A Comparative Study Of Several Uncertainties Theories

Fuzzy Mathematics, Rough Set Theory, Extentics and Set Pair Analysis are all the new development of the uncertain theory. Fuzzy mathematics is the carving of fuzzy phenomena or fuzzy conceptions and the description of fuzziness of thinking. Rough Set Theory is a tool of mathematics dealing with uncertain, inaccurate and incomplete information. Extentics has extended its focus of study objects to the quality, characteristics, and quantity value of matter, which makes a research on the variety of matter. Set Pair Analysis is a systematic analysis approach to make quantitative analysis of system differences and similarities by using connection number. These four approaches have provided forceful ways for the description of uncertainties of human thinking. This paper involves the relations of the mathematic foundationsof these four new-rising theories of uncertainties——Fuzzy Set, Rough Set, Extension Set andSet Pair Connection Degree.Firstly, it has defined rough dependent function in the form of U→ {-1,0,1} . A comparison is made in concept between Rough Set and Extension Set from the aspect of the union and intersection operations. Also new definitions of Extension Set operations are put forward.Secondly, the concept of Extension Set based on connection number is given and also some of its characteristics are discussed by combining Extension Set and Connection Degree together, which are the basic concepts of China's original subjects——Extentics and Set Pair Analysis.The classical Rough Set Theory is based on complete information system, which is actually not in reality for various reasons. The paper takes advantage of Set Pair Connection Degree to define upper and lower approximation of rough set in incomplete information system, which popularizes the application of rough set to incomplete information system to some extent.The last chapter introduces the achievements made by others in the combination of Rough Set and Fuzzy Mathematics.