Fuzzy Information Measure To Expand And Applications

The quantization of information is the 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 increasingly becomes an important task of us. The first kind of uncertainty studied by us is the probabilistic uncertainty. For this kind of uncertainty, we already have a good system. But with the development of science and technology, we found there are some other kinds of uncertainty such as fuzzy uncertainty, grey uncertainty and unascertainty 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 mathematics acts as a tool in dealing with the information of fuzzy uncertainty.In this paper, we mainly studied the entropy, similarity measure, distance measure and divergence measure in fuzzy mathematics, and hope to use our conclusions to solve those problems about uncertainty.In chapter two, we studied some properties of fuzzy divergence and discussed the relations between fuzzy entropy and fuzzy divergence, then we got some fuzzy entropy measures generated by these fuzzy divergence measures.In chapter three, we gave the definition of distance measures between in-tuitionistic fuzzy sets. Some distance measures are proposed and corresponding proofs are given. The relations between similarity measure and distance measure of intuitionistic fuzzy sets are analyzed. Finally, the distance measures of intuitionistic fuzzy sets are applied to pattern recognition.In chapter four, the axiom definitions of entropy and similarity measure of intuitionistic fuzzy sets based on the axiom definition of Liu's (1992) were proposed. Then several new similarity measures between intuitionistic fuzzy sets and its elements are presented. Finally, several entropy measures generated by similarity measures were presented.In chapter five, the hybrid sets that relates the fuzziness and probabilities were defined. The notion of hybrid partial entropy, hybrid relative entropy and hybrid relative coefficient were introduced, and their properties were studied. Further, an example was proposed to prove the usefulness of hybrid relative coefficient in our daily life.In chapter six, the hybrid uncertainty was discussed. Based on the theory of Shannon entropy, the hybrid entropy, conditional entropy, relative entropy, partial entropy and mutual entropy of hybrid sets were studied. Further,the relations of these measures were studied.