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Abstract
Rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. This paper presents an interval-valued rough intuitionistic fuzzy (IF) set model by means of integrating the classical Pawlak rough set theory with the interval-valued IF set theory. In this paper, we first introduce some concepts and properties of interval-valued IF set theory. Then, the rough approximations of an interval-valued IF set in the classical Pawlak approximation space and the generalised Pawlak approximation space are respectively defined, and some fundamental properties of the approximation operators are studied. Furthermore, by employing cut sets of interval-valued IF sets, classical representations of interval-valued rough IF approximation operators are presented, and the connections between special binary relations and interval-valued rough IF approximation operators are constructed. Finally, we discuss the knowledge reduction and knowledge discovery of the interval-valued IF information systems.
Acknowledgements
The author would like to thank the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 60773062), the Natural Science Foundation of Hebei Province of China (Grant No. 2008000633), the Key Scientific Research Project of Department of Education of Hebei Province of China (Grant No. 2005001D) and the Key Scientific and Technical Research Project of Ministry of Education of China (Grant No. 206012).