Abstract
The Rough set theory is a very successful tool to deal with vague, inconsistent, imprecise and uncertain knowledge. In recent years, rough set theory and its applications have drawn many researchers' interest progressively in one of its hot issues, viz. the field of artificial intelligence. An intuitionistic fuzzy (IF) set, which is a generalization of fuzzy set, has more practical and flexible real-world proficiency to characterize a complex information and provide a better glimpse to confront uncertainty and ambiguity when compared with those of the fuzzy set. Moreover, rough sets and intuitionistic fuzzy sets deal with the specific aspects of the same problem & imprecision, and their combination IF rough set has been studied by many researchers in the past few years. The present chapter deals with a review of IF rough set theory, their basic concepts, properties, topological structures, logic operators, approximation operators and similarity relations on the basis of axiomatic and constructive approaches. The characterization of IF rough sets based on various operators, similarity relations, distances, IF cut sets, IF coverings and inclusion degrees is also discussed. Moreover, several extensions of IF rough sets and their hybridization with other extended rough set theories are thoroughly surveyed. The applications of IF rough sets in different real-world problems are also discussed in detail.
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