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

  • 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

(0, 1)-Qualitative approximations of fuzzy sets are studied by using the core and support of a fuzzy set. 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 a (0, 1)-approximation of fuzzy sets are given, and algebraic operations based on various t- norms and fuzzy implications are established. From the logic view, a non-classical three-valued logic is introduced. Corresponding to this new non-classical three-valued logic, the related origins of t-norms and fuzzy implications are examined.