Fuzzy Uncertainty Measure A Number Of Thematic Studies

The nature of information is to clear or decrease the uncertainty, so that the research on the degree of uncertainty becomes the beginning point of the research on information theory. The uncertainty of information has many forms, such as probabilistic uncertainty, fuzzy uncertainty , resolutional uncertainty and unascer-tainty. The research on the probabilistic uncertainty has got fully developed and applied. This paper launch the research and discussion on the fuzzy entropy from the following aspects, according to the fuzzy uncertainty subject.In chapter 2, based on the axiomatic definition of fuzzy entropy, distance measure, similarity measure, proposed by X.C.Liu~[4], we offer some new similarity measure and fuzzy entropy caused by distance measure, similarity measure.In chapter 3, different with the former intersection and union calculation, we point out the addition, multiplication calculation of fuzzy set, and discuss the properties on these calculations of fuzzy entropy, distance measure and similarity measure.In chapter 4, we extend the concept of entropy in vague set , and definite the partial entropy, relative 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 5, for simplify some discussion of problems, we offer two kinds translation functions from vague set to fuzzy set, and discuss their nature;analyze the disadvantages of conception of fuzzy entropy in vague set. At last we give the limiting conditions of fuzzy entropy, and the fuzzy entropy formula according with the new limiting conditions.