Rebai, A., Martel, J.M.: A fuzzy bag approach to choosing the “best” multiattributed potential actions in a multiple judgement and non cardinal data context. Fuzzy Sets and Systems 87, 159–166 (1997)CrossRefMathSciNetGoogle Scholar
  26. 26.
    van Rijsbergen, C.J.: Information Retrieval, 2nd edn., Butterworth, London (1979)Google Scholar
  27. 27.
    Vapnik, V.: Statistical Learning Theory .Wiley, New York (1998)Google Scholar
  28. 28.
    Yager, R.R.: On the theory of bags. Int. J. General Systems 13, 23–37 (1986)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sadaaki Miyamoto
    • 1
  1. 1.Department of Risk Engineering, School of Systems and Information EngineeringUniversity of TsukubaIbarakiJapan

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