Study on the Solution of Fuzzy Relation Equations

• Main Authors: Yi-Ke Liaw, 廖宜科
• Other Authors: Wen-June Wang
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/18731179214155474163

碩士 === 國立中央大學 === 電機工程研究所 === 87 === This thesis studies two topics, one is the analysis on the product of fuzzy intervals multiplication and the other is the solution method of fuzzy relation equations. We propose the multiplication formulas of two fuzzy intervals or numbers in different cases in Chapter 2. The formulas are convenient for the use in computer program. Furthermore, in order to simplify the product calculation, the thesis also provides an approximation result of the product and proves that the approximation is reasonable. This thesis focuses on two directions on the solution of fuzzy relation equations. In Chapter 3, we consider the case that the solution of the fuzzy relation equation P。Q=R exists. We propose two new algorithms to solve the fuzzy relation equation with max-min composition and max-product composition respectively. These algorithms operate based on a matrix pattern systematically to get all the solutions of P efficiently and quickly. In Chapter 4, we consider the case that the solution of the fuzzy relation equation does not exist. Real-valued genetic algorithm (RVGA) is used to solve fuzzy relation equations with max-product composition.