On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators

  • Authors:

  • Lei Zhou;Wei-Zhi Wu;Wen-Xiu Zhang

  • Affiliations:

  • Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi 710049, PR China and School of Mathematics, Physics and Information Science, Zhejiang ...;School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Wenhua RD. 105, Zhoushan, Zhejiang 316004, PR China;Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi 710049, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

This paper presents a general framework for the study of relation-based (I,T)-intuitionistic fuzzy rough sets by using constructive and axiomatic approaches. In the constructive approach, by employing an intuitionistic fuzzy implicator I and an intuitionistic fuzzy triangle norm T, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of (I,T)-intuitionistic fuzzy rough approximation operators are examined. The connections between special types of intuitionistic fuzzy relations and properties of intuitionistic fuzzy approximation operators are established. In the axiomatic approach, an operator-oriented characterization of (I,T)-intuitionistic fuzzy rough sets is proposed. Different axiom sets characterizing the essential properties of intuitionistic fuzzy approximation operators associated with various intuitionistic fuzzy relations are explored.