On generalized intuitionistic fuzzy rough approximation operators

  • Authors:

  • Lei Zhou;Wei-Zhi Wu

  • 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, Zhoushan, Zhejiang 316004, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak's rough approximations have been made in the literature over the years. This paper proposes a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper intuitionistic fuzzy rough approximation operators induced from an arbitrary intuitionistic fuzzy relation are defined. Basic properties of the intuitionistic fuzzy rough approximation operators are then examined. By introducing cut sets of intuitionistic fuzzy sets, classical representations of intuitionistic fuzzy rough approximation operators are presented. The connections between special intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are further established. Finally, an operator-oriented characterization of intuitionistic fuzzy rough sets is proposed, that is, intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of intuitionistic fuzzy relations which produce the same operators.