Set Operations for L-Fuzzy Sets

  • Jouni Järvinen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4585)


In this paper, we introduce the operations of union, intersection, and complement for preorder-based fuzzy sets. The given operations are even capable of dealing with fuzzy sets that have membership degrees coming from different preordered sets. This enables us to handle the difficult situation in which one has different people giving judgements and they all like to use their own language and expressions.


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  1. 1.
    Birkhoff, G.: Lattice Theory, Colloquim publications, 3rd edn. vol. XXV, American Mathematical Society (AMS), Providence, Rhode Island (1995)Google Scholar
  2. 2.
    Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)MATHGoogle Scholar
  3. 3.
    Goguen, J.A.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18, 145–174 (1967)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Järvinen, J.: Lattice theory for rough sets. In: Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Järvinen, J., Kortelainen, J.: A unifying study between modal-like operators, topologies, and fuzzy sets. Fuzzy Sets and Systems 158, 1217–1225 (2007)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kortelainen, J.: On relationship between modified sets, topological spaces and rough sets. Fuzzy Sets and Systems 61, 91–95 (1994)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Lowen, R.: Fuzzy Set Theory: Basic Concepts, Techniques and Bibliography. Kluwer Academic Publishers, Norwell, MA (1996)MATHGoogle Scholar
  8. 8.
    Steiner, A.K.: The lattice of topologies: structure and complementation. Transactions of the American Mathematical Society 122, 379–398 (1966)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Zadeh, L.A.: From computing with numbers to computing with words – from manipulation of measurements to manipulation of perceptions. International Journal of Applied Mathematics and Computer Science 12, 307–324 (2002)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jouni Järvinen
    • 1
  1. 1.Turku Centre for Computer Science (TUCS), FI-20014 University of TurkuFinland

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