On Intuitionistic Fuzzy Rough Sets

A new type of intuitionistic fuzzy rough set is introduced by extending the definition of fuzzy rough sets proposed by A. Nakamura, into the intuitionists fuzzy context and it is proved that they coincide with Pawlak's rough set approximations in the crisp case.

Abstract

Rough set theory, fuzzy set theory and Intuitionistic fuzzy set theory deal with sets having imprecise boundaries. The contemporary concern about unravelling hidden knowledge from imperfect data and incomplete information systems has lead to many hybrid theories which combine rough set theory with fuzzy set theory and intuitionistic fuzzy set theory. In this paper, a new type of intuitionistic fuzzy rough set is introduced by extending the definition of fuzzy rough sets proposed by A. Nakamura, into the intuitionistic fuzzy context. The properties of these approximations are explored. A decomposition theorem for the proposed intuitionistic fuzzy rough lower and upper approximations is presented. Further, it is proved that they coincide with Pawlak's rough set approximations in the crisp case.