Conference Paper

Intuitionistic Fuzzy Approximations and Intuitionistic Fuzzy Sigma-Algebras.

DOI: 10.1007/978-3-540-79721-0_50 Conference: Rough Sets and Knowledge Technology, Third International Conference, RSKT 2008, Chengdu, China, May 17-19, 2008. Proceedings
Source: DBLP

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.

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