On measures of type-2 fuzzy sets

• Main Authors: Der-Chen Lin, 林德成
• Other Authors: Miin-Shen Yang
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/42726357119000209383

博士 === 中原大學 === 應用數學研究所 === 96 === Abstract In a practical complex system, humans sometimes use only binary logic theory for deducing some objects or information which is not sufficient to explain all situations. Thus, a fuzzy concept can be utilized for assisting deductions. As for some unclear, uncertain, and incomplete information, they can be compared and screened by measured value of fuzzy set. Additionally, the new definition and theorem of type-2 fuzzy sets proposed by Mendel and John in recent years have been widely studied and spread, and applied to many fields. This dissertation presents a relative definition of measurement of fuzzy degree, inclusion degree and similarity degree to type-2 fuzzy sets, and discusses certain relativity and properties among them. Illustrations for practical demand are used to show how to calculate the measurement of fuzzy degree, inclusion degree and similarity degree among type-2 fuzzy sets. Furthermore, in the discussion, the algorithm of Yang and Shish is used as a method for cluster analysis, and comparison is made with the results of Hung and Yang. According to different α-levels, these cluster results are reasonably included in a hierarchical tree.