Generalized fuzzy rough approximation operators determined by fuzzy implicators

  • Authors:

  • Wei-Zhi Wu;Yee Leung;Ming-Wen Shao

  • Affiliations:

  • School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316004, PR China;Department of Geography and Resource Management, The Chinese University of Hong Kong, Hong Kong and Institute of Environment, Energy and Sustainability, The Chinese University of Hong Kong, Hong K ...;Computer Engineering Institute, Qingdao Technological University, Qingdao, Shandong 266520, PR China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2013

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Abstract

In this paper, a general framework for the study of dual fuzzy rough approximation operators determined by a fuzzy implication operator I in infinite universes of discourse is investigated. Lower and upper approximations of fuzzy sets with respect to a fuzzy approximation space in infinite universes of discourse are first introduced. Properties of I-fuzzy rough approximation operators are then examined. An operator-oriented characterization of fuzzy rough sets is further proposed, that is, I-fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper I-fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators. Finally, a comparative study of I-fuzzy rough sets with fuzzy topological spaces is presented. It is proved that there exists a one-to-one correspondence between the set of all reflexive and T-transitive fuzzy approximation spaces and the set of all fuzzy Alexandrov spaces such that the lower and upper I-fuzzy rough approximation operators in a fuzzy approximation space are, respectively, the fuzzy interior and closure operators in a fuzzy topological space.