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Qualitative Approximations of Fuzzy Sets and Non-classical Three-Valued Logics (II)

  • Xiaohong Zhang
  • Yiyu Yao
  • Yan Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6401)

Abstract

(α,β)-qualitative approximations of fuzzy sets are studied by using a pair of subsets defined by an α-cut and a strong β-cut. This setting naturally leads to three disjoint regions and an analysis based on a three-valued logic. This study combines both an algebra view and a logic view. From the algebra view, the mathematical definition of an (α,β)-approximation of fuzzy sets is given, and algebraic operations based on various t-norms and fuzzy implications are established. From the logic view, two non-classical three-valued logics are introduced. Corresponding to these new non-classical three-valued logics, the related origins of t-norms and fuzzy implications are examined.

Keywords

Fuzzy set (α and β)-approximation non-truth functional logic three-valued logic 

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References

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    Wasilewska, A.: An Introduction to Classical and Non-Classical Logics. Suny, Stony Brook (2007)Google Scholar
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    Yao, Y.Y.: Crisp set approximations of fuzzy sets: a decision-theoretic rough sets perspective. Fuzzy Sets and systems (2008)Google Scholar
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    Zhang, X.H.: Fuzzy Logics and Algebraic Analysis. Science Press, Beijing (2008)Google Scholar
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    Zhang, X., Yao, Y., Zhao, Y.: Qualitative Approximations of Fuzzy Sets and Non-classical Three-Valued Logics (I). In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS(LNAI), vol. 6401, pp. 195–203. Springer, Heidelberg (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Xiaohong Zhang
    • 1
  • Yiyu Yao
    • 2
  • Yan Zhao
    • 2
  1. 1.Department of MathematicsNingbo UniversityNingboP.R. China
  2. 2.Department of Computer ScienceUniversity of ReginaReginaCanada

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