Intuitionistic fuzzy approximations and intuitionistic fuzzy sigma-algebras

Authors:
Wei-Zhi Wu;Lei Zhou
Affiliations:
School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, P.R. China;Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi, P.R. China
Venue:
RSKT'08 Proceedings of the 3rd international conference on Rough sets and knowledge technology
Year:
2008

Citing 3
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L-intuitionistic fuzzy σ-algebras

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Abstract

In this paper, concepts of intuitionistic fuzzy measurable spaces and intuitionistic fuzzy σ-algebras are first introduced. Relationships between intuitionistic fuzzy rough approximations and intuitionistic fuzzy measurable spaces are then discussed. It is proved that the family of all intuitionistic fuzzy definable sets induced from an intuitionistic fuzzy serial approximation space forms an intuitionistic fuzzy σ-algebra. Conversely, for an intuitionistic fuzzy σ-algebra generated by a crisp algebra in a finite universe, there must exist an approximation space such that the family of all intuitionistic fuzzy definable sets is the class of all measurable sets in the given intuitionistic fuzzy measurable space.