The Measurement Of Fuzzy Uncertainty Based On Inclusion Grades

The main task of information science is to clear the uncertainty and get the information. How much of the uncertainty is one important index to measure information. So the quantization of the uncertainty is the basic point in information theory. 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, the uncertainty of information bacome mome and more complication and diversification, especially, the fuzzy uncertainty arose many researchers' attention. Fuzzy mathematic acts as a tool in dealing with the information of fuzzy uncertainty. Entropy and distance measure can also be used to reflect the fuzzy uncertainty.Several aspects of quantitative measures of fuzziness had been studied in this paper:In chapter two, Based on axiomatization definitions of inclusion grades, several properties of inclusion grades is discussed. And through studying the relationship between fuzzy entropy and inclusion grades, new formulas of entropy and inclusion grades have been obtained. It can be found that the new formulas have stronger resolving power by example.In chapter three, By using the theory of fuzzy sets, we defined intuitionistic fuzzyσ-entropy,σ-distances measure andσ-inclusion grades. Some properties of them have been discussed, meanwhile, the theorem of distance measure which is reduced by entropy was given, several entropy and distance measure formulas were reduced through inclusion grades.