區間值之T遞移模糊聚類法

T-transitive Interval-valued Fuzzy Clustering

王景南(Ching-Nan Wang)

指導教授 ： 楊敏生

中原大學/理學院/應用數學研究所/博士(2013年)

https://doi.org/10.6840/cycu201300686

摘要

求解模糊關係的層次樹是近年來學者們相當關注的研究和應用主題，因為透過此樹形圖即可清楚的明瞭模糊關係之階層性的分群結果。目前大部分架構在模糊關係上的分群方法都是根據其隸屬度函數為實數值的型態。然而，在人類複雜的感官世界裡，使用
實數值型態的隸屬度函數實不足於充分地表達人們對事物認知的不確定性與混淆性，解決此一問題的方法是將實數值隸屬度函數擴充為區間值的型態。因此，在本篇論文中，我們首先利用區間值型態的隸屬度函數將模糊關係推廣至區間值型態的模糊關係，然後據此發展出一個架構在區間值之 T 遞移模糊聚類演算法，並透過兩個實例驗證了此演算法能有效合理的呈現適切之分群。最後，以台灣各級大學工學院之分項績效評鑑指標整合作為實務的應用，我們提供台灣評鑑協會(TWAEA)各個不同層次的關係標準下模糊聚類之建議，此一結果獲得該協會委員相當的認同。透過種種不同的案例，證實了本文所提出之聚類演算法是求解區間值型態模糊關係的層次樹之好工具。

關鍵字

績效評估 ； 區間值模糊關係 ； T遞移模糊關係 ； 聚類分析 ； 模糊集

並列摘要

Fuzzy relation with its partitioned tree for obtaining an agglomerative hierarchical
clustering has been widely studied and applied in recent years. Most fuzzy-relation-based
clustering approaches are based on real-valued memberships. However, interval-valued
memberships may be better than real-valued memberships to represent higher-order
imprecision and vagueness for human perception. Thus, this dissertation first extends fuzzy
relations to interval-valued fuzzy relations and then constructs a clustering algorithm based on
the proposed T -transitive interval-valued fuzzy relations. There are two interesting examples,
the characteristic beauty of Chinese characters and portraits of family member, to be applied
in this dissertation to demonstrate the efficiency and usefulness of the proposed method. In practical application, we utilize the proposed clustering method to performance
evaluations for academic departments of higher education by using actual engineering school data in Taiwan. The consequences of a hierarchical evaluation structure were thought to be more flexible and softer than the original one that the Taiwan Assessment and Evaluation
Association (TWAEA) committee adopted. Demonstrating by examples and practical
application, one who utilize the proposed clustering method in this dissertation to fuzzy data clustering may obtain better results.

並列關鍵字

T-transitive fuzzy relation ； Performance evaluation ； Interval-valued fuzzy relation ； Fuzzy set ； Cluster analysis

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