| Many scholars have researched the measure and transmission for information ,but there are too much problems of fuzzy information left in real life, we must solve or develop these problems such as measure and transmission etc. Based on some important basic theories for fuzzy information proposed by De Luca and Termini, the properties of fuzzy entropy are researched and extended in this paper, the inherence contact and translation for fuzzy entropy with distance measure are also discussed; give out the definition of quasi-fuzzy entropy, discuss its property, and the asymptotic boundary for it is also studied, get some significative results for the measure entropy whose fuzzy vector is boundless; afterward, fuzzy source is proposed, based on its statistic characteristic and asymptotic equality property, we study the fuzzy source coding theorem, propose the data compress scheme for fuzzy source sequence, construct a compress coding method-fuzzy Huffman coding which is a good code, it can be proved with numerical value example that this compression coding be effective and dependable; the last chapter ticks off some successful applications of information theory, including applications in analysis science, pattern recognition, image manipulation and so on. The production of this paper will accelerate the development of fuzzy information theory in theory or application, and possess applicable value.
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