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Cybernetics and Systems Analysis

, Volume 44, Issue 3, pp 333–340 | Cite as

Set coverings and tolerance relations

  • S. N. Gerasin
  • V. V. Shlyakhov
  • S. V. Yakovlev
Article

Abstract

Properties of tolerance relations and tolerance classes are studied. Tolerance classes are demonstrated to form carrier set coverings. The conditions are proved under which tolerance and equivalence classes coincide.

Keywords

tolerance relation adjacent classes and preclasses set covering functional relation 

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References

  1. 1.
    E. Zieman and O. B’yuneman, “Tolerant Spaces and Brain,” in: Na Puti k Teoreticheskoi Biologii, Mir, Moscow (1970), pp. 52–68.Google Scholar
  2. 2.
    Yu. A. Shreider, Equality, Similarity, and Order [in Russian], Mir, Moscow (1971).Google Scholar
  3. 3.
    Yu. A. Shreider, “Tolerance spaces,” Cybernetics, No. 2, 124–128 (1970).Google Scholar
  4. 4.
    S. M. Yakubovich, “Axiomatic similarity theory,” NTI, Ser. 2, No. 10, 15–19 (1968).Google Scholar
  5. 5.
    S. N. Gerasin, E. V. Sklyar, and V. V. Shlyakhov, “A property of tolerance relation,” Dop. NAN Ukr., No. 12, 58–62 (2003).Google Scholar
  6. 6.
    A. I. Maltsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).Google Scholar
  7. 7.
    V. P. Mashtalir, V. V. Shlyakhov, and S. V. Yakovlev, “Properties of multivalued mappings in recognition problems,” Dop. NAN Ukr., No. 12, 72–76 (2000).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • S. N. Gerasin
    • 1
  • V. V. Shlyakhov
    • 1
  • S. V. Yakovlev
    • 2
  1. 1.Kharkov National University of RadioelectronicsKharkovUkraine
  2. 2.Kharkov National University of Internal AffairsKharkovUkraine

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