Qualitative approximations of fuzzy sets and non-classical three-valued logics (II)

  • Authors:

  • Xiaohong Zhang;Yiyu Yao;Yan Zhao

  • Affiliations:

  • Department of Mathematics, Ningbo University, Ningbo, Zhejiang Province, P.R. China;Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada;Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada

  • Venue:
  • RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
  • Year:
  • 2010

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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.