本論文探討的主題包括模糊集合(Fuzzy set)之模糊性(Fuzziness)研究、模糊數(Fuzzy number)之次序(Lattice)問題及模糊系統的穩定性(Stability of fuzzy system)研究。 首先，第二章提及如何利用熵(Entropy)來量測一個模糊集合的模糊程度，進一步討論到熵的一些特性。另外亦提到資訊量(Information energy)的觀念，並研究熵和資訊量之間的關係。除此之外，第三章和第四章中所提之模糊集合經模糊數學運算(Arithmetic operation)或經擴充定理(Extension Principle)之後熵的變化亦是討論的重點。本論文提出幾個簡單的公式來求得運算後所得之模糊集合的熵值。接著，本論文第五章還提出一些簡單的方法來求熵值，利用這些方法我們不須做積分運算便可容易地得到一個模糊集合的熵值。 另外，本論文對於模糊數次序的問題亦有所探討，並提出一速算法來取代傳統複雜的方法。 最後，模糊系統穩定性的問題在附錄中被討論。 In this dissertation, fuzzy sets' fuzziness is our main study topic. By the way, the lattice of fuzzy numbers and the stability of fuzzy systems are also discussed. In Chapter 2, we investigate the entropy relationship between two same type of fuzzy sets and study some properties of the information energy. Then, the relationship between the information energy and the entropy of a fuzzy set is derived. Chapter 3 and Chapter 4 consider the entropy change of fuzzy numbers through arithmetic operations and function mapping. Several simple formulas to get the entropy value for the fuzzy numbers' sum and for the extension principle are proposed respectively. Chapter 5 proposes an new idea called "entropy unit" to get any fuzzy set's entropy value easily and quickly. Moreover, Chapter 6 try to simplify the operations of MIN and MAX of fuzzy numbers such that the operations of MIN and MAX can be implemented easily and quickly.
