Algebraic analysis of fuzzy indiscernibility

  • Jian-Ming Gao
  • Akira Nakamura
3. Fuzzy Sets
Part of the Lecture Notes in Computer Science book series (LNCS, volume 521)


First, this paper investigates a model of the database with fuzzy information and generalizes a class of fuzzy indiscernibility relations from the model. Next, this paper is focused on algebraic analysis of the fuzzy indiscernibility, i.e., defining an algebraic structure based on the fuzzy indiscernibility; showing the representation theorem and the center of a given algebra.


Fuzzy information system fuzzy indiscernibility representation theorem algebra of fuzzy indiscernibility center of an algbra 


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  1. [1]
    S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, 1980.Google Scholar
  2. [2]
    D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, 1980.Google Scholar
  3. [3]
    D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, Proceedings of Intern. Conf. Fuzzy Set in Informatics, Moscow, (1988)20–23.Google Scholar
  4. [4]
    L. Farinas del Cerro and H. Prade, Rough sets, twofold fuzzy sets and modal logic. Fuzziness in indiscernibility and partial information, The Mathematics of Fuzzy Systems, edited by A. D. Nola etc., Verlag TUV Rheinland, 1986.Google Scholar
  5. [5]
    R. Giles, Lukasiewicz logic and fuzzy sets, International J. on Man-Machine Studies, Vol.8, (1976) 313–327.Google Scholar
  6. [6]
    A. Nakamura, Fuzzy rough sets, Note on Multiple-Valued Logic in Japan, Vol.9, No.8, 1988.Google Scholar
  7. [7]
    A. Nakamura and J.M. Gao, A logic for fuzzy data analysis, to appear in Fuzzy Sets and Systems.Google Scholar
  8. [8]
    C. V. Negoita and D. A. Ralescu, Representation theorems for fuzzy concepts, Kybernetes, Vol.4 (1975)169–174.Google Scholar
  9. [9]
    Z. Pawlak, Information systems-theoretical foundations, Information Systems 6, (1981)205–218.CrossRefGoogle Scholar
  10. [10]
    L. A. Zadeh, Similarity relations and fuzzy orderings, Information Sciences 3 (1971)177–200.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jian-Ming Gao
    • 1
  • Akira Nakamura
    • 1
  1. 1.Department of Applied MathematicsHiroshima UniversityHigashi-HiroshimaJapan

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