Fuzzy Multisets and Their Generalizations

  • Sadaaki Miyamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2235)


Fuzzymultisets with infinitemembership sequences and their generalization using set-valued memberships are considered. Two metric spaces of the infinite fuzzy multisets are defined in terms of cardinality. One is the completion of fuzzy multisets of finite membership sequences; the other is derived from operations among fuzzy multisets and realvalued multisets. Theoretical properties of these infinite fuzzy multisets are discussed.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W.D. Blizard, Multiset theory, Notre Dame Journal of Formal logic, Vol. 30, No. 1,pp. 36–66, 1989.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    W.D. Blizard, Real-valued multisets and fuzzy sets, Fuzzy Sets and Systems,Vol. 33, pp. 77–97, 1989.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    B. Li, W. Peizhang, L. Xihui, Fuzzy bags with set-valued statistics, Comput. Math.Applic., Vol. 15, pp. 811–818, 1988.CrossRefGoogle Scholar
  4. 4.
    K.S. Kim and S. Miyamoto, Application of fuzzy multisets to fuzzy database systems,Proc. of 1996Asian Fuzzy Systems Symposium, Dec. 11–14, 1996, Kenting,Taiwan, R.O.C. pp. 115–120, 1996.Google Scholar
  5. 5.
    D.E. Knuth, The Art of Computer Programming, Vol.2 / Seminumerical Algorithms,Addison-Wesley, Reading, Massachusetts, 1969.MATHGoogle Scholar
  6. 6.
    Z.-Q. Liu, S. Miyamoto (Eds.), Soft Computing and Human-Centered Machines,Springer, Tokyo, 2000.Google Scholar
  7. 7.
    Z. Manna and R. Waldinger, The Logical Basis for Computer Programming, Vol.1: Deductive Reasoning, Addison-Wesley, Reading, Massachusetts, 1985.Google Scholar
  8. 8.
    S. Miyamoto, Fuzzy multisets with infinite collections of memberships, Proc. ofthe 7th International Fuzzy Systems Association World Congress (IFSA’97), June25–30, 1997, Prague, Chech, Vol.1, pp.61–66, 1997.Google Scholar
  9. 9.
    S. Miyamoto, K.S. Kim, An image of fuzzy multisets by one variable function andits application, J. of Japan Society for Fuzzy Theory and Systems, Vol. 10, No. 1,pp. 157–167, 1998 (in Japanese).Google Scholar
  10. 10.
    S. Miyamoto, K.S. Kim, Multiset-valued images of fuzzy sets, Proceedings of theThird Asian Fuzzy Systems Symposium, June 18–21, 1998, Masan, Korea, pp.543–548.Google Scholar
  11. 11.
    S. Miyamoto, Rough sets and multisets in a model of information retrieval, inF. Crestani and G. Pasi, eds., Soft Computing in Information Retrieval: Techniquesand Applications, Springer, pp. 373–393, 2000.Google Scholar
  12. 12.
    Z. Pawlak, Rough Sets, Kluwer, Dordrecht, 1991.Google Scholar
  13. 13.
    A. Ramer, C.-C. Wang, Fuzzy multisets, Proc. of 1996Asian Fuzzy Systems Symposium,Dec. 11–14, 1996, Kenting, Taiwan, pp. 429–434.Google Scholar
  14. 14.
    A. Rebai, Canonical fuzzy bags and bag fuzzy measures as a basis for MADM withmixed non cardinal data, European J. of Operational Res., Vol. 78, pp. 34–48, 1994.MATHCrossRefGoogle Scholar
  15. 15.
    A. Rebai, J.-M. Martel, A fuzzy bag approach to choosing the “best” multiattributedpotential actions in a multiple judgement and non cardinal data context,Fuzzy Sets and Systems, Vol. 87, pp. 159–166, 1997.CrossRefMathSciNetGoogle Scholar
  16. 16.
    R.R. Yager, On the theory of bags, Int. J. General Systems, Vol. 13, pp. 23–37,1986.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Sadaaki Miyamoto
    • 1
  1. 1.Institute of Engineering Mechnics and SystemsUniversity of TsukubaIbarakiJapan

Personalised recommendations