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論文中文名稱:模糊偏好關係整合於序率層級分析法之研究 [以論文名稱查詢館藏系統]
論文英文名稱:Integration of stochastic analytic hierarchy process with fuzzy preference relation [以論文名稱查詢館藏系統]
院校名稱:臺北科技大學
學院名稱:工程學院
系所名稱:土木工程系土木與防災碩士班
畢業學年度:105
畢業學期:第二學期
出版年度:106
中文姓名:劉國立
英文姓名:Guo-Li Liou
研究生學號:103428073
學位類別:碩士
語文別:中文
論文頁數:189
指導教授中文名:朱子偉
口試委員中文名:朱子偉;陳偉堯;謝龍生;張志新
中文關鍵詞:層級分析法序率層級分析法模糊偏好關係拉丁超立方取樣蒙地卡羅模擬正交取樣
英文關鍵詞:Analytic Hierarchy Process(AHP)Stochastic Analytic Hierarchy Process(SAHP)Fuzzy Preference Relation(FPR)Latin Hypercube Sampling(LHS)Monte Carlo Simulations(MCS)Orthogonal Sampling
論文中文摘要:層級分析法(Analytic Hierarchy Process, AHP)被廣泛應用在各個領域,由於它理論清晰且操作容易,故被使用在許多評估準則的決策問題中。然而,層級分析法在實際應用上也存在一些問題,例如當要素資訊不夠明確或是決策者缺乏足夠經驗判斷時,往往難以評定兩要素之間的相對重要性,抑或是當多評估準則數或高層級數時,決策者的判斷愈有可能產生前後不一致的情形,導致一致性比率(Consistency Ratio, CR)未通過標準,進而降低模式作業之效率。研究文獻指出結合蒙地卡羅模擬之序率層級分析法(Stochastic Analytic Hierarchy Process, SAHP)可改善要素評比時的不確定性,但在評估準則數較多或高層級數時,其一致性檢定通過率結果並不理想。此外,鑒於傳統層級分析法之評估尺度特性,Saaty建議以幾何平均之方式整合群體評估資料,然而在之前序率層級分析法計算機率分布之平均值時是使用算術平均的方式,導致所得機率分布無法真正代表原資料序列特性。
本研究旨在整合模糊偏好關係(Fuzzy Preference Relation, FPR)至序率層級分析法,並且修正計算機率分布之平均值時不合理之處。研究首先把傳統層級分析法之評估尺度轉換為模糊偏好關係之評估尺度,並改進應用Beta-PERT分布之不合理之計算,再應用蒙地卡羅模擬(Monte Carlo Simulations, MCS)結合拉丁超立方取樣(Latin Hypercube Sampling, LHS)建立序率化之成對比較矩陣,最後整合決策者群體對各要素的相對權重之共識,並應用於災害風險評估。研究結果顯示,修正序率層級分析法,藉由自然對數之函數轉換方式,能有效改善Beta-PERT分布計算平均值不合理之處,而模糊偏好關係整合於修正序率層級分析法後,除了評估尺度更符合習性,也確實能提升一致性檢定的通過率,加強了此方法之應用性。
論文英文摘要:The analytic hierarchy process(AHP) has proved to be a powerful tool to deal with complex multiple-criteria decision makings, and its multi-disciplinary applications have been widely published. However, there exit constraints and difficulties in practicing element comparisons, especially for inexperienced applicants or without sufficient element information. Moreover, too many elements in a hierarchy, on the other hand, will increase the possibility of comparison inconsistency, which further abates the applicability of AHP. In addition, literatures have shown that stochastic analytic hierarchy process(SAHP) integrated with Monte Carlo simulation effectively lessens the uncertainty in pairwise element comparison. Nevertheless, numerous element within a hierarchy usually result in high failure rate in consistency test. Besides, previous SAHP calculation adopted arithmetical mean instead of geometric mean for group aggregation, which may generate an unreasonable probability distribution.
Therefore, this study aims to integrate the Fuzzy Preference Relation(FPR) scale to SAHP and modify the unsound calculation of probability distribution. First, the judgment scale of traditional AHP was transformed to Fuzzy Preference Relation scale. Secondly, an extra natural logarithmic transformation was performed for each dara series prior to Beta-PERT distribution calculation. Next, Monte Carlo simulation integrated with Latin Hypercube Sampling were proceeded to create the stochastic pairwise comparison matrix and determine the relative weights of elements. The proposed method was further applied in disaster-risk assessments. The results indicate that the modified SAHP effectively alleviates the irrationality in calculating Beta-PERT distribution. Additionally, the integration of Fuzzy Preference Relation scale to modified SAHP not only provides a judgment scale closer to human behavior, but also elevates the successful rate in consistency test. Overall, it is concluded that the proposed methodology is feasible and enormously enhances the practical applications of AHP.
論文目次:中文摘要 i
英文摘要 iii
誌謝 v
目錄 vi
表目錄 viii
圖目錄 ix
第一章 緒論 1
1.1前言 1
1.2研究動機與目的 1
1.3研究架構及流程 2
第二章 文獻回顧 4
2.1層級分析法 4
2.2序率層級分析法 5
2.3模糊偏好關係 6
第三章 研究方法 7
3.1模糊偏好關係整合於序率層級分析法 7
3.1.1建立層級架構 8
3.1.2評估尺度 9
3.1.3建立成對比較矩陣 10
3.1.4一致性檢定 10
3.1.5機率分布 11
3.1.6不確定性分析 14
3.1.7建立序率成對比較矩陣 16
3.1.8相對權重 16
3.2模式建構 17
3.2.1評估指標選取 18
3.2.2淹水災害環境指標說明 18
3.2.3坡地災害環境指標說明 19
3.3問卷資料 20
第四章 結果分析 22
4.1 Beta-PERT分布參數 22
4.2相對權重計算與一致性檢定 22
4.3結果與討論 41
4.4案例應用 43
4.4.1災害風險評估方法說明 43
4.4.2災害風險評估結果 46
第五章 結論與建議 51
5.1結論 51
5.2建議 53
參考文獻 54
附錄A:專家意見評選表 58
附錄B:有效問卷資料 71
附錄C:Beta-PERT分布參數一覽表 87
附錄D:取樣結果一覽表 99
附錄E:配對結果一覽表 139
附錄F:災害環境因子調查結果 175
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論文全文使用權限:同意授權於2022-08-31起公開