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系統識別號 U0026-2606201415210500
論文名稱(中文) 直覺式模糊集群分析與效度指標
論文名稱(英文) Intuitionistic fuzzy hierarchical clustering and validity index
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系
系所名稱(英) Department of Industrial and Information Management
學年度 102
學期 2
出版年 103
研究生(中文) 蔡紹緯
研究生(英文) Shao-Wei Tsai
學號 R36011212
學位類別 碩士
語文別 中文
論文頁數 78頁
口試委員 指導教授-陳梁軒
口試委員-王泰裕
口試委員-謝中奇
口試委員-施勵行
中文關鍵字 直覺式模糊數  相似度計算  集群分析  分群效度指標 
英文關鍵字 Intuitionistic fuzzy sets  similarity  clustering  validity index 
學科別分類
中文摘要 集群分析為統計學上重要分析工具,其應用的領域相當多元,例如:將大量的顧客資訊,依照消費傾向進行分群,不同集群給予適當的行銷策略;將區域性生物進行分群,依照分群結果執行保育政策。傳統的集群分析中,資料與集群的關係屬於明確值,表示該資料只屬於一特定集群,然而由於現實環境的不確定性,我們經常無法將蒐集到的資料進行統計上的分群,因此使用模糊理論(Fuzzy Sets Theory)的方式,使資料和集群間的關係,以歸屬度函數方式表達,而不再是明確值,以保留資料完整性。
直覺式模糊(Intuitionistic Fuzzy Sets)為模糊理論之延伸,在歸屬度函數外,加入了非歸屬度函數衡量,因此直覺式模糊的表達可以更貼近現實環境,然而過往的研究中,較少提到以直覺式模糊的方式,整合集群分析之相關研究。且在過去的研究中,集群分析方法以及分群效度指標尚有不足的地方,因此本研究希望提供一個直覺式模糊結合集群分析之研究,以階層式合併方法進行分群,提供新的集群分析方式,並改進分群效度指標,使決策者有更良好的決策環境。
本研究模式分為三個階段,在前置階段專家會針對各個資料在不同屬性的表現進行評分,並將模糊性資料轉換為直覺式模糊值,再將各個專家的評估值進行合併;在計算階段,以直覺式模糊相似度計算方法,衡量資料間的相似程度,並進行階層式合併;最後的評估階段,則是運用改良的分群效度指標,找出最佳集群數。
本研究所提出直覺式模糊集群分析演算法與過去集群分析演算法相比,採用較嚴謹的相似度計算排除反直覺問題發生的可能性;以階層式架構的方式發展出可調整分群速度之較為彈性的分群演算法;提供更完整的分群效度指標,使決策者有更明確的決策資訊。
英文摘要 Clustering analysis is a traditional statistical tool that is used for data classification. While data is often described using crisp numbers, this has some limitations with regard to representing the uncertainties inherent in many situations, and thus so-called fuzzy approaches have been developed to deal with this. An intuitionistic fuzzy set (IFS) is a set of 2-tuple arguments, which are characterized by the properties of membership and non-membership. This paper develop a new clustering analysis method to carry out the data description by IFS. There are two stage in this method. In the calculating state, the similarity method proposed by Liang and Shi (2003) is used to measure the distance between two data points and then combine the most similar data. After data integration, the similarity between the integrated data and the rest of data is assessed, and if this similarity greater than the value of , which is decided by a decision-maker, then a second round of integrated is carried out. This then continues until all of the data is integrated, and then a hierarchical structure of the data cluster can be obtained. In the assessment stage, a modified version of the validity index proposed by Babak (2010) is used to measure the clustering results to find the optimal number of clusters. Comparison of the proposed method with other IFS clustering approaches shows that the method developed in this work achieves similar clustering results, but can return more distinct clusters to the decision-maker, and thus provide more useful information. In summary, this study provides a new IFS hierarchical clustering method that is more flexible than existing approaches and can produce clearer clustering results.
論文目次 摘要 I
Abstract II
誌謝 V
目錄 VI
圖目錄 VII
表目錄 VIII
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究限制 2
1.4 研究流程 3
1.5 論文架構 4
第二章 文獻探討 5
2.1 模糊集合理論 5
2.2模糊集群分析與直覺式模糊集群分析 9
2.3 相似度計算 18
2.4分群效度指標 28
2.5 小結 32
第三章 直覺式模糊分類法模式建構 34
3.1 研究構想 34
3.2 模式建構 36
3.3 小結 47
第四章 數據分析與比較 48
4.1範例演練 48
4.2 分群效度指標比較 54
4.3 分群方法比較 60
4.4 參數分析 63
第五章 結論與未來研究方向 68
5.1 研究成果 68
5.2 未來研究方向 69
參考文獻 70
附錄 75
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