進階搜尋


 
系統識別號 U0026-0812200911262431
論文名稱(中文) 模糊資料統計檢定模式之研究與應用
論文名稱(英文) The Research and Application of Statistical Testing Model with Fuzzy Data
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系碩博士班
系所名稱(英) Department of Industrial and Information Management
學年度 93
學期 2
出版年 94
研究生(中文) 陳正哲
研究生(英文) Cheng-Che Chen
電子信箱 chengche@cc.fec.edu.tw
學號 r3888103
學位類別 博士
語文別 中文
論文頁數 78頁
口試委員 指導教授-蔡長鈞
口試委員-吳植森
口試委員-陳梁軒
口試委員-周碩彥
召集委員-盧淵源
中文關鍵字 模糊製程能力指標  模糊相關係數  模糊資料  模糊數  假設檢定 
英文關鍵字 Fuzzy process capability index  Fuzzy data  Fuzzy correlation coefficient  Fuzzy number  Hypothesis testing 
學科別分類
中文摘要   統計之假設檢定已廣泛地應用於各領域, 其目的在於建立一套拒絕或接受假設的統計法則。當統計檢定模式中之數值資料為語意辭句或不明確數值時,則模式即成為模糊資料統計檢定模式。

  本文利用模糊集合之α截集與擴展法則,將模糊資料統計檢定模式簡化成一對有界且具有α水準參數之傳統統計檢定模式。在特定之α水準下,根據此對模式可求得檢定統計量之上下限;經由多個不同α水準之模糊檢定統計量的上下限,即可建構出模糊檢定統計量之歸屬函數。藉由此歸屬函數,可求得拒絕虛無假設之機率或可替代P值,經與顯著水準比較即可下統計決策。由於以歸屬函數形式表達模糊檢定統計量的值為一區間,因此能提供管理者更多之資訊。

  本研究發展隨機性檢定法與可替代P值檢定法,分別在母體變異數已知與未知時,進行單母體平均數之假設檢定。本文亦應用隨機性檢定法檢定兩常態母體平均數差之假設。不同於傳統檢定之二元決策:拒絕或接受虛無假設,本研究所提供之模糊決策可用來表示虛無假設被拒絕或接受之可能性。若相依樣本之模糊差異不服從常態分配時,則以符號距離排序法解模糊化,再利用傳統之符號檢定探討兩母體是否有差異。在明確數值資料下,本文所發展之模糊資料統計檢定模式會變為傳統之統計檢定模式。

  在語意辭句及資料不完全之情況下,本文以國內一所技術學院四技推薦甄試為應用實例,說明如何應用隨機性檢定法評估口試成績與書面審查成績不具有80%以上之高度相關。最後本研究亦使用隨機性檢定法於模糊資料製程能力指標 之假設檢定,以評估製程是否滿足能力需求與品質水準。經以上各項之分析探討,可顯示模糊資料統計檢定模式為研判模糊數據而下決策之有效方法。



英文摘要  Statistical hypotheses testing has been widely applied to different areas for establishing a set of statistical rules to reject or accept a hypothesis. The existing statistical testing models are limited to crisp data. This research proposes a fuzzy data statistical testing model to proceed statistical tests with fuzzy data.

 The idea is based on the α-cuts and extension principle to a fuzzy data statistical testing model to a family of crisp statistical testing model, which can be described by a pair of parametric programs, to find the lower and upper bounds of the efficiency measures at α level. From different levels α, the membership function of fuzzy test statistic can be constructed correspondingly. Based on these membership functions, we can derive the probability of rejecting null hypothesis or an alternative p-value, which is used to compare with the significant level to make a statistical decision. Since the value of fuzzy test statistic expressed by membership function is in the form of interval, more information is provided for management.

 This research develops two approaches, a randomized test approach and an alternative p-value approach, to proceed statistical tests of mean for normal population with known and unknown population variance. The tests of central tendency of two dependent populations concerning paired fuzzy sample differences using the randomized test approach is also discussed in this thesis. Unlike classical tests, which provide only binary decisions, fuzzy decision, proposed by this research, can be used to show the possibility of rejecting or accepting the null hypothesis. When the distribution is non-normal, a signed distance method is used to determine the distance between two fuzzy numbers and to define ranking. After the fuzzy problem is defuzzified, the classical sign test is applied to determine whether the medians of two populations are equal. When the data are crisp, the proposed method reduces to the classical testing methods.

 When data is in the form of linguistic and incomplete, tests of correlation coefficient between interview scores and academic scores from of candidates for admission to a college in Taiwan is to demonstrate the interpretation of test of correlation coefficient with fuzzy data. The correlation between those two scores does not exceed 80% and is insignificant. Finally, the tests of fuzzy data process capability index using the randomized test approach is discussed to judge whether a process meets the present quality requirement and runs under the desired quality condition. It is shown that the fuzzy data statistical testing model is an effective approach to analysis data and make decision under fuzzy environment.



論文目次 中文摘要.....I
英文摘要.....II
致 謝...III
圖 目 錄.....VI
表 目 錄.....VIII
第一章 緒論.....1
第一節 研究動機.....1
第二節 研究目的.....1
第三節 研究架構.....2
第二章 文獻探討.....4
第一節 明確的統計假設,明確的需求,但資料是模糊的檢定模式.....4
第二節 明確的需求,明確的資料,但統計假設是模糊的檢定模式.....6
第三節 明確的統計假設,明確的資料,但需求是模糊的檢定模式.....7
第四節 明確的需求,但統計假設與資料是模糊的檢定模式.....8
第五節 模糊相關係數.....8
第六節 模糊製程能力指標.....9
第七節 文獻回顧結語.....10
第三章 隨機性檢定法與可替代P值檢定法.....12
第一節 隨機性檢定法.....12
第二節 可替代P值檢定法.....27
第四章 模糊資料雙母體平均數差之假設檢定.....39
第一節 兩獨立模糊樣本常態母體平均數差之假設檢定.....39
第二節 兩相依模糊樣本母體平均數差之假設檢定.....45
第五章 模糊資料相關係數之假設檢定.....52
第一節 模糊資料相關係數等於零之假設檢定.....52
第二節 模糊資料相關係數不等於零之假設檢定.....57
第六章 模糊資料製程能力指標 之假設檢定.....62
第一節 製程能力指標.....62
第二節 製程能力指標 之評估與檢定.....64
第七章 結論與未來研究方向.....69
參考文獻.....71
附 錄.....75

參考文獻 1. Arnold, B. F.,1995, Statistical tests optimally meeting certain fuzzy requirements on the power function and on the sample size, Fuzzy Sets and Systems 75, 365-372.
2. Bustince, H. and P. Burillo, 1995, Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 74, 237-244.
3. Casals, M. R., M. A. Gil and P. Gil, 1986a, The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information, European Jouranl of Operational Research 27, 371-382.
4. Casals, M. R., M. A. Gil and P. Gil, 1986b, On the use of Zadeh’s probabilistic definition for testing statistical hypotheses from fuzzy information, Fuzzy Sets and Systems 20,175-190.
5. Casals, M. R. and M. A. Gil, 1989, A note on the operativeness of Neyman-Pearson tests with fuzzy information, Fuzzy Sets and Systems 30, 215-220.
6. Casals, M. R., and P. Gil, 1994, Bayesian sequential test for fuzzy parametric hypotheses from fuzzy information, Information Sciences 80, 283-298.
7. Chan, L. K., S. W. Cheng and F. A. Spiring, 1988, The robustness of the process capability index to departures from normality, In: Statistical Theory and Data Analysis II, (Proc. Second Pacific Area Statistical Conference), Tokyo, 223-239.
8. Chaudhuri, B. B. and A. Bhattacharya, 2001, On correlation between two fuzzy sets, Fuzzy Sets and Systems 118, 447-456.
9. Chiang, D. A. and N. P. Lin, 1999, Correlation of fuzzy sets, Fuzzy Sets and Systems 102, 221-226.
10. Chou, Y. M. and D. B. Owen, 1989, On the distributions of the estimated process capability indices, Commun. Statist. – Theory and Methods 18(12), 4549-4560.
11. Chou, Y. M., D. B. Owen and S. A. Borrego, 1990, Lower confidence limits on process capability indices, Journal of Quality Technology 22(3), 223-229.
12. Delgado, M., J. L. Verdegay and M. A. Vila, 1985, Testing fuzzy hypotheses. A Bayesian approach, In: M. M. Gupta and A. Kandel, W. Bandler and J. B. Kiszka(eds.), Approximate Reasoning In Expert Systems, (Elsevier, Amsterdam), 307-316.
13. Dubois, D. and H. Prade, 1978, Operations on fuzzy numbers, International Journal of Systems Science 9, 613-626.
14. Dubois, D. and H. Prade, 1981, Addition of interactive fuzzy numbers, IEEE Transactions on Automatic Control 26, 926-936.
15. Dubois, D. and H. Prade, 1986, Fuzzy sets and statistical data, European Journal of Operational Research 25, 345-356.
16. Gebhardt, J., M. A. Gil and R. Kruse, 1998, Fuzzy set-theoretic methods in statistics, in: R. Slowinski (Ed.), Handbook on Fuzzy Sets, Fuzzy Sets in Decision Analysis, Operations Research, and Statistics, vol. 5, Kluwer Academic Publishers, New York, 311-347.
17. Gerstenkorn, T. and J. Manko, 1991, Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems 44,39-43.
18. Gertner, G. Z. and H. Zhu, 1996, Bayesian estimation in forest surveys when samples or prior information are fuzzy, Fuzzy Sets and Systems 77, 277-290.
19. Gil, M. A., N. Corral and P. Gil, 1985, The fuzzy decision problem: an approach to the point estimation problem with fuzzy information, European Journal of Operational Research 22, 26-34.
20. Gil, M. A., N. Corral and P. Gil, 1988, The minimum inaccuracy estimates in tests for goodness of fit with fuzzy observations, Journal of Statistical Planning and Inference 19, 95-115.
21. Grzegorzewski, P., 2000, Testing statistical hypotheses with vague data, Fuzzy Sets and Systems 112, 501-510.
22. Grzegorzewski, P., 2001, Fuzzy tests-defuzzification and randomization, Fuzzy Sets and Systems 118, 437-446.
23. Hong, D. H. and S. Y. Hwang, 1995, Correlation of intuitionistic fuzzy sets in probability space, Fuzzy Sets and Systems 75, 77-81.
24. Hung, W. L. and J. W. Wu, 2002, Correlation of intuitionistic fuzzy sets by centroid method, Information Sciences 144, 219-225.
25. Kane, V. E., 1986, Process capability indices, Journal of Quality Technology 18(1), 41-52.
26. Kotz, S. and C. R. Lovelace, 1998, Process Capability Indices in Theory and Practice, London.
27. Kruse, R. and K. D. Meyer, 1987, Statistics with vague data, in: Series B: Mathematical and Statistical Methods, Reidel, Dordrecht, The Netherlands.
28. Kruse, R. and K. D. Meyer, 1988, Confidence intervals for the parameters of a linguistic random variable, In: Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making and J. Kacprzyk and M. Fedrizzi (eds.), (Springer, Berlin), 113-123.
29. Kwakernaak, H., 1978, Fuzzy random variables I: Definitions and theorems, Information Sciences 15, 1-29.
30. Lee, H. T., 2001, index estimation using fuzzy numbers, European Journal of Operational Research 129, 683-688.
31. Li, H., D. B. Owen and S. A. Borrego, 1990, Lower confidence limits on process capability indices based on the range, Commun. Statist. – Simul. 19(1), 1-24.
32. Lin, F. T., 2002, Fuzzy job-shop scheduling based on ranking level ( , 1) interval-valued fuzzy numbers, IEEE Transactions on Fuzzy Systems 10(4), 510-522.
33. Liu, S. T. and C. Kao, 2002, Fuzzy measures for correlation coefficient of fuzzy numbers, Fuzzy Sets and Systems 128, 267-275.
34. Mendenhall, W., D. D. Wackerly and R. L. Scheaffer, 1998, Mathematical Statistics with Applications, 5th ed. (PWS-KENT, Boston).
35. Montenegro, M., M. R. Casals, M. A. Lubiano and M. A. Gil, 2001, Two-sample hypothesis tests of means of a fuzzy random variable, Information Sciences 133, 89-100.
36. Ohta, H. and H. Ichihashi, 1988, Determination of single-sampling attribute plans based on membership functions, International Journal of Production Research 26, 1477-1485.
37. Puri, M. L. and D. A. Ralescu, 1986, Fuzzy random variables, Journal of Mathematical Analysis and Applications 114, 409-422.
38. Römer, C. and A. Kandel, 1995, Statistical tests for fuzzy data, Fuzzy Sets and Systems 72, 1-26.
39. Saade, J. J., 1994, Extension of fuzzy hypothesis testing with hybrid data, Fuzzy Sets and Systems 63, 57-71.
40. Saade, J. J. and H. Schwarzlander, 1990, Fuzzy hypothesis testing with hybrid data, Fuzzy Sets and Systems 35, 197-212.
41. Son, J. Ch., I. Song and H. Y. Kim, 1992, A fuzzy decision problem based on the generalized Neyman-Pearson criterion, Fuzzy Sets and Systems 47, 65-75.
42. Schnatter, S., 1992, On statistical inference for fuzzy data with applications to descriptive statistics, Fuzzy Sets and Systems 50, 143-165.
43. Schnatter, S., 1993, On fuzzy Bayesian inference, Fuzzy Sets and Systems 60, 41-58.
44. Tanaka, H., T. Okuda and K. Asai, 1979, Fuzzy information and decision in statistical model, In: Advances in Fuzzy Sets Theory and Applications, (North-Holland), 303-320.
45. Wang, G. and X. Li, 1999, Correlation and information energy of interval-valued fuzzy numbers, Fuzzy Sets and Systems 103, 169-175.
46. Watanabe, N. and T. Imaizumi, 1993, A fuzzy statistical test of fuzzy hypotheses, Fuzzy Sets and Systems 53, 167-178.
47. Yager, R. R., 1981, A procedure for ordering fuzzy subsets of the unit interval, Information Sciences 24,143-161.
48. Yao, J. S. and C. M. Hwang, 1996, Point estimation for the n sizes of random sample with one vague data, Fuzzy Sets and Systems 80, 205-215.
49. Yao, J. S. and K. M. Wu, 2000, Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems 116,275-288.
50. Yongting, C., 1996, Fuzzy quality and analysis on fuzzy probability, Fuzzy Sets and Systems 83, 283-290.
51. Yu, C., 1993,Correlation of fuzzy numbers, Fuzzy Sets and Systems 55, 303-307.
52. Zadeh, L. A., 1965, Fuzzy sets, Information and Control 8,338-353.
53. Zadeh, L. A., 1968, Probability measures of fuzzy events, Journal of Mathematical Analysis and Applications 23, 421-427.
54. Zadeh, L. A., 1975, The concept of a linguistic variable and its application to approximate reasoning, parts 1 and 2, Information Sciences 7, 199-249, 301-357.
55. Zadeh, L. A., 1976, The concept of a linguistic variable and its application to approximate reasoning, part 3, Information Sciences 9, 43-80.
56. Zadeh, L. A., 1978, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, 3-28.
57. Zimmermann, H. J., 1996, Fuzzy Set Theory and Its Applications, 3rd ed. (Kluwer Academic Publisher, Boston).
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2006-05-23起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2006-05-23起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw