型II模糊集合的模糊熵
摘要
型II模糊集合(Type-2 Fuzzy sets)改善了傳統的模糊集合(Type-1 Fuzzy sets)中的不確定因素(Uncertainty)與模糊度（Fuzziness）。在日常實務中，同樣一個物件，也會因為觀點不同，其模糊程度也不同。如何
決定其模糊程度呢？模糊度最普遍的量測就是模糊熵(entropy) ，有許多數學家在研究模糊熵，並對模糊熵提出不同的量測公式。

本論文以Mendel與 John(2001)所提出的新的模糊集合與定理為基礎，提出一個新的型II模糊集合的模糊熵量測公式。藉由一些例子來和其他量測公式做比較，結果發現: 我們的量測公式更具有彈性和實用性。

Entropy of Type-2 Fuzzy sets
Abstract
Type-2 fuzzy sets improve uncertainty and fuzziness of Type-1 fuzzy sets. In daily life, the degree of fuzziness is not the same because the same object would have different degrees of fuzziness due to different viewpoints. How the degree of fuzziness of type-2 fuzzy sets will be decided? The most common measurement of the degree of fuzziness is “entropy” and the definitions of “entropy” are widely varied.
This dissertation, based on Mendel and John’s theorem, developed a new measure for type-2 fuzzy sets. Some examples are also presented for comparisons of the newly developed measure with the existing measure. After finishing all the comparisons, we found that our method is more flexible and practical than the existing measure.

參考文獻

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