姓名 謝碧雪 系所 應用數學系 職稱 教授 校內分機 559 EMAIL shieh@mail.nutn.edu.tw 辦公室 C101 網址 專長/研究領域 模糊數學、圖論、無母數統計極限理論

 著作名稱： 微積分 年度： 2002 類別： 專書 摘要： 關鍵字： 著作名稱： Solving infinite fuzzy relation equations on a complete Brouwerian lattice 年度： 2014 類別： 期刊論文 摘要： This work investigates the problem of solving a fuzzy relation equation where are given elements of a complete Brouwerian lattice and J is an infinite index set. This problem is an extension problem of the work of Wang et al. [12, 20, 22, 24]. The solution set comprises attainable and unattainable solutions. Attainable solutions are proved to be completely determined by the maximum solution and all of the minimal solutions. Therefore, finding all of the minimal solutions is critical to solving the complete solution. Hence, this work presents an efficient algorithm for determining all of the minimal solutions, in the sense that each produced solution is a minimum and no duplicate solutions exist. 關鍵字： Infinite fuzzy relation equations, sup-min composition, Brouwerian lattice, minimal solutions, attainable solutions. 著作名稱： Linear optimization problem constrained by fuzzy max-min relation equations 年度： 2013 類別： 期刊論文 摘要： Fang and Li introduced the optimization model with a linear objective function and constrained by fuzzy max–min relation equations. They converted this problem into a 0–1 integer programming problem and solved it using the jump-tracking branch-and-bound method. Subsequently, Wu et al. improved this method by providing an upper bound on the optimal objective value and presented three rules for simplifying the computation of an optimal solution. This work presents new theoretical results concerning this optimization problem. They include an improved upper bound on the optimal objective value, improved rules for simplifying the problem and a rule for reducing the solution tree. Accordingly, an accelerated approach for finding the optimal objective value is presented, and represents an improvement on earlier approaches. Its potential applications are discussed. 關鍵字： Linear optimization, Branch-and-bound method, Fuzzy relations, Fuzzy relation equations, Max–min composition 著作名稱： Solution to the covering problem 年度： 2013 類別： 期刊論文 摘要： This work is motivated by recent investigations that reveal the intractability of the covering problem. Current methods for solving this problem lack an explicit procedure. Therefore, they are of limited value. This work presents the steps for solving such problems using a novel algorithm. The search performance is better than that achieved in other works. Some numerical examples are presented to demonstrate the performance and to compare it with the performance of other methods. The proposed algorithm can be utilized to solve fuzzy relation equations that exhibit the zero-or-greatest property. 關鍵字： Covering problem, Combinatorial problem, Minimal covering, Fuzzy relation equatio, Minimal solution 著作名稱： B. S. Shieh*, Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint, Information Sciences 181 (2011) 832-841 (SCI, I.F. 3.291). 年度： 2011 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh*, A note on a paper by Molai and Khorram, Applied Mathematics and Computation 216 (2010) 3419-3422 (SCI. I.F. 1.124). 年度： 2010 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh*, Deriving minimal solutions for fuzzy relation equations with max-product composition, Information Sciences 178 (2008) 3766-3774 (SCI, I.F. 3.291). 年度： 2008 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B.S.shieh,infinite fuzzy relation equations with continuous t-norms, Information Sciences, 178(2008)1961-1967(SCI,I.F.2.147) 年度： 2008 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B.S.shieh,infinite fuzzy relation equations with max-min composition, Internal Journal of Uncertainty, Fuzziness Knowledge-Based Systems, Vol.16, No.1(2008)19-33(SCI,I.F0.430) 年度： 2008 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, Solutions of fuzzy relation equations based on continuous t-norms, Information Sciences, 177, 4208-4215 (SCI, I.F. 1.003, 2006). 年度： 2007 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, Super edge-and point-connectivities of the Cartesian product of regular graphs, NETWORKS, Vol. 40(2), 91-96 (2002). (SCI) (NSC 89-2218-E-041-001) 年度： 2002 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, C. D. Lea, The jump sizes of the product-limit estimator under random censorship, Sankhya: The Indian Journal of Statistics, Vol. 62, Series A, 80-85 (2000)(SCI). 年度： 2000 類別： 期刊論文 摘要： 關鍵字： 著作名稱： W. S. Chiue, B. S. Shieh , On connectivity of the Cartesian product of two graphs, Applied Mathematics and Computation 102, 129-137 (SCI). 年度： 1999 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, An approach to centroids of fuzzy numbers, International Journal of Fuzzy Systems, Vol. 9, No. 1,51-54(EI). 年度： 2007 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, G. T. F. Wu, K. T. Sun (2005). A representation of the operations MAX and MIN on fuzzy numbers. International Journal of Fuzzy Systems, Vol. 7, No. 1, 40-42 (EI). 年度： 2005 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, G. T. F. Wu, K. T. Sun (2005). The relationship between fuzzy numbers of the same shape. International Journal of Fuzzy Systems, Vol. 7, No. 3, 133-139 (EI). 年度： 2005 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, On pairwise disjoint paths of the Cartesian product of graphs, Journal of the Chinese Institute of Electrical Engineering, Vol. 10, 319-322 (EI). 年度： 2003 類別： 期刊論文 摘要： 關鍵字： 著作名稱： 乘除互逆概念學習之探討 年度： 2013 類別： 期刊論文 摘要： 本研究旨在探討國小三年級學童在解乘除文字題時，以一貫性的乘法策略解 所有的乘除文字題，亦即每一題乘除文字題皆以乘法算式填充題列式並以直式算 則（含乘法及除法）解出答案。讓學童經驗、察覺、並歸納互逆概念的完整性。 研究者依據乘除互為反運算的概念自編教材，透過實驗教學的方式，將乘除概念 同時學習。本研究以研究者任教的班級為實驗班，學生人數26 人，取同校同年 級班級為對照班，人數30 人。實驗結果，實驗班後測成績87.46，對照班76.93， p 值為0.044，顯示實驗班在解乘除文字題之能力表現是高於對照班的，「以乘法 策略解乘除文字題」的教學策略確實可提升學生的解題能力。再者，實驗班延後 測的平均分數是89.61，t 值（後測-延後測）為-2.15，相依樣本t 檢定之p 值為 0.34，大於0.05，顯示此實驗教學具有學習保留效果。再深入研究，發現學童的 解題能力能延伸至五年級「怎樣列式」單元。研究者進行研究的同時，並對學童 進行訪談，了解其乘除互逆概念學習的完整歷程。 關鍵字： 乘除互逆、乘法策略、國小三年級 著作名稱： A new approach for ranking fuzzy numbers 年度： 2013 類別： 期刊論文 摘要： Abstract In many fuzzy decision problems, ranking fuzzy numbers is an important procedure. Because of the imperfection and fuzziness of thinking, we need a method to compare fuzzy numbers. So far, a great deal of research has been obtained. Some of them use the centroid point of fuzzy numbers as an index to rank the fuzzy numbers. Having reviewed the previous researches, we found that almost each of them tried to use a formula to rank the fuzzy numbers. However, most of them hardly can rank with intuition consistently in all cases. Therefore, a new method of ranking fuzzy numbers is proposed and compensates for these shortcomings. It uses three indices to differentiate between fuzzy numbers. The representation location of fuzzy number A is a top priority. The place that the largest membership function grade happened is the second . And then is A S which means the remainder area is the last. Finally, efficiency and superiority of the proposed method are illustrated by some numerical examples. 關鍵字： fuzzy number, ranking 著作名稱： Bih-Sheue Shieh, Cheun-Der Lea (2004). The jump sizes of self-consistent estimators of the survival function under doubly censored data. Journal of Statistical Research (JSR), Vol. 38, No. 2, 183-196. 年度： 2004 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, C. D. Lea, The almost sure convergence of weighted generalized empirical DF, Journal of Statistical Research, Vol. 35, No. 2, 81-91 (2001). 年度： 2001 類別： 期刊論文 摘要： 關鍵字： 著作名稱： B. S. Shieh, G. T. F. Wu, K. T. Sun, Using -cuts viewpoint in developing the shape change on the same shaped fuzzy numbers with operations, 第十二屆模糊理論及其應用研討會 (2004). 年度： 2004 類別： 研討會 摘要： 關鍵字：