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題名 模糊相關係數及其應用
作者 江彥聖
貢獻者 吳柏林
江彥聖
關鍵詞 模糊相關係數
模糊區間
模糊資料
Fuzzy correlation coefficient
Fuzzy interval
Fuzzy data
日期 2008
上傳時間 17-Sep-2009 13:49:23 (UTC+8)
摘要 科學研究中,我們常關注變數間是否存在某種相關,及其相關的程度與方向。但傳統的相關分析方法,並不適用於更能表達真實情況的模糊資料。

在統計學中,討論資料之相關性的統計量有許多,本研究旨在針對討論兩變數間之線性關係的皮爾森相關係數 (Pearson Product-Moment Correlation Coefficient),以模糊統計方法的角度,提出合理的模糊直線相關係數定義,以協助處理區間模糊資料,瞭解模糊資料間的線性關係。
In the scientific research, we often pay attention to whether there are some relations between two variables, and the strength and direction of a linear relationship. But the traditional statistics method is not suitable for the fuzzy data.

There are a lot of statistics of discussing the relevance between two variables. In this study, a modified method, combining Pearson Product-Moment Correlation Coefficient and fuzzy theory, was applied to deal with the fuzzy data, and find the linear relation among them.
參考文獻 [1] 王文俊 (1997)。認識Fuzzy。台北:全華書局。
[2] 阮亨中、吳柏林(2000)。模糊數學與統計應用。台北:俊傑。
[3] 吳柏林(2005)。模糊統計導論:方法與應用。台北:五南。
[4] 吳柏林(2002)。現代統計學。台北:前程。
[5] 吳柏林(1997)。社會科學研究中的模糊邏輯與模糊統計分析。國立政治大學研究通訊,7,17-38。
[6] 吳柏林(1995)。模糊統計分析:問卷調查研究的新方向。國立政治大學研究通訊,2, 65-80。
[7] 李允中、王小璠、蘇木春 (2003)。模糊理論及其應用。全華科技圖書股份有限公司。
[8] 林原宏(2007)。模糊理論在社會科學研究的方法論之回顧。量化研究學刊,第一卷,第一期,2007,53-84。
[9] 馮國臣、任麗偉(2007) 模糊理論-基礎與應用。台北:新文京開發。
[10] 藎壚(1991)。實用模糊數學。台北:亞東。
[11] Amo, A., Montero, J., Biging, G. and Cutello, V. (2004). Fuzzy classification systems, European Journal of Operational Research, 156(2), 495.
[12] Buckley, J. J. (2004). Fuzzy Statistics, Springer-Verlag, Heidelberg, Germany.
[13] Carrano A. L., Taylor, J. B., Young, R E., Lemaster R. L. and Saloni, D. E. (2004). Fuzzy knowledge-based modeling and statistical regression in abrasive wood machining, Forest Products Journal, 54(5), 66-72.
[14] Dorsey, D. W., and Coovert, M. D. (2003).Mathematical modeling of decision making: A soft and fuzzy approach to capturing hard decisions, Human Factors, 45(1), 117.
[15] Gorsevski, P. V., Gessler, P. E., and Jankowsk, P. (2003). Integrating a fuzzy k-means classification and a Bayesian approach for spatial prediction of landslide hazard, Journal of Geographical Systems, 5(3),223.
[16] Klir, G and Yuan, (1995). Fuzzy Sets and Fuzzy Logic-Theory and Applications. Prentice-Hall, Upper Saddle River, Ni.
[17] Park, K. and Kim, S. (1996). A note on the fuzzy weighted additive rule. Fuzzy Sets and Systems, 77, 315-320.
[18] Shiang-Tai Liu, Chiang Kao (2002)。 ‘Fuzzy measures for correlation coefficient of fuzzy numbers’, Fuzzy Sets and Systems, 128, p.267-275
[19] Wang, H. and Bell, P. (1996). Fuzzy clustering analysis and multifactor evaluation for students’ imaginative power in physics problem solving. Fuzzy Sets and Systems, 78, 95-105.
[20] Zadeh, L. A., 1965, Fuzzy sets. Information and Control, 8, 338-353.
[21] Zadeh, L. A., 1975, The concept of a linguistic variable and its application to approximate reasoning. Information Science, 8, 199-249(I), 301-357(II).
[22] Zadeh, L. A., 1978, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3-28.
描述 碩士
國立政治大學
應用數學研究所
95972008
97
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0095972008
資料類型 thesis
dc.contributor.advisor 吳柏林zh_TW
dc.contributor.author (Authors) 江彥聖zh_TW
dc.creator (作者) 江彥聖zh_TW
dc.date (日期) 2008en_US
dc.date.accessioned 17-Sep-2009 13:49:23 (UTC+8)-
dc.date.available 17-Sep-2009 13:49:23 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:49:23 (UTC+8)-
dc.identifier (Other Identifiers) G0095972008en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32599-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 95972008zh_TW
dc.description (描述) 97zh_TW
dc.description.abstract (摘要) 科學研究中,我們常關注變數間是否存在某種相關,及其相關的程度與方向。但傳統的相關分析方法,並不適用於更能表達真實情況的模糊資料。

在統計學中,討論資料之相關性的統計量有許多,本研究旨在針對討論兩變數間之線性關係的皮爾森相關係數 (Pearson Product-Moment Correlation Coefficient),以模糊統計方法的角度,提出合理的模糊直線相關係數定義,以協助處理區間模糊資料,瞭解模糊資料間的線性關係。
zh_TW
dc.description.abstract (摘要) In the scientific research, we often pay attention to whether there are some relations between two variables, and the strength and direction of a linear relationship. But the traditional statistics method is not suitable for the fuzzy data.

There are a lot of statistics of discussing the relevance between two variables. In this study, a modified method, combining Pearson Product-Moment Correlation Coefficient and fuzzy theory, was applied to deal with the fuzzy data, and find the linear relation among them.
en_US
dc.description.tableofcontents 摘要 v
Abstract vi
目次 vii
圖目次 viii
表目次 ix
1、 前言 1
2、 研究方法 2
2.1 模糊統計量 2
2.2 傳統線性相關係數與模糊線性相關係數 12
3、 實例應用 17
3.1 教學年資與教師專業成長指標重要性之模糊線性相關係數 17
3.2 兩個教師專業成長指標重要性之模糊線性相關係數 21
4、 結論與建議 23
5、 參考文獻 24


圖目次

圖2.1 專家對「有效使用教學媒體與教具」重要性隸屬度函數 3
圖2.2 評選教師對教科書的滿意程度之三角形隸屬度函數 6
圖2.3 三角形隸屬度函數的 截集 8
圖2.4 為實數, 為區間模糊數之資料分布圖 13
圖2.5 與 均為區間模糊數之資料分布圖 14
圖2.6 處理模糊變數之線性相關係數流程 15

表目次

表2.1 專家對「有效使用教學媒體與教具」重要性隸屬度函數 3
表2.2 考生對97年指定考科數學乙的難易看法隸屬度 4
表2.3 評選教師對教科書的滿意程度 5
表2.4 試教委員對試教老師的表現滿意隸屬度 7
表2.5 教師評估學生在課堂表現的用心隸屬度 9
表2.6 老師對某轉學生的日常生活表現滿意程度隸屬度 10
表3.1 專家對「經常使用教學媒體與教具輔助教學」指標之重要性隸屬度 17
表3.2 專家的教學年資與對該指標重要性看法的模糊區間 19
表3.3 不同的 值與對應的模糊線性相關係數 20
表3.4 專家對「詳盡批改作業以了解學生個別學習盲點」指標之重要性隸屬度 21
表3.5 兩指標之模糊區間 21
表3.6 不同的 值與對應的模糊線性相關係數 22
zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0095972008en_US
dc.subject (關鍵詞) 模糊相關係數zh_TW
dc.subject (關鍵詞) 模糊區間zh_TW
dc.subject (關鍵詞) 模糊資料zh_TW
dc.subject (關鍵詞) Fuzzy correlation coefficienten_US
dc.subject (關鍵詞) Fuzzy intervalen_US
dc.subject (關鍵詞) Fuzzy dataen_US
dc.title (題名) 模糊相關係數及其應用zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] 王文俊 (1997)。認識Fuzzy。台北:全華書局。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。台北:俊傑。zh_TW
dc.relation.reference (參考文獻) [3] 吳柏林(2005)。模糊統計導論:方法與應用。台北:五南。zh_TW
dc.relation.reference (參考文獻) [4] 吳柏林(2002)。現代統計學。台北:前程。zh_TW
dc.relation.reference (參考文獻) [5] 吳柏林(1997)。社會科學研究中的模糊邏輯與模糊統計分析。國立政治大學研究通訊,7,17-38。zh_TW
dc.relation.reference (參考文獻) [6] 吳柏林(1995)。模糊統計分析:問卷調查研究的新方向。國立政治大學研究通訊,2, 65-80。zh_TW
dc.relation.reference (參考文獻) [7] 李允中、王小璠、蘇木春 (2003)。模糊理論及其應用。全華科技圖書股份有限公司。zh_TW
dc.relation.reference (參考文獻) [8] 林原宏(2007)。模糊理論在社會科學研究的方法論之回顧。量化研究學刊,第一卷,第一期,2007,53-84。zh_TW
dc.relation.reference (參考文獻) [9] 馮國臣、任麗偉(2007) 模糊理論-基礎與應用。台北:新文京開發。zh_TW
dc.relation.reference (參考文獻) [10] 藎壚(1991)。實用模糊數學。台北:亞東。zh_TW
dc.relation.reference (參考文獻) [11] Amo, A., Montero, J., Biging, G. and Cutello, V. (2004). Fuzzy classification systems, European Journal of Operational Research, 156(2), 495.zh_TW
dc.relation.reference (參考文獻) [12] Buckley, J. J. (2004). Fuzzy Statistics, Springer-Verlag, Heidelberg, Germany.zh_TW
dc.relation.reference (參考文獻) [13] Carrano A. L., Taylor, J. B., Young, R E., Lemaster R. L. and Saloni, D. E. (2004). Fuzzy knowledge-based modeling and statistical regression in abrasive wood machining, Forest Products Journal, 54(5), 66-72.zh_TW
dc.relation.reference (參考文獻) [14] Dorsey, D. W., and Coovert, M. D. (2003).Mathematical modeling of decision making: A soft and fuzzy approach to capturing hard decisions, Human Factors, 45(1), 117.zh_TW
dc.relation.reference (參考文獻) [15] Gorsevski, P. V., Gessler, P. E., and Jankowsk, P. (2003). Integrating a fuzzy k-means classification and a Bayesian approach for spatial prediction of landslide hazard, Journal of Geographical Systems, 5(3),223.zh_TW
dc.relation.reference (參考文獻) [16] Klir, G and Yuan, (1995). Fuzzy Sets and Fuzzy Logic-Theory and Applications. Prentice-Hall, Upper Saddle River, Ni.zh_TW
dc.relation.reference (參考文獻) [17] Park, K. and Kim, S. (1996). A note on the fuzzy weighted additive rule. Fuzzy Sets and Systems, 77, 315-320.zh_TW
dc.relation.reference (參考文獻) [18] Shiang-Tai Liu, Chiang Kao (2002)。 ‘Fuzzy measures for correlation coefficient of fuzzy numbers’, Fuzzy Sets and Systems, 128, p.267-275zh_TW
dc.relation.reference (參考文獻) [19] Wang, H. and Bell, P. (1996). Fuzzy clustering analysis and multifactor evaluation for students’ imaginative power in physics problem solving. Fuzzy Sets and Systems, 78, 95-105.zh_TW
dc.relation.reference (參考文獻) [20] Zadeh, L. A., 1965, Fuzzy sets. Information and Control, 8, 338-353.zh_TW
dc.relation.reference (參考文獻) [21] Zadeh, L. A., 1975, The concept of a linguistic variable and its application to approximate reasoning. Information Science, 8, 199-249(I), 301-357(II).zh_TW
dc.relation.reference (參考文獻) [22] Zadeh, L. A., 1978, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3-28.zh_TW