Advertisement

Fuzzy Subsets

  • John N. Mordeson
  • Premchand S. Nair
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 46)

Abstract

In 1965, Lofti Zadeh published his seminal paper “Fuzzy Sets” [11] which described fuzzy set theory and consequently fuzzy logic. The purpose of Zadeh’s paper was to develop a theory which could deal with ambiguity and imprecision of certain classes or sets in human thinking, particularly in the domains of pattern recognition, communication of information, and abstraction. This theory proposed making the grade of membership of an element in a subset of a universal set a value in the closed interval [0,1] of real numbers.

Keywords

Equivalence Relation Similarity Relation Fuzzy Subset Fuzzy Relation Fuzzy Graph 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications, Mathematics in Science and Engineering, Vol. 144, Academic Press, Inc., Orlando, Florida, 1980.Google Scholar
  2. 2.
    Kandel, A., Fuzzy Mathematical Techniques with Applications, Addison-Wesley Pub. Co. 1986.MATHGoogle Scholar
  3. 4.
    Klir, G.J., U. St. Clair, U.H., and Yuan, B., Fuzzy Set Theory, Foundations and Applications, Prentice Hall, Upper Saddle River, N.J., 1997.Google Scholar
  4. 5.
    Klir, G.J. and Folger, T.A., Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, N.J., 1988.MATHGoogle Scholar
  5. 6.
    Klir, G.J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, N.J., 1995.MATHGoogle Scholar
  6. 7.
    Mordeson, J. N. and Nair, P.S., Fuzzy Mathematics: An Introduction for Engineers and Scientists, Studies in Fuzziness and Soft Computing, Physica-Verlag, Heidelberg, Germany, 1998.Google Scholar
  7. 8.
    Rosenfeld, A., Fuzzy graphs. In: L. A. Zadeh, K. S. Fu and M. Shimura, Eds., Fuzzy Sets and Their Applications, Academic Press, New York, 77–95, 1975.Google Scholar
  8. 9.
    Tamura, S., Higuchi, S., and Tanaka, K., Pattern Classification Based on Fuzzy Relations, IEEE Trans. SMC-1, 61–66, 1971.Google Scholar
  9. 10.
    Yeh, R. T. and Bang, S.Y., Fuzzy graphs, fuzzy relations, and their applications to cluster analysis. In: Zadeh, L. A., K. S. Fu and M. Shimura, Eds., Fuzzy Sets and Their Applications, Academic Press, New York, 125–149, 1975.Google Scholar
  10. 11.
    Zadeh, L. A., Fuzzy sets, Inform. and Control, 8: 338–353, 1965.MathSciNetMATHCrossRefGoogle Scholar
  11. 12.
    Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1: 3–28, 1978.MathSciNetMATHCrossRefGoogle Scholar
  12. 13.
    Zadeh, L.A., Similarity relations and fuzzy orderings, Inform. Sci., 3: 177–200, 1971.MathSciNetMATHCrossRefGoogle Scholar
  13. 14.
    Zimmermann, H.J., Fuzzy Set Theory and Its Applications, Second Edition, Kluwer Academic Publishers, Boston, Dordrecht/London, 1991.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • John N. Mordeson
    • 1
  • Premchand S. Nair
    • 2
  1. 1.Center for Research in Fuzzy Mathematics and Computer ScienceOmahaUSA
  2. 2.Department of Mathematics and Computer ScienceCreighton UniversityOmahaUSA

Personalised recommendations