架構在Sugeno積分上關於模糊集合的Belief及 Plausibility函數的推廣

Generalization of belief and plausibility functions to fuzzy sets based on Sugeno integral

黃朝銘(Chao-Ming Hwang)

指導教授 ： 楊敏生

中原大學/理學院/應用數學系/博士(2007年)

https://doi.org/10.6840/cycu200700269

摘要

摘要
在實際的系統中總是存在著不確定性。而在科學中，處理不確定性已經有幾十年的歷史了。在傳統上，機率是最常被使用在不確定性的模型中，近來，架構在Dempster-Shafer 理論上的Belief 及 Plausibility函數已經變成另一種測量不確定性的型式，這些測量函數如今已被廣泛地研究及應用在許多的領域上。另外，模糊集合的觀念也已成功地被使用在處理當不明確邊際出現時的部份隸屬函數的量測上。當複雜的系統出現時，模糊集合是非常好用的。至今有很多關於模糊集合的Belief及Plausibility函數的推廣文章。在本論文中，我們將提出一個架構在Sugeno積分上關於模糊集合的Belief及Plausibility函數的推廣，跟一些已被提出的方法作比較。結果顯示出此推廣效果是比較好的，尤其當模糊的焦點元素改變時較能獲得更多的訊息。

關鍵字

模糊集合 ； Sugeno積分 ； 相信函數及似然函數

並列摘要

Abstract
Uncertainty has been treated in science for several decades. It always exists in real systems. Probability has been traditionally used in modeling uncertainty. Belief and plausibility functions based on Dempster-Shafer theory (DST) become a type of measuring uncertainty where they have been widely studied and applied in diverse areas. On the other hand, fuzzy sets have been successfully used as the idea of partial memberships of multiple classes for the presentation of un-sharp boundaries. It is well used as the representation of human knowledge in complex systems. Nowadays, there exist several generalizations of belief and plausibility functions to fuzzy sets in the literature. In this paper, we propose a new generalization of belief and plausibility functions to fuzzy sets based on Sugeno integral. We then make the comparisons of the proposed generalization with some existing methods. The results show that our proposed generalization has better effectiveness than most existing methods, especially for being able to catch more information to the change of fuzzy focal elements.

並列關鍵字

Sugeno integral. ； a belief function and a plausibility function ； Fuzzy Sets

參考文獻

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