Between Vague Sets Fuzzy Uncertainty Measure

The quantization of information is starting point of information theory. Shannon pointed out that the function of communication was to let the receivers get some information from what has been transmitted, and then erase the uncertainty before communication. So the study of uncertainty becomes animportant task of us. The uncertainty of information has many forms, such as probabilistic uncertainty,fuzzy uncertainty,resolutional uncertainty and so on. The research on the probabilitic uncertainty has got fully developed and applied. With the development of science and technology, we found there are some other kinds of uncertainty, such as grey uncertainty , uncertainty and so on.For these new kinds of uncertainty , we hope there's some known knowledge can deal with them, such as in fuzzy information theory, fuzzy mathematic acts as a tool in dealing with the information of fuzzy uncertainty. In this paper, we mainly studied entropy, similarity measure, dinstance measure.In chapter two, we extend the concept of entropy in vague set, and define the partial entropy and relative coefficient of vague set, and analyze the nature of these measures, and show the application of the relative coefficients in real life by example.In chapter three, A new similarity measure between vague sets based on information entropy was proposed, and its properties is discussed. This new method is illustrated by comparison with the present measure methods that it has stronger discrimination. Finally, the similarity measures between vague sets are applied to pattern recognition.In chapter four, we give the definition of distance measures between vague sets, some distance measure are proposed and correspondind measure and distance measure of vague sets are analyzed, finally, the distance measure of vague sets are applied to pattern recognition.