在型II模糊集合上的量測

摘要在實際複雜系統中，人類對某些事物或信息之推理，有時只使用二元邏輯理論並不足以解釋所有情形，此時可用模糊概念加以輔助推論。對於某些不清晰的、不確定的、不完整的信息，可經由模糊集合之測量值來進行比較與篩選，最近更由Mendel與John所提出新的模糊集合之定義與定理，被廣泛的研究推廣並應用在許多領域。在本論文中我們將呈示有關於型II模糊集合之模糊程度與包攝程度及相似程度的量測之定義，以及討論他們之間的某些相關性及性質。為了實務上的需要將以舉例說明之方式，呈示了如何計算介於型II模糊集合之間的模糊程度與包攝程度及相似程度之量測。而且為了便於討論，我們將應用Yang與Shish之演算法，作為聚類分析的方法，並與Hung與Yang的結果作一些比較。根據不同的水準，這些聚類結果是很合理的包含於一層次樹中。

關鍵字

相似量測；模糊量測；包攝量測；型II模糊集合

並列摘要

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.