Multisets and Fuzzy Multisets

  • Sadaaki Miyamoto
Part of the Computer Science Workbench book series (WORKBENCH)


Multisets, also called bags, are relatively unknown to researchers, partly because it has weaker mathematical properties and has been considered that applications are relatively limited.


Fuzzy Number Membership Degree Fuzzy Relation Possibility Distribution Structure Query Language 
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]
    J.-P. Banatre and D. Le Metayer, “Programming by multiset transformation,” Comm. ACM, Vol. 36, No.1, pp. 98–111, 1993.CrossRefGoogle Scholar
  2. [2]
    W. D. Blizard, “Multiset theory,” Notre Dame Journal of Formal logic, Vol. 30, No.1, pp. 36–66, 1989.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    P. Bosc, “Some approaches for processing SQLf nested queries,” International Journal of Intelligent Systems, Vol. 11, No.9, 613–632, 1996.CrossRefGoogle Scholar
  4. [4]
    J. Celko, Joe Celko’s SQL for Smarties: Advanced SQL Programming, Morgan Kaufmann, 1995.Google Scholar
  5. [5]
    D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum, New York, 1988.MATHGoogle Scholar
  6. [6]
    K. S. Kim and S. Miyamoto, Application of fuzzy multisets to fuzzy database systems, Proc. of 1996 Asian Fuzzy Systems Symposium, Dec. 11-14, 1996, Kenting, Taiwan, R.O.C. pp. 115–120, 1996.Google Scholar
  7. [7]
    D. E. Knuth, The Art of Computer Programming, Vol.2/ Seminumerical Algorithms, Addison-Wesley, Reading, Massachusetts, 1969.MATHGoogle Scholar
  8. [8]
    A. Klausner and N. Goodman, Multirelations-semantics and languages, Proc. VLDB85, Aug. 21-23, Stockholm, pp. 251–258, 1985.Google Scholar
  9. [9]
    R. Kruse, J. Gebhardt, and F. Klawonn, Foundations of Fuzzy Systems, Wiley, Chichester, 1994.Google Scholar
  10. [10]
    B. Li, W. Peizhang, and L. Xihui, Fuzzy bags with set-valued statistics, Comput. Math. Applic., Vol. 15, pp. 811–818, 1988.Google Scholar
  11. [11]
    B. Li, Fuzzy bags and applications, Fuzzy Sets and Systems, Vol. 34, pp. 61–71, 1990.CrossRefMATHGoogle Scholar
  12. [12]
    L. Libkin and L. Wong, Query languages for bags and aggregate functions, J. Comput. Sys. Sci., Vol. 55, pp. 241–272, 1997.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    S. MacLane and G. Birkoff, Algebra, 2nd ed, Macmillan, New York, 1979.Google Scholar
  14. [14]
    Z. Manna and R. Waldinger, The Logical Basis for Computer Programming, Vol. 1: Deductive Reasoning, Addison-Wesley, Reading, Massachusetts, 1985.Google Scholar
  15. [15]
    S. Miyamoto, Fuzzy Sets in Information Retrieval and Cluster Analysis, Kluwer Academic Publishers, Dordrecht, 1990.MATHGoogle Scholar
  16. [16]
    Z. Pawlak, Rough Sets, Kluwer, Dordrecht, 1991.MATHGoogle Scholar
  17. [17]
    Z. Pawlak, Hard and soft sets, In: W. Ziarko (ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Proceedings of the International Workshop on Rough Sets and Knowledge Discovery (RSKD’93), Banff, Alberta, Canada, October 12-15, Springer-Verlag, Berlin, pp. 130–135, 1993.Google Scholar
  18. [18]
    T. Radecki, Level fuzzy sets, J. of Cybernetics, Vol. 7, pp. 189–198, 1977.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    A. Rebai, Canonical fuzzy bags and bag fuzzy measures as a basis for MADM with mixed non cardinal data, European J. of Operational Res., Vol. 78, pp. 34–48, 1994.CrossRefMATHGoogle Scholar
  20. [20]
    A. Rebai and J.-M. Martel, A fuzzy bag approach to choosing the “best” multiattributed potential actions in a multiple judgement and non cardinal data context, Fuzzy Sets and Systems, Vol. 87, pp. 159–166, 1997.MathSciNetCrossRefGoogle Scholar
  21. [21]
    A. Ramer and C.-C. Wang, Fuzzy multisets, Proc. of 1996 Asian Fuzzy Systems Symposium, Dec. 11-14, 1996, Kenting, Taiwan, R.O.C., pp. 429–434, 1996.Google Scholar
  22. [22]
    J. D. Ullman, Principles of Database and Knowledge-Base Systems: Vol. 1, Computer Science Press, Rockville, Maryland, 1988.Google Scholar
  23. [23]
    R. R. Yager, On the theory of bags, Int. J. General Systems, Vol. 13, pp. 23–37, 1986.MathSciNetCrossRefGoogle Scholar
  24. [24]
    R. R. Yager, Cardinality of fuzzy sets via bags, Mathl. Modelling, Vol. 9, pp. 441–446, 1987.MathSciNetCrossRefMATHGoogle Scholar

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© Springer-Verlag Tokyo 2000

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  • Sadaaki Miyamoto

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