The study of fuzziness for fuzzy sets

• Main Authors: CHIH-HUI CHIU, 邱智煇
• Other Authors: W. J. WANG
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/677kqk

博士 === 國立中央大學 === 電機工程研究所 === 88 === 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.