# 臺灣博碩士論文加值系統

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 摘 要 在1976年 Jain [10] 提出使用模糊來作決策，因此在實數領域，這些模糊數排序的方法漸漸被研究與應用； (如 Bortolan [3], Chen [4],Choobineh and Li [7], Kim and Park [12],Liou and Wang [14], Yager [18] 等等、、、。 )現今這些方法都傾向簡模糊化到實數值上。事實上，因為測量值常常是模糊不確定的，所以系統在作決策科學計算時，也依照模糊集的理論為基礎。Jain [10,11] 首先使用模糊數排序方法來對系統作決策且也使決策者能夠作決策。如今模糊數排序已在模糊環境作決策時扮演著重要角色。 在這篇論文第二節裡，我們先有一些論文回顧。Jain [10,11]首先將模糊數排序的方法用在模糊環境來作決策;後來 Chen [4] 提出最大集和最小集的模糊排序方法，改進了 Jain [10,11]的排序指標;然而這Chen [4] 所提出的排序方法總是受資料集中最大集和最小集的影響;因此 Liou and Wang [14] 發表總積分值的排序方法，一般來說 Liou 的方法比 Chen 的方法好。但是這總積分值仍然受到選取參數的控制，雖然參數自由選取帶來伸展的彈性，但當選取的參數值改變時，這排序的結果也會因此隨著改變。然而我們並不知道何時這參數的值才會是最佳的。我們提出新的區間排序方法，這方法改善Liou and Wang [14] 的缺點。在第三節裡我們將提出這方法和其性質；在第四節裡我們提出數個例子和比較的結果。
 Abstract Since Jain [10] proposed decision-making in the presence of fuzzy variables in 1976, various approaches to ranking fuzzy numbers are studied and applied in substantive areas(see Bortolan [3], Chen [4],Choobineh and Li [7], Kim and Park [12],Liou and Wang [14], Yager [18] etc.)Totally, these methods tend to defuzzify an intrinsically fuzzy rating into a crisp rating.Actually, because the nature of measurement is fuzzy very often,system evaluation in decision science could be made on the basis of fuzzy sets. Jain [10,11] first use fuzzy numbers to assess the decision system based on ranking these fuzzy numbers and making their decisions by decision makers. Now ordering fuzzy numbers play an important role on decision-making in a fuzzy environment. In this thesis, in Section 2 we have literature review. Jain [10,11] first presented decision-making in fuzzy environment on the basis of ranking fuzzy numbers. Then Chen [4] proposed the maximizing set and minimizing set for ranking fuzzy numbers to improve the ranking index of Jain [10,11]. However, the ranking method in Chen [4] is always influenced by x_max and x_min in the maximum and the minimum values of the data set. Therefore, Liou and Wang [14] proposed ranking method of total integral value. In general, Liou's method is better than Chen [4]. But the total integral value is still controlled by a choosen value of parameter. Although free choice of parameter brings flexible elasticity,when the choice value of parameter changes, the ranking results also change according to the choice.However,we do not know where the value is optimal.We propose a new method based on interval ranking.The proposed method will improve the weakness of Liou and Wang [14].The proposed method and its property are presented in Section 3. Finally, some numerical examples and comparisons are made in Section 4. \end{document}
 1. Introduction …………………………………………. 1 2. Motivation and Literature Review …………………..3 3. A New Approach to Interval Method …………………12 4. Numerical Examples and Comparative Example ………17 5. Conclusion ………………………………………………25 Reference………………………………………………….. 26 Appendix …………………………………….…………….27 第一節 簡介…………………………. 1 第二節 動機與論文回顧 ……………….2 第三節 新的區間排序方法 ……………10 第四節 數個比較的例子 ………………15 第五節 結論 ……………………………23 參考文獻 ……………………………… 24
 參考文獻[1] S.M. Baas and H. Kwakernaak, Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica (1977) 47-58.[2] J.F. Baldwin and N.C.F. Guild Comments on the fuzzy max operator of Dubios and prade,Internat. J. Systems Sci.(1979) 1063-1064.[3] G. Bortolan and R. Degani, A review of some method for ranking fuzzy subsets,Fuzzy Sets and Systems(1985) 1-19.[4] S.H. Chen, Ranking fuzzy numbers with maximizing set and minimizing set,Fuzzy Sets and Systems(1985) 113-129.[5] S.J. Chen and C.L. Hwang, Fuzzy multiple attribute decision making methods and applications, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York (1992).[6] C.H. Cheng, A new approach for ranking fuzzy numbers by distance method,Fuzzy Sets and Systems (1998) 307-317.[7] F. Choobineh and Huishen Li, An index for orderingfuzzy numbers,Fuzzy Sets and Systems(1993) 287-294.[8] D. Dubois and H. Prade, Operations on fuzzy numbers, Internat. J. Systems Sci.(1978) 613-626.[9] J. Efstathiou and R.M. Tong, Ranking fuzzy number sets using linguistic preference relations Proceedings of the 10^thInternatioonal Symposium on Multiple-Valued Logic, Northwestern University, Evanston (1980) 137-142.[10]R. Jain, Decision-making in the presence of fuzzy variables,IEEE Trans. Systems, Man, and Cybernetices (1976) 698-703.[11]R. Jain, A procedure for multi-aspect decision makingusing fuzzy sets,Internat. J. Systems Sci.(1977) 1-7.[12]K. Kim and K.s. Park, Ranking fuzzy numbers with index ofoptimism,Fuzzy Sets and Systems(1990) 143-150.[13] E.S. Lee and R.L. Li, Comparison of fuzzy numbers based onprobability measure of fuzzy events,Computer and Mathematics with Applications(1988) 887-896.[14]T.S. Liou and M.J.J. Wang, Ranking fuzzy numbers withintegral value,Fuzzy Sets and Systems(1992) 247-255.[15]S. Mabuchi, An approach to the comparison of fuzzysubsets with a-cut dependent index,IEEE Trans. Systems, Man, and CyberneticsSMC-18,No (1988) 264-272.[16]R.M. Tong and P.P. Bonissone, Linguistic solutions tofuzzy decision problems,Tims Studies in the Management Science 20 H.J. Zimmermann (ed), Elsevier Science Publisher B.V., North-Holland (1984) 323-334.[17] R.R. Yager, On a general class of fuzzy connectives,Fuzzy Sets and Systems(1980) 235-242.[18]R.R. Yager, On choosing between fuzzy subsets,Kybernetes(1980) 151-154.[19]R.R. Yager, A Procedure for ordering fuzzy subsets ofthe unit interval,Inform. Sci.(1981) 143-161.[20]M.S. Yang and C.H. Ko, On cluster-wise fuzzy regressionanalysis,IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics (1997) 1-13.[21]H.J. Zimmermann,Fuzzy Sets Theory and its Applications.(Kluwer, Dordrecht, 1991).
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