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研究生:楊志清
研究生(外文):Yang, Chih Ching
論文名稱:模糊資料之相關係數研究及其應用
論文名稱(外文):Evaluating Correlation Coefficient with Fuzzy Data and Its Applications
指導教授:鄭宇庭鄭宇庭引用關係
指導教授(外文):Cheng, Yu Ting
學位類別:博士
校院名稱:國立政治大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
畢業學年度:101
語文別:中文
論文頁數:65
中文關鍵詞:模糊區間模糊區間相關係數模糊區間自相關係數
外文關鍵詞:Fuzzy interval correlationFuzzy dataAuto-Correlation coefficient
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近年來,由於人類對自然現象、社會現象或經濟現象的認知意識逐漸產生多元化的研判與詮釋,也因此致使人類思維數據化的概念已逐漸廣泛的被應用,對數據分析已從傳統以單一數值或平均值的分析作法,演變為考量多元化數值的分析作為。有鑑於此,在數據資料具備「模糊性」特質的現今,藉由模糊區間的演算方法,進一步探討之間的關係。
傳統的統計分析,對於兩變數間線性關係的強度判斷,一般是藉由皮爾森相關係數(Pearson’s Correlation Coefficient)的方法予以衡量,同時也可以經由係數的正、負符號判斷變數間的關係方向。然而,在現實生活中無論是環境資料或社會經濟資料等,均可能以模糊的資料型態被蒐集,如果當資料型態係屬於模糊性質時,將無法透過皮爾森相關係數的方法計算。
因此,本研究欲研擬一個較簡而易懂的方法,計算模糊區間資料的相關係數,據以呈現兩組模糊區間資料的相互影響程度。此外,若時間性之模糊區間資料被蒐集之際,我們亦提出利用中心點與長度之模糊自相關係數(ACF with the Fuzzy Data of Center and Length;簡稱CLACF)及模糊區間資料之自相關函數(ACF with Fuzzy Interval Data;簡稱FIACF)的方法,探討時間性模糊資料的自相關係數予以衡量。

The classical Pearson’s correlation coefficient has been widely adopted in various fields of application. However, when the data are composed of fuzzy interval values, it is not feasible to use such a traditional approach to evaluate the correlation coefficient. In this study, we propose the specific calculation of fuzzy interval correlation coefficient with fuzzy interval data to measure the relationship between various stocks.
In addition, in time series analysis, the auto-correlation function (ACF) can evaluate the effect of stationary for time series data. However, as the fuzzy interval data could be occurred, then the classical time series analysis will be not applied. In this paper, we proposed two approaches, ACF with the fuzzy data of center and length (CLACF) and ACF with fuzzy interval data (FIACF), to calculate the auto-correlation coefficient for fuzzy interval data, and use the scheme of Mote Carlo simulation to illustrate the effect of evaluation methods. Finally, we offer empirical study to indentify the performance of CLACF and FIACF which may measure the effect of lagged period of fuzzy interval data for daily price (low, high) of the Centralized Securities Trading Market and the result show that the effect of evaluation lagged period via CLACF and FIACF may response the effect more easily than classical evaluation of ACF for the close price of Centralized Securities Trading Market.

目 錄 I
表目錄 II
圖目錄 III
第壹章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 5
第三節 研究流程 5
第貳章 文獻回顧 8
第一節 模糊集合與運算 8
第二節 模糊相關係數 10
第三節 模糊相關係數應用之文獻探討 20
第參章 研究方法 22
第一節 模糊區間相關係數 22
第二節 模糊區間自相關係數 24
第肆章 研究分析 28
第一節 模擬分析 28
第二節 實證分析 47
第伍章 結論 60
參考文獻 63
一、中文部分 63
二、英文部分 63
一、中文部分
1.吳柏林,1994,時間數列分析導論,台北:華泰書局。
2.吳柏林,2005,模糊統計導論:方法與應用,台北:五南出版社。
3.阮亨中、吳柏林,2000,模糊數學與統計應用,台北:俊傑書局。
4.謝名娟、吳柏林,2012, 高中學生時間運用與學習表現關聯之研究:模糊相關的應用,教育政策論壇,第15卷第1期,頁157-176。
二、英文部分
1.Arulchinnappan, S., Karunakaran, K. and Rajendran, G., 2011, The use of fuzzy correlation to identify people at risk of oral cancer. European Journal of Scientific Research, 52(3), 332-338.
2.Buckley, J. J., 2003, Fuzzy probabilities: New Approach and Applications. Physics-Verlag, Heidelberg, Germany.
3.Buckley, J. J., 2003, Fuzzy statistics. Springer-Verlag, Heidelberg, Germany.
4.Bustince, H. and Burillo, P., 1995, Correlation of interval-valued intuitionistic fuzzy set. Fuzzy Sets and Systems, 74, 237-244.
5.Carlsson, C. and Fuller, R., 2001, On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems, 122, 315-326.
6.Chaudhuri, B. B. and Bhattacharya, A., 2001, On correlation between two fuzzy sets. Fuzzy Sets and Systems, 118, 447-456.
7.Cheng, Y. T. and Yang, C. C. (2013). An Approach of Stocks Substitution Strategy Using Fuzzy Interval Correlation Coefficient. Communications in Statistics - Simulation and Computation. (accepted)
8.Chiang, D. and Lin, N. P., 1999, Correlation of fuzzy sets. Fuzzy Sets and Systems, 102, 221-226.
9.Dubois, D. and Prade, H., 1987, The mean value of a fuzzy number. Fuzzy Sets and Systems, 24, 279-2300.
10.Glavo, T. and Mesiar, R., 2001, Generalized Medians. Fuzzy Sets and Systems, 124, 59-64.
11.Heilpern, S., 1992, The expected value of a fuzzy number. Fuzzy Sets and Systems, 47, 81-86.
12.Hsu, H. and Wu, B., 2010, An innovative approach on fuzzy correlation coefficient with interval data. International Journal of Innovative Computing, Information and Control, 6(3), 1-13.
13.Hung, W. L. and Wu, J. W., 2001, A note on the correlation of fuzzy numbers by Expected interval. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9, 517-523.
14.Hung, W. L. and Wu, J. W., 2002, Correlation of fuzzy numbers by α-cut method. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10, 725-735.
15.Korner, R., 1997, On the variance of fuzzy random variables. Fuzzy Sets and Systems, 92, 83-93.
16.Kwakernaak, H., 1978, Fuzzy Random Variables. Part I: Definitions and theorems. Information Sciences, 15, 1-15.
17.Lin, N. P. and Chueh, H., 2007, Fuzzy correlation rules mining. Proceedings of the 6th WSEAS International Conference on Applied Computer Science, Hangzhou, China, April, 13-18.
18.Liu, S. and Kao, C., 2002, Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems, 128, 267-275.
19.Wu, H. C., 1999, Probability density functions of Fuzzy Random Variables. Fuzzy Sets and Systems, 105, 139-158.
20.Yang, C. C., Wu, B. and Sriboonchitta, S., 2012, A New Approach on Correlation Evaluation with Fuzzy Data in Econometrics. International Journal of Intelligent Technologies and Applied Statistics, 5(2), 109-120.
21.Yu, C., 1993, Correlation of fuzzy numbers. Fuzzy Sets and Systems, 55, 303-307.
22.Zadeh, L. A., 1965, Fuzzy Sets. Information and Control, 8, 228-353.

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