Measure Of The Information. Uncertainty And Its Application

Transmission of information is at the heart of what we call communication. As an area of concern, it is quite important to study the quantization of information, which is the cornerstone of the information scientific research.In 1948, in the introduction to his classic paper, C.Shannon wrote: "The fundamental problem of communication is that of reproducing at the point either exactly or approximately a message selected at another point." To solve that problem, he created, a completely new branch of applied mathematics, which is today called information and/or coding theory.The information Shannon studied is the probabilistic uncertainty. As science and technology develops, people realize that there are other kinds of uncertainty, such as fuzzy uncertainty, grey uncertainty and uncertainty. In this paper, we mainly study fuzzy uncertainty.In the introduction chapter, we give a brief illustration of the background and the central ideal of this paper. The symbols and the axiom definitions of fuzzy entropy, distance measure and divergence measure are also presented.In chapter two, the relations between fuzzy entropy and distance measure are studied. Some new formulas about properties of σ -entropy and σ-distance measure are proposed.In chapter three, we mainly study the relations between distance measure and divergence measure. Some examples are given. The properties of local divergence measure are also studied.In chapter four, we apply fuzzy information method in image processing. A class of image metrics is denned based on the fuzzy cross-entropy. It is very useful in measuring image distortion.