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| Title: | 模糊資料相關係數及在數學教育之應用
Correlation of fuzzy data and its applications in mathematical education |
| Authors: | 林立夫 |
| Contributors: | 吳柏林
林立夫 |
| Keywords: | 模糊統計
區間模糊數
模糊相關係數
Fuzzy statistics
Interval fuzzy number
Fuzzy correlation coefficient |
| Date: | 2010 |
| Issue Date: | 2011-10-05 14:39:45 (UTC+8) |
| Abstract: | 兩變數之間是否相關，以及相關的程度與方向是統計研究學者所關注的一項課題。傳統上使用皮爾森相關係數(Pearson’s Correlation Coefficient)來表達兩實數變數間線性關係的強度與方向。然而，對於反映人類思維不確定性的模糊資料而言，傳統的相關分析方法卻有不足與不適用之缺失。
本論文的主要目的在於尋求一個合理、適用的區間模糊資料相關係數，提供研究者簡單且容易計算的模糊相關係數求法，用以了解區間模糊資料間的相關程度。接著利用轉換離散型模糊數成為區間模糊數的方式，處理離散型模糊資料間的相關係數。最後，以國中數學教學現場所調查的資料做實例應用。
In statistical studies, the correlation between two variables and its strength and direction are always concerned. Traditionally, the Pearson’s Correlation Coefficient is used to convey the linear relationship between two variables. However, the traditional correlation analysis is not applicable to the fuzzy data which are able to reflect more appropriately the uncertainty of human thinking.
The main purpose of the study is to find a reasonable and usable correlation coefficient of interval fuzzy data which provides researchers a simple and easy way to calculate and find the fuzzy correlation coefficient. Meanwhile, it can help us understand the correlation of interval fuzzy data. Moreover, we use the process of transforming discrete fuzzy number into the interval fuzzy number to deal with the correlation coefficient of discrete fuzzy data. Finally, we utilize the data from mathematics teaching in junior high school for application. |
| Reference: | [1]江彥聖 (2008)。模糊相關係數及其應用。碩士論文，國立政治大學，台北市。
[2]吳柏林 (2005)。模糊統計導論：方法與應用。台北：五南。
[3]Buckley, J. J. (2003). Fuzzy Probabilities: New Approach and Applications, Physics-Verlag, Heidelberg, Germany.
[4]Buckley, J. J. (2004). Fuzzy Statistics, Springer-Verlag, Heidelberg, Germany.
[5]Carlsson, C., Fuller, R. (2001). On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122, 315-326.
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[8]Gebhardt, J., Gil, M. A., and Kruse, R. (1998). Fuzzy set-theoretic methods in statistics, in: R. Slowinski(Ed.), Handbook on Fuzzy Sets, Fuzzy Sets in Decision Anaysis, Operations Research, and Statistics, vol. 5, Kluwer Academic Publishers, New York, 311-347.
[9]H. T. Nguyen and B. Wu (2006) Fundamentals of Statistics with Fuzzy Data. New York：Springer.
[10]Heilpern, S. (1992). The expected value of a fuzzy number, Fuzzy Sets and Systems 47, 81-86.
[11]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.
[12]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.
[13]Korner, R. (1997). On the Variance of Fuzzy Random Variables, Fuzzy Sets and Systems Vol. 92, 83-93.
[14]Liu, S. T. and Kao, C. (2002). Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems 128, 267-275
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[16]Zadeh, L.A., (1965). Fuzzy sets. Information and Control 8, 338-353. |
| Description: | 碩士
國立政治大學
應用數學系數學教學碩士在職專班
97972014
99 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0097972014 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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