| Rough set theory, first introduced by Zdzislaw Pawlak in 1982, is a new mathe-matical approach to deal with vague concepts and incomplete information. Using the concepts of lower and upper approximations in rough set theory, it is possible to find a reduct of the original attributes contained in databases, as well as to obtain the de-cision rules from the knowledge hidden in information systems. Nowadays, rough set theory has been used successfully in the area of artificial intelligence, machine learning, knowledge discovery, decision analysis, data mining, etc.Rough set theory is mainly concerned with the coarseness of the information. Fuzzy set theory, on the other hand, offers a variety of techniques for analyzing imprecise data. They are distinct and complementary generalizations of classical set theory for modeling vagueness and uncertainty. Therefore, it seems natural to combine these two theories to construct a reinforced hybrid method to process the uncertain knowledge. In the recent years, numerous papers have been published that discuss the relationships between fuzzy set and rough set, and with the possibility of combining them.In practice, the attributes of the data can be presented in linguistic terms, that will usually have a fuzzy nature. So there is a need to improve its performance by extending the classical rough set approach to the fuzzy environment. Also, the condition of an equivalence relation is too stringent to limits the application domain of the theory. One generalization approach is to consider a similarity relation, even a fuzzy relation, rather than the equivalence relation used in the traditional rough set. The results of these studies lead to the introduction of fuzzy rough set.Essentially, fuzzy rough set is still a rough set, which is the extension of rough set in the fuzzy environment. Also we can say that the fuzzy rough set is the fuzzy generalization of rough set theory, or the development of the rough set theory based on the fuzzy logic.A rough set model has three elements:the universe U, the crisp set X, the equiva-lence relation R, and there are three ways to extend the rough set model:generalizing to two universities, extending to fuzzy set, bringing in fuzzy relation.The concept of fuzzy rough sets was initially proposed by Dubois and Prade (1990). By extending the crisp set X to the fuzzy set F, Dubois and Prade defined the notion of rough fuzzy set (a special case of fuzzy rough sets), and fuzzy rough set with respect to the fuzzy relation R.Up to now, the most distinguish studies were made by Radzikowska and Kerre (2002). They defined a broad family of fuzzy rough sets, each one of which, called an (T, I)-fuzzy rough set, is determined by an implicator I and a triangular norm T.It is a new idea to discuss the fuzzy rough model on two universes. In this circum-stances, the lower/upper approximation of a fuzzy set is a fuzzy set in another universe. This research is initially proposed by Wu (2003) and MI (2004).Research in this thesis aims to find some novel approaches to extend the existing models of fuzzy rough sets, especially based on the non-classical fuzzy set, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets. The first chapter outlines the basic ideas of rough set and fuzzy theory and proposes a survey on the research of fuzzy rough set theory. The focus of the second chapter is to generalize the Radzikowska-Kerre definition and to present a more general model of fuzzy rough sets, called (⊥,(?))-fuzzy rough sets, based on fuzzy logical operators and two universes. In the third chapter, we rebuild the rough set on the interval-valued fuzzy set, and propose a new type of interval-valued fuzzy rough set based on fuzzy coverings. By introducing the interval-valued fuzzy logical operators into the fuzzy rough set model, the fourth chapter is to construct a more general new model named as interval-valued intuitionistic fuzzy rough sets. In the fifth chapter, in order to investigate the character of household income segregation, we apply the fuzzy rough theory to get the decision rules and improve the performance of Schelling's Segregation Model. The last chapter concludes this thesis.
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