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題名 模 糊 無 母 數 統 計 檢 定 及 其在 高 齡 化 社 會 調 查 之 應 用
The Fuzzy nonparametric statistical test and its application on the survey of an aging society
作者 趙淑倫
貢獻者 吳柏林
Wu, Berlin
趙淑倫
關鍵詞 反模糊化轉換
模糊統計分析
中位數檢定
變異數檢定
高齡化社會
counter-fuzzy transformation
fuzzy statistical analysis
median test
variance test
aging society
日期 2011
上傳時間 17-Apr-2012 09:16:02 (UTC+8)
摘要 在逐漸高齡化的社會中,關注老人的生活議題並加以分析益顯重要。在研究老人問題時,由於研究對象均曾經歷不同的時空背景與人生閱歷,各個體間存在的差異極大;不同族群的老人對其所慣用語彙的理解與表達亦不盡相同。故若利用傳統的統計分析研究結果,強迫人們採用二元邏輯的方式思考與解釋,可能會導致偏差或錯誤的結論。且傳統的統計檢定方法,往往假定取樣的樣本滿足某個分配,因而導致過多的解釋,影響決策品質。
因此,為避免因誤解老人而造成虛耗社會成本,使有限的社會資源得以充分運用,本文於研究老人身心特質與個人期待時,嘗試以模糊理論的軟計算,提出反模糊化轉換。並應用中位數檢定及變異數檢定,建立當統計參數為模糊數或模糊區間時之小樣本無母數模糊統計檢定方法模型。由實證例子分析結果顯示,我們提出的檢定方法,能有效分析模糊樣本的問題,並進而期望能對老人議題的分析和決策有所貢獻,及將此方法運用於其它模糊性議題之研究。
In a gradually aging society, it is important to pay attention to and then analyze elderly people’s life issues. When a study about elderly people is undertaken, the subjects are very inconsistent given their diverse life experience, and various subgroups of subjects have quite different understanding of and way of expressing a vocabulary. Therefore, analyzing study result with conventional statistical analysis method, which forces thinking in a binary logic way, may lead to biased or erroneous conclusion. Furthermore, a conventional statistical test, usually assuming a certain distribution for its samples, may lead to exaggerated explanation, which is detrimental to the quality of a decision.
So, in order to avoid the waste of our social cost from misunderstanding of the elderly, and to make the most use of our limited social resource, when we investigated the elderly people’s personal characteristics and expectations, we tried to apply the soft calculation of the fuzzy theory, proposed the counter-fuzzy transformation, and, by using the median test and variance test, established a nonparametric fuzzy statistical model for small-sized samples and for parameters of the fuzzy number or fuzzy interval types. The analyses of real-world examples demonstrated that this method of statistical test can analyze the problems of fuzzy samples, and can hopefully contribute to improved analysis and decision making of the elderly people’s issues, and apply this method on the investigation of other fuzzy social issues.

Key words: counter-fuzzy transformation, fuzzy statistical analysis, median test, variance test, aging society.
參考文獻 1. 吳柏林(2005)。模糊統計導論方法與應用, 頁159-173。台北:五南書局。
2. 阮亨中、吳柏林(2000)。模糊數學與統計應用,頁233-250; 頁319-341。台北:俊傑書局。
3. 吳柏林(1999)。現代統計學,頁252-255。台北:五南書局。
4. 顏月珠(1992)。無母數統計方法,頁180-183。台北 : 三民書局。
5. 王文俊(2007)。認識 Fuzzy,頁22-29。台北:全華書局。
6. 劉應明、任平(1994)。模糊數學,頁33-34;頁66-67。台北 : 凡異書局。
7. Larson, R., Hostetler, R. and Edwards B. H. (2008). Essential Calculus: Early Transcendental Functions. Houghton Mifflin Company, Boston, New York.
8. Nguyen, H.T. and Wu, B. (2006) Fundamentals of Statistics with Fuzzy Data.
9. Chen S.Y. (2006) “Nonparametric test with fuzzy data,” NCCU. Master Thesis.
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
98972003
100
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098972003
資料類型 thesis
dc.contributor.advisor 吳柏林zh_TW
dc.contributor.advisor Wu, Berlinen_US
dc.contributor.author (Authors) 趙淑倫zh_TW
dc.creator (作者) 趙淑倫zh_TW
dc.date (日期) 2011en_US
dc.date.accessioned 17-Apr-2012 09:16:02 (UTC+8)-
dc.date.available 17-Apr-2012 09:16:02 (UTC+8)-
dc.date.issued (上傳時間) 17-Apr-2012 09:16:02 (UTC+8)-
dc.identifier (Other Identifiers) G0098972003en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/52770-
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) 98972003zh_TW
dc.description (描述) 100zh_TW
dc.description.abstract (摘要) 在逐漸高齡化的社會中,關注老人的生活議題並加以分析益顯重要。在研究老人問題時,由於研究對象均曾經歷不同的時空背景與人生閱歷,各個體間存在的差異極大;不同族群的老人對其所慣用語彙的理解與表達亦不盡相同。故若利用傳統的統計分析研究結果,強迫人們採用二元邏輯的方式思考與解釋,可能會導致偏差或錯誤的結論。且傳統的統計檢定方法,往往假定取樣的樣本滿足某個分配,因而導致過多的解釋,影響決策品質。
因此,為避免因誤解老人而造成虛耗社會成本,使有限的社會資源得以充分運用,本文於研究老人身心特質與個人期待時,嘗試以模糊理論的軟計算,提出反模糊化轉換。並應用中位數檢定及變異數檢定,建立當統計參數為模糊數或模糊區間時之小樣本無母數模糊統計檢定方法模型。由實證例子分析結果顯示,我們提出的檢定方法,能有效分析模糊樣本的問題,並進而期望能對老人議題的分析和決策有所貢獻,及將此方法運用於其它模糊性議題之研究。
zh_TW
dc.description.abstract (摘要) In a gradually aging society, it is important to pay attention to and then analyze elderly people’s life issues. When a study about elderly people is undertaken, the subjects are very inconsistent given their diverse life experience, and various subgroups of subjects have quite different understanding of and way of expressing a vocabulary. Therefore, analyzing study result with conventional statistical analysis method, which forces thinking in a binary logic way, may lead to biased or erroneous conclusion. Furthermore, a conventional statistical test, usually assuming a certain distribution for its samples, may lead to exaggerated explanation, which is detrimental to the quality of a decision.
So, in order to avoid the waste of our social cost from misunderstanding of the elderly, and to make the most use of our limited social resource, when we investigated the elderly people’s personal characteristics and expectations, we tried to apply the soft calculation of the fuzzy theory, proposed the counter-fuzzy transformation, and, by using the median test and variance test, established a nonparametric fuzzy statistical model for small-sized samples and for parameters of the fuzzy number or fuzzy interval types. The analyses of real-world examples demonstrated that this method of statistical test can analyze the problems of fuzzy samples, and can hopefully contribute to improved analysis and decision making of the elderly people’s issues, and apply this method on the investigation of other fuzzy social issues.

Key words: counter-fuzzy transformation, fuzzy statistical analysis, median test, variance test, aging society.
en_US
dc.description.tableofcontents 第1章 前言 1

第2章 思維的模糊性 3
2.1模糊理論 3
2.2隸屬度函數 4

第3章 模糊數與反模糊化轉換 7
3.1模糊數 7
3.2反模糊化轉換 12
3.3有關反模糊化轉換的一些性質 14

第4章 中位數檢定 18
4.1模糊中位數 18
4.2中位數檢定法 22
4.3變異數檢定法 27

第5章 實例研究 32
5.1應用離散型模糊數分析和檢定老人外出時間 32
5.2應用連續區型梯形模糊數分析和檢定理想中的退休年齡 35
5.3應用連續型梯形模糊數分析和檢定老人看電視時間 37
5.4比較應用連續型梯形模糊數及離散型模糊數分析和檢定是否為成功生活的老人 40

第6章 結論與討論 48

參考文獻 49
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098972003en_US
dc.subject (關鍵詞) 反模糊化轉換zh_TW
dc.subject (關鍵詞) 模糊統計分析zh_TW
dc.subject (關鍵詞) 中位數檢定zh_TW
dc.subject (關鍵詞) 變異數檢定zh_TW
dc.subject (關鍵詞) 高齡化社會zh_TW
dc.subject (關鍵詞) counter-fuzzy transformationen_US
dc.subject (關鍵詞) fuzzy statistical analysisen_US
dc.subject (關鍵詞) median testen_US
dc.subject (關鍵詞) variance testen_US
dc.subject (關鍵詞) aging societyen_US
dc.title (題名) 模 糊 無 母 數 統 計 檢 定 及 其在 高 齡 化 社 會 調 查 之 應 用zh_TW
dc.title (題名) The Fuzzy nonparametric statistical test and its application on the survey of an aging societyen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. 吳柏林(2005)。模糊統計導論方法與應用, 頁159-173。台北:五南書局。zh_TW
dc.relation.reference (參考文獻) 2. 阮亨中、吳柏林(2000)。模糊數學與統計應用,頁233-250; 頁319-341。台北:俊傑書局。zh_TW
dc.relation.reference (參考文獻) 3. 吳柏林(1999)。現代統計學,頁252-255。台北:五南書局。zh_TW
dc.relation.reference (參考文獻) 4. 顏月珠(1992)。無母數統計方法,頁180-183。台北 : 三民書局。zh_TW
dc.relation.reference (參考文獻) 5. 王文俊(2007)。認識 Fuzzy,頁22-29。台北:全華書局。zh_TW
dc.relation.reference (參考文獻) 6. 劉應明、任平(1994)。模糊數學,頁33-34;頁66-67。台北 : 凡異書局。zh_TW
dc.relation.reference (參考文獻) 7. Larson, R., Hostetler, R. and Edwards B. H. (2008). Essential Calculus: Early Transcendental Functions. Houghton Mifflin Company, Boston, New York.zh_TW
dc.relation.reference (參考文獻) 8. Nguyen, H.T. and Wu, B. (2006) Fundamentals of Statistics with Fuzzy Data.zh_TW
dc.relation.reference (參考文獻) 9. Chen S.Y. (2006) “Nonparametric test with fuzzy data,” NCCU. Master Thesis.zh_TW