Constructive Research Of Generalized Rough Approximation Operators On Interval-Valued Fuzzy Set

This dissertation comes from"The Nature Science Foundation of Henan Province"Research on Theories of Flexibility of Interval Logic"(NO.0611053900) and"The Key Scientific and Technological Project of Henan Province"Research on Flexible Control Model and its System based on Interval Structure"(NO.092102210149).Pawlak's Rough set model is a powerful mathematical tool for dealing with imprecise, uncertainty, incompleteness and vagueness of knowledge in information systems, and the extension of classical rough set theory is an important subject of studying rough set. Fuzzy rough set is put forward by Dubios and Prade in 1992, which carries out the amalgamation between fuzzy set theory and rough set theory. Furthermore, an equivalence relation is a key and primitive notion in Pawlak's rough set model. This equivalence relation, however, seems to be a very stringent condition that may limit the application domain of the rough set model. To solve this problem, several authors have generalized the notion of approximation operators by using nonequivalence binary relations. The most important of them is rough set theory based on generalized binary relation discussed by Yao et al. recently, professor Wu and Mi have defined the generalized fuzzy rough set theory based on the studying of fuzzy rough set theory and generalized rough set theory.Most researches on fuzzy rough set theory concentrate on point-valued fuzzy sets and point-valued fuzzy binary relations. But describing inkling by point-valued may lose some available information in the real-life information systems sometimes, and if describing by interval-valued, we may acquire a better impact than by point-valued. This paper carries out an amalgamation between interval-valued fuzzy set and generalized rough set theory and put forward generalized interval-valued rough fuzzy set and generalized interval-valued fuzzy rough set. In this paper, the constructive study of approximation operators is emphasized. The innovation and main results are summarized as follows:1. The lower and upper approximation operators of generalized rough fuzzy sets are expanded to interval, and new lower and upper approximation operators of generalized interval-valued rough fuzzy sets are proposed by the decomposition theorem of the interval-valued fuzzy sets. We prove that the two kinds of operators are equivalent at generalized approximation space formed by any classical binary relations.2. Lower and upper approximation operators of generalized fuzzy rough sets are mended from dual properties and extended their definition to interval. These operators are proved to be equivalent to generalized interval Dubois fuzzy rough approximation operators in a generalized approximation space formed by any interval-valued fuzzy binary relations.3. Typical properties of operators defined in the paper are discussed under different classical binary relation or interval-valued fuzzy binary relation.Because the core of rough set is to educe a pair of lower and upper approximation operators from approximation space, so the constructive research of approximation operators on interval-valued fuzzy set have a important meaning to study the interval-valued fuzzy rough set theory.