Theory And Application Research On Rough Sets And Vague Sets

Rough set is a valid mathematical theory developed in recent years, which has the ability to deal with imprecise, uncertain, and vague information. The start point of rough set theory solving problems is indiscernible nature knowledge in information system. Vague set is a new mathematical theory provided by W. L. Gau and D. J. Bueher in 1993, which has the ability to deal with vague information. In nature, vague set is development of fuzzy set. In comparison with fuzzy set, vague set is better for expressing vague information precisely, and has the preponderance in processing vague information.An important application of rough set is to reduce the dimension of information system(i.e. knowledge reduction). The knowledge reduction includes data reduction and attribute reduction. Decision table is a special and important information system. Many decision problems can be expressed with decision table, and this tool contributes to decision application. This paper analyses the disadvantage of the present decision attribute reduction, and a new method is proposed, which is attribute reduction approach based on the equivalent classes. And this approach is implemented by VC/C++. After studying properties of decision table fully, the number of elements needed for both compatible decision table and incompatible decision table are introduced, which plays an important role in data collecting. Besides, the relationship of attribute reduction between complete decision table and incomplete decision table is discussed, which has an importing meaning for attribute reduction of incomplete decision table, and a new method of it is presented.The concept of fuzzy entropy was proposed by Zadeh early, and it is a tool of describing fuzzy information amount. In the fuzzy set theory and vague set theory, fuzzy entropy is one of the most important researches. And it introduces the fuzzy set theory and vague set theory to the applicationof fuzzy clustering , pattern identification , image manipulation and so on. The paper analyses the demerits of the present fuzzy entropy constructing method of vague set, and provides a new approach.Though rough set and vague set theory are used to study the information uncertainty in the information systems, the starting point and characteristics of both are different, and they are complementary. Now the literatures about the fusion study between fuzzy set and rough set are numerous, but the literatures about the fusion study between vague set and rough set are little. So rough vague set theory is presented after fusion study between vague set and rough set. And the fuzzy entropy> rough-degree^ similarity measures of rough vague set are further studied. In addition, the construction and axiomatic research of generalized rough vague set are discussed. At last the paper applies the rough vague set theory to the attribute reduction of vague decision table.