臺灣博碩士論文加值系統

在決策的環境中，資訊的衡量通常是不精確的，決策者評估方案經常在不確定的環境中作決策。模糊理論能在評估方案時，提供決策者以口語化語意，主觀的衡量不精確的資訊，以解決不確定決策問題。決策者根據決策方案的評估準則，構建方案所衡量的資訊，運用模糊理論整合資訊，將決策方案的資訊表示為可衡量的模糊數，使方案評估的問題轉換為模糊數排序的問題。
目前之模糊數排序法大多使用面積衡量、重心衡量或總積分值的觀念，而導出模糊數之排序，這些方法在運用時必須先給予模糊數歸屬函數的數學函數，再運用積分導出模糊數之排序。然而，在模糊決策的環境中，決策者在有限的資訊下，欲獲得歸屬函數的的數學函數有時是困難的，因此這些排序法，在實務的應用將會受到限制。
本研究運用 alpha-cut 的觀念，提出全凌越排序指標、alpha -cut信度排序指標，與整合信號與雜訊的排序指標等三項。這三項指標之定義分別為
(1) 全凌越排序指標，可視為 alpha -cut 的個數、樂觀指標、及模糊數 alpha -cut的左、右凌越值等三項因子所構成的函數。
(2) alpha -cut信度的排序指標，視為 alpha -cut 的個數、模糊數 alpha -cut 的左、右凌越值、及 alpha -cut 為權重等三項因子所構成的函數。
(3) 整合信號與雜訊的排序指標，視 alpha -cut 的個數、樂觀指標、模糊數 alpha -cut 的左、右凌越值、 alpha -cut 為權重及信號與雜訊比 ( Signal/Noise Ratio)等五項因子所構成的函數。
本研究所提出的指標是以alpha -cut處理模糊資訊，不僅可處理連續型的模糊數，亦可處理離散型的模糊數、非正規化模糊數、歸屬函數是未知的模糊數及純數值與模糊數排序比較，經與其他排序法在各種模糊數排序例子之比較，驗證本研究所提之排序指標是個很好的排序指標。

Decision makers usually perform imprecise evaluations for a set of alternatives in an uncertain environment, because of the lack of precise information, such as unquantifiable information, incomplete information, nonobtainable information and partial ignorance. To resolve this problem, fuzzy set theory has been extensively used. Fuzzy numbers are applied to represent the imprecise measurements of different alternatives. This leads that the evaluations of a set of alternatives are actually the ranking of the aggregated fuzzy numbers.
The ranking process leads to determine a decision-maker’s preference order of fuzzy numbers. Adopting the concept of alpha-cut, this research specifically develops three ranking methods, namely the total dominance index, the weighted belief measurement index and Integrated Signal/Noise (S/N) index. The total dominance index is defined as the function of the number of alpha-cuts, the index of optimism and the left and right spreads at some alpha — cuts of fuzzy numbers, while the weighted belief measurement index includes the elements in the total dominance index and the weighted average on the basis of alpha—cuts. In addition, the Integrated Signal/Noise index incorporates the signal/noise (S/N) ratio into the weighted belief measurement index.
The proposed three ranking methods are simple and efficient in terms of the calculations and comparisons. Unlike the existing integral approaches and area measurements, in the proposed approaches membership functions are not necessary to be known in advance. Only several alpha-cuts are needed for obtaining the index value. In addition, the proposed methods also can be used for ranking nonlinear fuzzy numbers, discrete fuzzy numbers and a pure number.

封面
摘要
誌謝
目錄
表目錄
圖目錄
符號表
第一章、緒論
1.1、動機與目的
1.2、研究步驟
1.3、研究大綱
第二章、文獻探討
2.1、模糊數的基本定義
2.2、模糊數排序的分類
2.3、a-cuts的排序指標
2.4、面積衡量的排序指標特色
2.5、模糊數排序指標之模式
第三章、全凌越排序指標
3.1、全凌越排序指標之構建
3.2、全凌越排序指標的模式
3.3、全凌越指標的特性
3.4、a-cuts的個數和樂觀指標參數與全凌越指標的關係
3.5 小結
第四章、考慮a-cuts為權重之排序法
4.1、信度排序指標
4.1.1 信度的序指標的構建模式
4.1.2 信度排序指標的特性
4.2 整合信號與雜訊的排序指標
4.2.1 模糊數的量(quantity)
4.2.2 模糊數的質(quality)
4.2.3 整合信號與雜訊的排序指標
4.2.4 整合信號與雜訊指標的性質
4.2.5 探討整合信號與雜訊指標參數的影響力
4.2.6 整合信號與雜訊指標的例子
4.3 小結
第五章、模糊數排序指標之比較與應用例
5.1、模糊數排序指標之比較
5.2 模糊數排序指標之應用例
第六章、結論
參考文獻

[1] J.M. Adamo, Fuzzy decision trees, Fuzzy Sets and Systems
4, 207-219, (1980).
[2] J. Baldwin and N. Guild, Comparison of fuzzy sets on
the same decision space, Fuzzy Sets and Systems 2, 213-233
, (1979).
[3] S. Bass and H. Kwakernaak, Rating and Ranking of
multiple-aspect alternatives using fuzzy sets, Automatica
13, 47-58, (1977).
[4] G. Bortolan and R. Degani, A review of some methods for
ranking fuzzy subsets, Fuzzy Sets and Systems 15, 1-19,
(1985).
[5] J. Buckley, Ranking alternatives using fuzzy numbers, Fuzzy
Sets and Systems 15 , 21-31, (1985).
[6] J. Buckley and S. Chanas, A fast method of ranking
alternatives using fuzzy numbers, Fuzzy Sets and Systems
30, 337-339, (1989).
[7] W. Chang, Ranking of fuzzy utilities with triangular
membership function, Proceedings of the International
Conference on Policy Analysis and Information System, 263-
272, (1981)
[8] S.H. Chen, Ranking fuzzy numbers with maximizing set and
minimizing set, Fuzzy Sets and Systems 17, 113-129, (1985).
[9] S.J. Chen and C.L. Hwang, Fuzzy Multiple Attribute Decision
Making, Springer, New York, (1992).
[10] C.B. Chen and C.M. Klein, A simple approach to ranking a
group of aggregated fuzzy utilities, IEEE Transactions on
Systems, Man, and Cybernetics 27, 26-35, (1997).
[11] C.B. Chen and C.M. Klein, An efficient approach to solving
fuzzy MADM problems, Fuzzy Sets and Systems 88, 51-67,
(1997).
[12] L.H. Chen and H.W. Lu, An approximate approach for ranking
fuzzy numbers based on left and right dominance, Computers
and Mathematics with Applications, (forthcoming).
[13] C. H. Cheng, A new approach for ranking fuzzy numbers by
distance method, Fuzzy Sets and Systems 95, 307-317,
(1998).
[14] F. Choobineh and H. Li, An index for ordering fuzzy
numbers, Fuzzy Sets and Systems 54, 287-294, (1993).
[15] M. Delgado, J.L. Verdegay, and M.A. Villa, A procedure for
ranking fuzzy numbers using fuzzy relations, Fuzzy Sets
and Systems 26, 49-62, (1988).
[16] D. Dubois and H. Prade, Operations on fuzzy numbers,
International Journal of System Science 9, 613-626, (1978).
[17] D. Dubois and H. Prade, Ranking of fuzzy numbers in the
setting of possibility theory, Information Sciences 30,
183-224, (1983).
[18] J. Efstathiou and R. Tong, Ranking fuzzy sets using
linguistic preference relations, Proc. 10th International
Symposium on Multiple-Valued Logic, Northwestern
University, Evanston, 137-142, (1980).
[19] P. Fortemps and M. Roubens, Ranking and defuzzification
methods based on area compensation, Fuzzy Sets and Systems
82, 319-330, (1996).
[20] A.N.S. Freeling, Fuzzy sets and decision analysis, IEEE
Transactions on Systems, Man, and Cybernetics 10, 341-354,
(1980).
[21] C. C. Huang, A study on the fuzzy ranking and its
application on the decision support systems, Ph.D.
dissertation, Tamkang Univ., Taiwan, R.O.C., (1989).
[22] R. Jain, Decision making in the presence of fuzzy
variables, IEEE Transactions on Systems, Man, and
Cybernetics 6, 698-703, (1976).
[23] R. Jain, A procedure for multiple-aspect decision making
using fuzzy sets, International Journal of System Science
8, 1-7, (1977).
[24] A. Kaufmann and M.M. Gupta, Introduction to Fuzzy
Arithmetic: Theory and Applications, 2nd ed., Van Nostrand
Reinhold, New York (1991).
[25] E. Kerre, The use of fuzzy set theory in
electrocardiological diagnostics, in: M. Gupta and E.
Sanchez, Ed., Approximate Reasoning in Decision Analysis,
North-Holland, Amsterdam, 277-282, (1982).
[26] K. Kim and K. Park, Ranking fuzzy numbers with index of
optimism, Fuzzy Sets and Systems 35, 143-150, (1990).
[27] W. Kolodziejczyk, Orlovsky’s concept of decision-making
with fuzzy preference relation further results, Fuzzy Sets
and Systems 19, 11-20, (1986).
[28] E.S. Lee and R.J. Li, Comparison of fuzzy numbers based on
the probability measure of fuzzy events, Computers and
Mathematics with Applications 15, 887-896, (1988).
[29] T.S. Liou and M.J. Wang, Ranking fuzzy numbers with
integral value, Fuzzy Sets and Systems 50, 247-255, (1992).
[30] G. Mabuchi, An approach to the comparison of fuzzy subsets
with an—cut dependent index, IEEE Transactions on
Systems, Man, and Cybernetics 18, 264-272, (1988).
[31] C. McCahone, Fuzzy set theory applied to production and
inventory control, Ph.D. Thesis, Department of Industrial
Engineering, Kansas State University, 1987.
[32] S. Murakami, S. Maeda, and S. Imamura, Fuzzy decision
analysis on the development of centralized regional energy
control systems, Reprints IFAC Conf. on Fuzzy Information,
Knowledge Representation and Decision Analysis, 353-358,
(1983).
[33] K. Nakamura, Preference relation on a set of fuzzy
utilities as a basis for decision making, Fuzzy Sets and
Systems 20, 147-162, (1986).
[34] G. Taguchi and D. Clausing, Introduction to Quality
Engineering, Asian Productivity Organization, (1986).
[35] R.M. Tong and P.P. Bonissone, Linguistic solutions to
fuzzy decision problems, In: TIMS/Studies in the
Management Science 20, 323-334, (1984).
[36] T.Y. Tseng , C.M. Klein, and M.S. Leonard, A formalism for
comparing ranking procedures, Proceeding of the 7th Annual
Meeting of the North American Fuzzy Information Processing
Society, NAFIPS , 231-235, (1988).
[37] T.Y. Tseng and C.M. Klein, New algorithm for the ranking
procedure in fuzzy decision making, IEEE Transactions on
Systems, Man, and Cybernetics 19, 1289-1296, (1989).
[38] Y. Tsukamoto, P.N. Nikiforuk, and M.M. Gupta, On the
comparison of fuzzy sets using fuzzy chopping, In: H.
Akashi (Ed.), Control Science and Technology for Progress
of Society, New York, 46-51, (1983).
[39] S.R. Watson, J.J. Weiss, and M.L. McDonnell, Fuzzy
decision analysis, IEEE Transactions on Systems, Man, and
Cybernetics 9, 1-9, (1979).
[40] R.R. Yager, Ranking fuzzy subsets over the unit interval,
Proceedings of the 1978 CDC, 1435-1437, (1978).
[41] R.R. Yager, On a general class of fuzzy connectives, Fuzzy
Sets and Systems 4, 235-242, (1980).
[42] R.R. Yager, On choosing between fuzzy subsets, Kybernetes,
9, 151-154, (1980).
[43] R.R. Yager, A procedure for ordering fuzzy subsets of the
unit interval, Information Sciences 24, 143-161, (1981).
[44] L.A. Zadeh, Fuzzy sets, Information. and Control 8, 338-
353, (1965).
[45] H.J. Zimmermann, Fuzzy Set Theory and Its Applications,
2nd ed., Kluwer Academic Publishers,
Boston/Dordrecht/London, (1991).
[46] 劉祥泰，模糊資料包絡分析模式之求解與應用，國立成功大學工業
管理科學系博士論文，八十八年。