          系統識別號 U0026-2611201318050000 論文名稱(中文) 直覺式模糊集評估指標與區間值排序函數 論文名稱(英文) Developing Measures and Interval-valued Ranking Functions based on Intuitionistic Fuzzy Sets 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 1 出版年 102 研究生(中文) 涂謙誠 研究生(英文) Chien-Cheng Tu 學號 R38981073 學位類別 博士 語文別 英文 論文頁數 83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-陳世彬召集委員-陳振明 中文關鍵字 直覺式模糊集  區間值直覺式模糊集  評估指標  雙重兩極性  排序函數 英文關鍵字 intuitionistic fuzzy set  interval-valued intuitionistic fuzzy set  measure  dual bipolar  ranking function 學科別分類 中文摘要 在Atanassov(1986)所提出的直覺式模糊集(IFS)的諸多評估指標之中，如鄰近度，基數，距離，相似度，關聯性以及評估函數，經常可應用於處理許多相關問題；然而區間值的資料型態似乎能廣義的使用於IFS，因而衍生出區間值直覺式模糊集(IvIFS)的排序議題，其困難來自於其同時具有區間值的歸屬程度與區間值的非歸屬程度之特殊性。本論文提出了迥異於過去觀點的上述IFS相關評估指標定義以及IvIFS排序函數。首先提出的是基於自身IFS相較於其他的IFS所呈現出來的相對程度所定義的四項函數，稱之為優越性(superiority)，非劣等性(non-inferiority)，明確性(determinacy)與非猶豫性(non-hesitancy)，藉此以組成了所謂雙重兩極性(dual bipolar)尺度，也就是介於優越至於非劣等以及明確至於非猶豫的雙重尺度。此時根據雙重兩極性尺度所提出的直覺式模糊集(IFS)評估指標便根據相關公理加以定義。更憑藉圖形的呈現加以驗證存在於過去與本論文提出的評估指標之間的一致程度。其次此種以IvIFS表示的排序函數乃是藉由其自身凌駕於或者是不被凌駕於其它的IvIFS作為考量依據，而且是以IFS的雙重屬性與凌駕(dominance)概念為基礎。此排序函數的設計除了使用IFS之歸屬度與非歸屬度的臨界值之外，還將IvIFS之間以彼此相對的凌駕程度納入考量。此外本論文針對兩個IvIFS之間一旦滿足四項提出之排序函數就形成特有的偶配對(dual couple)關係加以定義，且證明提出的五項排序函數能夠完全區別所有之IvIFS，所提出的評估指標以及排序函數皆能夠顯現出IFS與IvIFS的獨有特質。此外，藉由配置不同程度之雙重兩極性尺度與不同比例的相對凌駕程度將決策者態度植入IFS評估指標與IvIFS排序函數。最終藉由四個範例驗證IFS評估指標與IvIFS排序函數的應用性與效能展現。 英文摘要 Measures of intuitionistic fuzzy sets (IFSs), such as subsethood, cardinality, distance, similarity, correlation, and evaluation functions, are often used in application problems. The interval-valued data used by IFSs can express the comprehensive uncertainty of IFSs. However, the ranking of interval-valued intuitionistic fuzzy sets (IvIFSs) is difficult since they include the interval values of membership and non-membership. This research investigates such measures of IFS and ranking functions for IvIFSs from various perspectives. Firstly, based on the relative relations of an IFS to other IFSs, four functions, namely superiority, non-inferiority, determinacy, and non-hesitancy, are constructed, which consist of dual bipolar scales, namely (superiority, non-inferiority) and (determinacy, non-hesitancy). Then, the proposed measures of IFSs are axiomatically defined using the dual bipolar scales. Geometrical demonstrations in general show consistency between the proposed measures and existing ones. Secondly, the proposed ranking functions consider the degree to which an IvIFS dominates and is not dominated by other IvIFSs. Based on the bivariate framework and the dominance concept, the functions incorporate not only the boundary values of membership and non-membership, but also the relative relations among IvIFSs in comparisons. The relationship for two IvIFSs that satisfy the dual couple is defined based on four proposed ranking functions. Importantly, the five proposed ranking functions can achieve a full ranking for all IvIFSs. Therefore, the proposed measures and ranking functions can highlight the significant features of IFSs and IvIFSs. In addition, the attitude of decision-makers is also implanted in measures of IFSs and ranking functions of IvIFSs to allocate the importance in the dual bipolar scales and the various kinds of dominance respectively. Four examples are used to demonstrate the applicability and performance of the proposed measures of IFSs and ranking functions of IvIFSs. 論文目次 摘 要 I Abstract II Acknowledgements III List of Tables VI List of Figures VII Chapter 1 Introduction 1 1.1 Background 1 1.2 Measures and ranking functions 3 1.3 Motivation and objectives 5 1.4 Organization 5 Chapter 2 Preliminaries 7 2.1 Basic definitions 7 2.2 Measures and Operators 10 2.3 Ranking functions of IvIFSs 14 Chapter 3 Dual bipolar measures of IFSs 20 3.1 Motivations 20 3.2 Measures 23 3.2.1 Subsethood for IFSs 24 3.2.2 Cardinality for IFSs 25 3.2.3 Distance and Similarity Measures for IFSs 26 3.2.4 Correlation measure for IFSs 31 3.2.5 Evaluation Functions for IFSs 32 Chapter 4 Ranking functions of IvIFSs 35 4.1 Composite score function 36 4.2 Composite accuracy function 39 4.3 Definiteness function 40 4.4 Exactness function 41 4.5 Vagueness function 42 4.6 Discussion of properties 43 4.7 Ranking procedure 44 Chapter 5 Numerical illustrations 47 5.1 Multi-attribute decision-making problem by IFSs 47 5.2 Medical diagnosis problem by IFSs 50 5.3 Adaptive Ranking Orders of IvIFSs 52 5.4 Comparative Ranking Orders of Subtle IvIFSs 54 Chapter 6 Conclusions 60 Bibliography 62 Appendix 68 A-I: Proof of Theorem 3-1 68 A-II: Proof of Corollary 3-1 71 A-III: Proof of Theorem 3-2 74 A-IV: Proof of Theorem 3-3 75 A-V: Proof of Theorem 3-4 75 A-VI: Proof of Theorem 4-1 78 A-VII: Proof of Theorem 4-2 78 A-VIII: Proof of Theorem 4-3 81 參考文獻 Atanassov, K. 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