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題名 模糊集合與模糊矩陣及其應用
Fuzzy set theory and fuzzy matrix with its applications作者 黃振家 貢獻者 吳柏林
黃振家關鍵詞 模糊集合
隸屬度函數
模糊矩陣
有向圖
fuzzy set
membership function
fuzzy matrix
directed graph日期 2010 上傳時間 4-Sep-2013 15:15:00 (UTC+8) 摘要 本文以人對事物現象認識的感覺與模糊性作為切入點，闡述模糊性是人對事物認識的一種表徵及反應。然後，引入模糊集合的定義及刻劃模糊集合的表示函數—隸屬度，對模糊集合的各種運算、模糊矩陣、模糊差集以及宇集等內容進行較詳細的討論，並以各種事例說明一些相關概念和運算。最後，再深入探討如何以模糊矩陣表示圖學中有向圖的問題。
This article is to focus on the understanding of human being to the phenomenon of things as well as the fuzziness. Then, by applying the definition of the fuzzy set and explaining the membership of fuzzy set, we are going to have a detailed discussion of the operation of fuzzy set, fuzzy matrix, fuzzy subtraction and universal set. Examples are given to demonstrate some of the related concepts and expression. Next, further questions about how to display directed graph in the graph theory with fuzzy matrix will be discussed .參考文獻 [1]吳柏林(2003)，現代統計學，五南書局，台北。[2]吳柏林(2005)，模糊統計導論-方法與應用，五南書局，台北。[3]吳柏林(1996)，社會科學研究中的模糊邏輯與模糊統計分析，中國統計通訊7(11)，14-27。[4]吳柏林，楊文山(1997)，模糊統計在社會調查分析的應用，社會科學計量方法發展與應用，楊文山主編：中央研究院中山人文社會科學研究所，289-316。[5]阮亨中，吳柏林(2000)，模糊數學與統計應用，俊傑書局，台北。[6]林信成，彭啟峰(1994)，Oh！Fuzzy 模糊理論剖析，第三波文化事業股份有限公司。[7]Cano, J.C. and Nava, P.A. (2002), A fuzzy method for automatic generation of membership function using fuzzy relations from training examples, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings, pp.158-62.[8]Czogala, E., Drewniak, J. and Pedrycz, W. (1982), Fuzzy relation equations on a finite set, Fuzzy Sets and Systems, 7, pp.89–101.[9]Fang, S.-C and Li, G. (1999), Solving fuzzy relation equations with a linear objective function, Fuzzy Sets and Systems, 103(1), pp.107-113.[10]Hung, T., Ngyyen and Wu, B. (2006), Fundamentals of Statistics with Fuzzy Data, Spring-Verlag.[11]Kosko, B. (1993), Fuzzy thinking: the new science of fuzzy logic, Hyperion, New York.[12]Luoh, L., Wang, W.J. and Liaw, Y.K. (2003), Matrix-pattern-based computer algorithm for solving fuzzy relation equations, IEEE Transactions on Fuzzy Systems, 11(1), pp.100-108.[13]Wu, B. and Sun, C. (1996), Fuzzy statistics and computation on the lexical semantics, Language, Information and Computation (PACLIC 11), 337-346, Seoul, Korea.[14]Zadeh, L.A. (1965), Fuzzy Sets, Information and Control, 8, 338-353.[15]Zimmermann, H.J. (1991), Fuzzy Set Theory and Its Applications, Boston: Kluwer Academic. 描述 碩士
國立政治大學
應用數學系數學教學碩士在職專班
96972009
99資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096972009 資料類型 thesis dc.contributor.advisor 吳柏林 zh_TW dc.contributor.author (Authors) 黃振家 zh_TW dc.creator (作者) 黃振家 zh_TW dc.date (日期) 2010 en_US dc.date.accessioned 4-Sep-2013 15:15:00 (UTC+8) - dc.date.available 4-Sep-2013 15:15:00 (UTC+8) - dc.date.issued (上傳時間) 4-Sep-2013 15:15:00 (UTC+8) - dc.identifier (Other Identifiers) G0096972009 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60079 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系數學教學碩士在職專班 zh_TW dc.description (描述) 96972009 zh_TW dc.description (描述) 99 zh_TW dc.description.abstract (摘要) 本文以人對事物現象認識的感覺與模糊性作為切入點，闡述模糊性是人對事物認識的一種表徵及反應。然後，引入模糊集合的定義及刻劃模糊集合的表示函數—隸屬度，對模糊集合的各種運算、模糊矩陣、模糊差集以及宇集等內容進行較詳細的討論，並以各種事例說明一些相關概念和運算。最後，再深入探討如何以模糊矩陣表示圖學中有向圖的問題。 zh_TW dc.description.abstract (摘要) This article is to focus on the understanding of human being to the phenomenon of things as well as the fuzziness. Then, by applying the definition of the fuzzy set and explaining the membership of fuzzy set, we are going to have a detailed discussion of the operation of fuzzy set, fuzzy matrix, fuzzy subtraction and universal set. Examples are given to demonstrate some of the related concepts and expression. Next, further questions about how to display directed graph in the graph theory with fuzzy matrix will be discussed . en_US dc.description.tableofcontents 1.前言 42. 模糊集合 62.1模糊集合與隸屬度 62.2模糊集合運算 82.3模糊矩陣 113.模糊集合關係矩陣與運算 133.1 二元對比排序法 133.2 模糊資料與軟運算 163.3 模糊關係 194.模糊矩陣的圖學表示與分解定理 234.1有向圖, 通路及其表示 234.2 有向圖的連通性 264.3 有向圖的鄰接矩陣 284.4 模糊矩陣的伴隨圖 294.5 模糊矩陣分解定理 335.結論 36參考文獻 37 zh_TW dc.format.extent 763915 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096972009 en_US dc.subject (關鍵詞) 模糊集合 zh_TW dc.subject (關鍵詞) 隸屬度函數 zh_TW dc.subject (關鍵詞) 模糊矩陣 zh_TW dc.subject (關鍵詞) 有向圖 zh_TW dc.subject (關鍵詞) fuzzy set en_US dc.subject (關鍵詞) membership function en_US dc.subject (關鍵詞) fuzzy matrix en_US dc.subject (關鍵詞) directed graph en_US dc.title (題名) 模糊集合與模糊矩陣及其應用 zh_TW dc.title (題名) Fuzzy set theory and fuzzy matrix with its applications en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1]吳柏林(2003)，現代統計學，五南書局，台北。[2]吳柏林(2005)，模糊統計導論-方法與應用，五南書局，台北。[3]吳柏林(1996)，社會科學研究中的模糊邏輯與模糊統計分析，中國統計通訊7(11)，14-27。[4]吳柏林，楊文山(1997)，模糊統計在社會調查分析的應用，社會科學計量方法發展與應用，楊文山主編：中央研究院中山人文社會科學研究所，289-316。[5]阮亨中，吳柏林(2000)，模糊數學與統計應用，俊傑書局，台北。[6]林信成，彭啟峰(1994)，Oh！Fuzzy 模糊理論剖析，第三波文化事業股份有限公司。[7]Cano, J.C. and Nava, P.A. (2002), A fuzzy method for automatic generation of membership function using fuzzy relations from training examples, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings, pp.158-62.[8]Czogala, E., Drewniak, J. and Pedrycz, W. (1982), Fuzzy relation equations on a finite set, Fuzzy Sets and Systems, 7, pp.89–101.[9]Fang, S.-C and Li, G. (1999), Solving fuzzy relation equations with a linear objective function, Fuzzy Sets and Systems, 103(1), pp.107-113.[10]Hung, T., Ngyyen and Wu, B. (2006), Fundamentals of Statistics with Fuzzy Data, Spring-Verlag.[11]Kosko, B. (1993), Fuzzy thinking: the new science of fuzzy logic, Hyperion, New York.[12]Luoh, L., Wang, W.J. and Liaw, Y.K. (2003), Matrix-pattern-based computer algorithm for solving fuzzy relation equations, IEEE Transactions on Fuzzy Systems, 11(1), pp.100-108.[13]Wu, B. and Sun, C. (1996), Fuzzy statistics and computation on the lexical semantics, Language, Information and Computation (PACLIC 11), 337-346, Seoul, Korea.[14]Zadeh, L.A. (1965), Fuzzy Sets, Information and Control, 8, 338-353.[15]Zimmermann, H.J. (1991), Fuzzy Set Theory and Its Applications, Boston: Kluwer Academic. zh_TW
