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 Title: 區間模糊相關係數及其在數學成就評量Fuzzy correlation with interval data and its application in the evaluation of mathematical achievement Authors: 羅元佐Ro, Yuan Tso Contributors: 吳柏林羅元佐Ro, Yuan Tso Keywords: 模糊相關係數區間資料數學成就評量Fuzzy correlationinterval dataevaluation of mathematical achievement Date: 2010 Issue Date: 2011-10-05 14:39:40 (UTC+8) Abstract: 在統計學上，我們常使用皮爾森相關係數(Pearson’s Correlation Coefficient)來表達兩變數間線性關係的強度，同時也表達出關係之方向。傳統之相關係數所處理的資料都是明確的實數值，但是當資料是模糊數時，並不適合使用傳統的方法來計算模糊相關係數。而本研究探討區間模糊樣本資料值求得模糊相關係數，首先將區間型模糊資料分為離散型和連續型，提出區間模糊相關係數定義，並提出廣義誤差公式，將相關係數作合理的調整，使所求的出相關係數更加精確。在第三章我們以影響數學成就評量的因素，作實證研究分析，得出合理的分析。而此相關係數定義和廣義誤差公式也能應用在兩資料值為實數或其中一筆資料值為實數的情況，可以解釋更多在實務上所發生的相關現象。In the statistic research, we usually express the magnitude of linear relation between two variables by means of Pearson’s Correlation Coefficient, which is also used to convey the direction of such relation. Traditionally, correlation coefficient deals with data which consist of specific real numbers. But when the data are composed of fuzzy numbers, it is not feasible to use this traditional approach to figure out the fuzzy correlation coefficient. The present study investigates the fuzzy samples of interval data to find out the fuzzy correlation coefficient. First, we categorize the fuzzy interval data into two types: discrete and continuous. Second, we define fuzzy correlation with interval data and propose broad formulas of error in order to adjust the coefficient more reasonably and deal with it more accurately. In Chapter Three, we conduct empirical research by the factor which affects the evaluation of mathematical achievement to acquire reasonable analysis. By doing so, broad definition of coefficient and formulas of error can also be applied to the conditions of either both values of the data are real number or one value of the data is real number, and can explain more related practical phenomenon. Reference: [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：俊傑書局。[3]吳柏林(2005)。模糊統計導論：方法與應用。台北：五南書局。[4]吳柏林(003)。現代統計學。台北：五南書局。[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]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。[8]林原宏(2004)。模糊相關係數。教育研究月刊，第122期，教育學科教室，心理測驗與統計，122,148-149。[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]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.[11]Chaudhuri, B. B., and Bhattacharya, A. (2001). On correlation between two fuzzy sets. Fuzzy Sets and Systems, 118,447-456.[12]Dorsey, D. W., and Coovert, M. D. (2003). Mathematical modeling of decisionmaking: A soft and fuzzy approach to capturing hard decisions, Human Factors,45(1), 117.[13]Gorsevski, P. V., Gessler, P. E., and Jankowsk, P. (2003). Integrating a fuzzyk-means classification and a Bayesian approach for spatial prediction oflandslide hazard, Journal of Geographical Systems, 5(3),223.[14]Hung, W. L, and Wu, J. W. (2001). A note on the correlation of fuzzy numbers byExpected interval. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9,517-523.[15]Klir,G.F. and Folger,T.A.(1988) Fuzzy Sets,Uncertainly and Information. Englewood Gliffs,NJ: Prentice Hall.[16]Liu, S. T. ,& Kao, C.(2002). Fuzzy measures for correlation of fuzzy numbers.Fuzzy Sets and Systems, 128,267-275.[17]Park, K. and Kim, S. (1996). A note on the fuzzy weighted additive rule. FuzzySets and Systems, 77, 315-320.[18]Regin, C. C. (2000). Fuzzy-Set social science. Chicago: University of ChicagoPress.[19]Smithson,M. (1987). Fuzzy Set analysis for behavioral and social sciences. New York. Springer-Verlag.[20]Yu, C. (1993) Correlation of fuzzy numbers. Fuzzy Sets and Systems 55,303-307.[21]Zadeh L.A. (1965) Fuzzy set. Information and Control, Vol. 8,338-353.[21]Zadeh, L. A., 1975, The concept of a linguistic variable and its application toApproximate 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 Setsand Systems, 1, 3-28.[23]Zimmermann, H.J. (1991) Fuzzy Set Theory and Its Applications. Boston: Kluwer Academic. Description: 碩士國立政治大學應用數學系數學教學碩士在職專班9797200299 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0097972002 Data Type: thesis Appears in Collections: [Department of Mathematical Sciences] Theses

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