臺灣博碩士論文加值系統

在現今高度競爭的環境中，生產成本的降低為廠商生存的重要因素。因此，決策者所要面臨的問題之一便是如何在特定的產量下，以尋求生產成本的最小化問題，而此類問題傳統上可以由數學規劃模式加以求解，以獲得資源配置之最佳化。然而，在有些實際狀況下，生產要素的價格常因缺乏歷史資料的參考而呈現不確定的現象，致使傳統的分析方法難以使用。在Bellman與Zadeh提出模糊理論的概念後，許多學者便將數學規劃問題應用於模糊環境中。但是，在現有的模糊數學規劃模式中，在許多學者所做的研究所得到的目標值均為明確數值，以致於喪失了模糊資料的特性，且有些模式的求解方法則過於複雜，因而降低了模式的應用性。
　　本研究旨在於建立一套具有通常性且易於求解的要素配置模式，來解決生產成本最小化的問題，以提供決策者實質上的幫助。當生產要素價格為模糊數值時，其總生產成本亦為模糊數值，本研究試著以Yager排序法將成本函數中的模糊要素係數排序，先將其轉換為明確數值，之後再利用傳統數學規劃模式來求解。此種求解方法亦與在模糊決策中經常使用的重心法相互比較，而兩種方法所求解的結果，再透過其他三種常用的模糊數值排序法，來分析其中的差異性。結果顯示當要素價格為對稱的模糊數值時，重心法與Yager排序法所求解的結果會相同；而在要素價格為非對稱模糊數值時，Yager排序法所得到的結果優於重心法。故Yager排序法為此類問題的較佳求解方法。本研究將求解要素配置問題的觀念，應用於單位運輸成本為模糊數值的運輸問題之求解。結果亦顯示，透過Yager排序法之求解方式，比較能夠獲得較低的總運輸成本。

The reduction of production cost plays an important role for business firms to survive in the highly competitive market. Then, to find the minimum value of the production cost at a given production quantity is a problem of resource allocation which can be solved to decision maker by the mathematical programming models. However, in the real-life situation, sometimes the prices of the input factors in the models are fuzzy due to lack of historical data, making the classical analysis technique not applicable. Since Bellman and Zadeh proposed the concept of fuzzy set theory, many scholars have devised fuzzy mathematical programming models and the associated solution methods for wider applications. But, most of the existing studies on fuzzy mathematical programming models only provide crisp solutions and some models are too complicated which are not suitable for the decision maker.
　　This paper tries to develop a generalized method to construct the factor allocation model to find the optimal production cost for the managers. When the prices of the input factor are fuzzy, the production cost will be fuzzy as well. The Yager’ s ranking method is used to transform the fuzzy production cost into crisp value, and then the firm’s optimal policy can be determined via the classical mathematical programming model. The method is be compared with the centroid method used in many fuzzy decision-making problems by solving some examples of different fuzzy parameters with various spreads. Three ranking methods of different types will be used to find the difference of the two methods. The results show that the Yager’ s ranking method is better than centroid method when the fuzzy numbers of the input factors are disssymmetric. Finally, the solving procedure is utilized to solve the transportation problem with fuzzy cost coefficients. The results also show that the Yager’ s ranking method is superior to the centriod method.

摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章 緒論 1
第一節 研究背景與研究動機 1
第二節 研究目的 3
第三節 研究流程 4
第二章 文獻探討 6
第一節 模糊數學規劃 6
第二節 模糊排序法 9
第三章 模糊要素配置問題的求解程序 13
第一節 要素配置問題導論 13
第二節 重心法之求解程序 16
第三節 Yager模糊數值排序法之求解程序 19
第四章 兩種求解方法之比較 23
第一節 不同展度下模糊要素價格之組合所求解的結果 23
第二節 比較函數排序法的比較結果 27
第三節 左側分數及右側分數排序法的比較結果 30
第四節 漢明距離排序法的比較結果 34
第五節 本章結論 40
第五章 求解方法在模糊運輸問題之應用 41
第一節 運輸問題的導論 41
第二節 運輸單體法在傳統運輸問題之求解步驟 44
第三節 模糊單位運送成本下運輸問題之重心法求解程序 50
第四節 模糊單位運送成本下運輸問題之Yager排序法求解程序 54
第五節 兩種求解方法之比較 57
第六節 本章結論 59
第六章 結論 60
第一節 研究結果 60
第二節 未來研究方向 61
參考文獻　………………….. 62

陸海文，2001，模糊數值排序法之探討，國立成功大學管理科學系博士論文，台南。
Baas, S.M. and H. Kwakernaak, 1997, Rating and ranking of multiple aspect alternative using fuzzy sets, Automatica 13, 47-58.
Baldwin, J.F. and N.C. Guild, 1979, Comparison of fuzzy sets on the same decision space, Fuzzy Sets and Systems 2, 213-231.
Bellman, R.E. and L.A. Zadeh, 1970, Decision–making in a fuzzy environment, Management Science 17B, 141-164.
Browing, E.K. and M.A. Zupan, 2002, Microeconomics-Theory and Application, 7th ed., John Wiley & Sons, New York.
Buckley, J.J., 1988, Possibilistic linear programming with triangular fuzzy numbers, 　Fuzzy Sets and Systems 26, 135-138.
Buckley, J.J. and S. Chanas, 1989, A fast method of ranking alternatives using fuzzy numbers , Fuzzy Sets and Systems 30, 337-339.
Cadenas, S. and J.L. Verdegay, 2000, Using ranking functions in multiobjective fuzzy linear programming, Fuzzy Sets and Systems 111, 47-53.
Chanas, S. and D. Kuchta, 1996, A concept of the optimal solution of the transportation problem with fuzzy fuzzy cost coefficients, Fuzzy Sets and Systems 82, 299-305.
Chen, L.H. and T.W. Chiou, 1997, A fuzzy credit-rating approach for commercial loans: A Taiwan case, Omega 27, 407-419.
Chen, S.H., 1985, Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems 17, 113-129.

Chen, S.J. and C.L. Hwang, 1992, Fuzzy Multiple Attribute Decision Making, Springer-Verlag, New York.
Delgado, M., J.L. Verdegay, and M.A. Villa, 1988, A procedure for ranking fuzzy numbers using fuzzy relations, Fuzzy Sets and Systems 26, No. 1.
Dubois, D. and H. Prade, 1980, Systems of linear fuzzy constraints, Fuzzy Sets and Systems 3, 37-48.
Dubois, D. and H. Prade, 1983, Ranking of fuzzy numbers in the setting of possibility theory, Information Sciences 30, 183-224.
Efstathiou, J. and R. Tong, 1980, Ranking fuzzy sets using linguistic preference relations, Proceedings of the 10th International Symposium on Multiple-Valued Logic, Northwestern University, Evanston, 137-142.
Freeling, A.N.S., 1979, Decision analysis and fuzzy sets, Masters Thesis, Cambridge University, England.
Fortemps, P. and M. Rouben, 1996, Ranking and defuzzification methods based on area compensation, Fuzzy Sets and Systems 82, 319-330.
Guo, P. and H. Tanaka, 2001, Fuzzy DEA：a perceptual evaluation method, Fuzzy Sets and Systems 119, 149-160.
Guu, S.M. and Y.K. Wu, 1999, Two-phase approach for solving the fuzzy linear programming problems, Fuzzy Sets and Systems 107, 191-195.
Hillier, F.S. and G.J. Lieberman, 2001, Introduction to Operations Research, 7th ed., Mc Graw Hill, Boston.
Inuiguchi, M. and H. Inuiguchi, 1990, Relative modalities and their use in possibilistic linear programming, Fuzzy Sets and Systems 35, 303-323.
Inuiguchi, M., M. Sakawa, and Y. Kume, 1994, The usefulness of possibilistic programming in production planning problems, International Journal of Production Economic 33, 45-52.
Jahanshahloo, G.R., M. Soleimani-damaneh, and E. Nasrabadi, 2004, Measure of efficiency in DEA with fuzzy input-output levels：a methodology for assessing, ranking and imposing of weights restrictions, Applied Mathematics and Computation 156, 175-187.
Jain, R., 1976a, Outline of an approach for the analysis of fuzzy systems, International Journal of Control, Vol. 23, 627-640.
Jain, R., 1976b, Decision making in the presence of fuzzy variables, IEEE Transaction on Systems, Man, and Cybernetics, Vol. SMC-6, 698-703.
Jain, R., 1977, A procedure for multi-aspect decision making using fuzzy sets, International Journal of System Science, Vol. 8, 1-7.
Julien, B., 1994, An extension to possibilistic linear programming, Fuzzy Sets and Systems 64, 195-206.
Kao, C. and S.T. Liu, 2000, Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems 113, 427-437.
Kao, C. and S.T. Liu, 2003, A mathematical programming approach to fuzzy efficiency ranking, International Journal of Production Economics 86, 145-154.
Kolodziejczyk, W., 1986, Orlovsky，s concept of decision-making with fuzzy preference relation-further results, Fuzzy Sets and Systems 19, 11-20.
Korhonen, P.J., 1986, A hierarchical interactive method for ranking alternatives with multiple qualitative criteria, European Journal of Operational Research, Vol. 24, 265-276.
Lai, Y.J. and C.L. Hwang, 1981, A new approach to some possibilistic linear programming problem, Fuzzy Sets and Systems 35, 143-150.
Lee, E.S. and R.L. Li, 1988, Comparison of fuzzy numbers based on the probability measure of fuzzy event, Computer and Mathematics with Applications, Vol. 15, 887-896.
Lee, H.T., 2001, Cpk index estimation using fuzzy number, European Journal of Operational Research 129, 683-688.
Lin, C.J. and U.P Wen, 2004, A labeling algorithm for the fuzzy assignment problem, Fuzzy Sets and Systems 142, 373-391.
LINGO Systems Inc., 1999, LINGO User’s Guide, LINDO Systems Inc., Chicago.
Liu, S.T. and C. Kao, 2004, Solving fuzzy transportation problems based on extension principle, European Journal of Operational Research 153, 661-674.
Mabuchi, S., 1988, An approach to the comparison of fuzzy subsets with an α-cut dependent index, IEEE Transaction on Systems, Man, and Cybernetics, Vol. SMC-18, 264-272.
Maleki, H.R., M. Tata, and M. Mashinchi, 2000, Linear programming with fuzzy variables, Fuzzy Sets and Systems 109, 21-33.
McCahone, C., 1987, Fuzzy Set Theory Applied to Production and Inventory Control, Department of Industrial Engineering, Kansas State University.
Murakami, S., S. Maeda, and S. Imamura, Fuzzy decision analysis on the development of centralized regional energy control system, IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis, 363-368.
Nakamura, K., 1986, Preference relation in a set of fuzzy utilities as a basis for decision making, Fuzzy Sets and Systems 20, 147-162.
Nasrabadi, M.M. and E. Nasrabadi, 2004, A mathematical-programming approach to fuzzy linear regression analysis, Applied Mathematics and Computation 155, 873-881.
Orlovsky, S.A., 1980, On formulation of a general fuzzy mathematical programming problem, Fuzzy Sets and Systems 3, 311-321.
Orlovsky, S.A., 1984, Multiobjective programming problems with fuzzy parameters, Control and Cybernetic 13, 175-183.
Parra, M.A., A.B. Terol, and M.V.R. Uria, 1999, Solving the multiobjective possibilistic linear programming problem, European Journal of Operational Research 117, 175-182.
Perloff, J.M., 1999, Microeconomics, Addison-Wesley, New York.
Reklaitis, G.V., A. Ravindran, and K.M. Ragsdell, 1983, Engineering Optimization, John Wiley & Sons, New York.
Rao, S.S., 1996, Engineering Optimization-Theory and Practice, 3rd Ed., John Wiley & Sons, New York.
Sinha, S., 2003, Fuzzy mathematical programming applied to multi-level programming problems, Computers and Operations Research 30, 1259-1268.
Tanaka, H. and K. Asai, 1984, Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems 13, 275-289.
Tanaka, H., T. Okuda, and K. Asai, 1974, On fuzzy mathematical programming, Journal of Cybernetics 3, 37-46.
Teng, J.Y. and G.H. Tzeng, 1996, A multiobjective approach for selecting non-independent transportation investment alternatives, Transportation Research B, Vol. 30, No. 4, 291-307.
Tong, R.M. and P.P. Bonissone, 1984, Linguistic solutions to fuzzy decision problems, TIMS/Studies in the Management Science, Vol. 20, 323-334.
Tseng, T.Y., C.M. Klein, and M.S. Leonard, 1988, A formalism for comparing ranking procedures, Proceedings of the 7th Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS , 231-235.
Tseng, T.Y. and C.M. Klein, 1989, New algorithm for the ranking procedure in fuzzy decision making, IEEE Transactions on Systems, Man and Cybernetics 19, 1289-1296.

Tsukamoto, Y., P.N. Nikiforuk, and M.M. Gupta, 1983, On the comparison of fuzzy sets using fuzzy chopping, In: H. Akashi, Control Science and Technology for Progress of Society, Pergamon Press, New York, 46-51.
Verma, R., M. Biswal, and A. Biswal, 1997, Fuzzy programming technique to solve multiple objective transportation problems with some nonlinear membership functions, Fuzzy Sets and Systems 91, 37-43.
Wang, M.J. and T.C. Chang, 1995. Tool steel materials selection under fuzzy environment, Fuzzy Sets and Systems 72, 263-270.
Watson, S.R., J.J. Weiss, and M.L. Donnell, 1979, Fuzzy decision analysis, IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-9, 1-9.
Wayne, L.W., 2000, Operations Research: Applications and Algorithms, 3rd ed., International Thomson Publishing Asia a Division of Thomson Asia Pte Ltd.
Werners, B., 1987. Interactive multiple objective programming subject to flexible constraints, European Journal of Operational Research 31, 342-349.
Yang, R., Z. Wang, P.A. Heng, and K.S. Leung, 2004, Fuzzy numbers and fuzzification of the Choquet Integral, Fuzzy Sets and Systems 153, 95-113.
Yager, R.R., 1980a, On choosing between fuzzy subsets, Kybernetes, Vol. 9, 151-154.
Yager, R.R., 1980b, On a general class of fuzzy connectives, Fuzzy Sets and Systems 4, 235-242.
Yager, R.R., 1981, A procedure for ordering fuzzy subsets of the unit interval, Information Sciences 24, 143-161.
Zadeh, L.A., 1978, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, 3-28.
Zimmermann, H.J., 1978, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems 1, 45-55.
Zimmermann, H.J., 1985, Application of fuzzy set theory to mathematical programming, Information Sciences 36, 29-58.
Zimmermann, H.J., 2001, Fuzzy Set Theory and Its Application, 4th ed., Kluwer Academic Publisher, Boston.