臺灣博碩士論文加值系統

無母數效率及生產分析的先決假設為必要的資料已被正確地提供。
然而這個假設在實際上並不一定永遠成立，在實務中，生產活動的實際生產表現—投入與產出項資料常可能由於無法預知或控制之因素，導致資料無法準確估計而無法直接以確定數值表示。因此，本研究將考量各受測單位生產表現之可能性，以區間型態表示受測單位可能發生之生產表現，較能適當的表示受測單位之生產訊息，區間值資料所代表的是實際上可能發生的範圍而非資料不確定性的機率分佈。
本研究目的在於面對區間樣本資料下技術效率推估。首先提出在區
間樣本資料下生產可能集合以及效率前緣推估必須滿足的性質。滿足所有性質假設之生產可能集合即為一合理之推論技術效率前緣。本研究依資料包絡分析法模型—FDH模型與VRS模型之建構基礎，分別建立其區間資料下之生產可能集合，並驗證其生產可能集合都能滿足其應有之必要性質，證明其為合理之推論技術效率前緣，才可正確地對區間受測單位進行技術效率值之評估。

Non-parametric efficiency and productivity analysis assumes deterministic data are properly provided. This underlying assumption however is not always true in reality.
In this work, we investigate how to estimate technical efficiency when only interval data are given due to imprecise information. Rather than assuming the probability distributions of data uncertainty, interval data represent the ranges for possible realization. We approach the problem by proposing some necessary properties for proper estimations of efficient frontiers and technical efficiency based on interval data. Two estimation models with respect to the conventional deterministic models -free disposal hull (FDH) and variable returns to scales (VRS)-are also proposed. It is shown that both proposed models satisfy the necessary properties, and thus they are appropriate estimations.

中文摘要i
英文摘要ii
誌謝iii
目錄iv
圖目錄v
第一章緒論1
第二章非明確資料下之技術效率相關研究 3
2.1 隨機資料包絡分析法 3
2.2 模糊資料包絡分析法 4
2.3  區間資料包絡分析法 6
第三章技術效率 8
3.1 基本定義 8
3.2 推論生產可能集合 11
3.3 圖例說明 12
第四章 區間資料下之技術效率模式 15
4.1   區間型態資料 15
4.2   區間資料之推論技術效率 18
第五章非凸性假設下之技術效率模式 23
5.1 FDH模式之推論生產可能集合 23
5.2 驗證FDH模式之推論區間生產可能集合 26
5.3 FDH模式之區間技術效率估計 31
5.4 FDH模式之技術效率估計圖說明 32
第六章凸性假設下之區間技術效率模型37
6.1 VRS之推論生產可能集合 37
6.2 驗證VRS模式之技術效率估計 39
6.3 VRS模式之技術效率圖例說明 44
第七章結論49
參考書目51

[1] Banker, R. D. (1984). Some models for estimating technical and scale inefficiencies in
data enveropment analysis, Management Science , pp. 1078-1092.
[2] Banker, R.D. (1993) Maximum likelihood, consistency and data envelopment analysis: a
statistical foundation. Management Science, 39(10),pp.1265-1273
[3] Bauer, P.W. (1990). Recent developments in the econometric estimation of frontiers, Journal
of Econometrics , 46, pp. 39-56.
[4] Carlsson, C. C., and Korhonen, P. (1986, August). A parametric approach to fuzzy linear
programming, Fuzzy Sets and Systems , 20 (1), pp. 17-30.
[5] Charnes, A., Cooper, W. W., (1963).Deterministic equivalents for optimizing and satisficing
under chance constraints, Operational Research , 11, pp. 18-39.
[6] Charnes, A., Cooper, W. W., and Rhodes, E. (1978).Measuring the efficiency of decision
making units, European Journal of Operational Research , 2 (6), pp. 429-444.
[7] Cooper, W. W., Park, S. K., and Yu, G. (1999). IDEA and ARIDEA: Models for dealing
with imprecise data in DEA, Management Science , pp. 597-607.
[8] Despotis, D. K. (2002). Data envelopment analysis with imprecise data, European Journal
of Operational Research , pp. 429-444.
[9] Entani, T., Maeda, T., and Tanaka, H. (2002). Dual models of interval DEA and its extension
to interval data, European Journal of Operational Research , 136, pp. 32-45.
[10] Emrouznejad, A., Parker, B., and Tavares, G. (2008).Evaluation of research in efficiency
and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA,
Journal of Socio-Economics Planning Science, 42 (3), pp. 151-157.
[11] Farrell, M. J. (1957). Journal of the Royal Statistical Society, Series A , 120 (3), pp. 253-
281.
[12] Ferrier, G.D., Lovell, C.A.K., (1990). Measuring cost efficiency in banking: econometric
and linear programming evidence, J. Econ., 46(1-2), pp. 229-245.
[13] Greene, W. H. (1993).The Econometric Approach to Efficiency Analysis, In H. O. Fried,
C. A. K. Lovell, and S. S. Schmidt (Eds.),The Measurement of Productive Efficiency, New
York: Oxford University Press.
[14] Guo, P., and Tanaka, H. (2001). Fuzzy DEA:a perceptual evaluation method, Fuzzy Sets
and Systems , 119, pp. 149-160.
[15] Hougaard, J. L. (1999). Fuzzy scores of technical effciency,European Journal of Operational
Research , 115 (3), pp. 529-41.
[16] Huang, T.H., and Wang, M.H., (2002).Comparison of economic efficiency estimation
methods: parametric and nonparametric techniques, The Manchester School , 70(5): pp.
682-709.
[17] Huang, Zhimin and Susan X. Li, Chance Constrained Programming And Stochastic Dea
Models, School of Business , Adelphi University, Garden City, New York.
[18] Jahanshahloo, R. G., Hosseinzadeh Lofti, F., and Bagherzadeh Valami, H. (2006).
Malmquist Productivity Index with interval and fuzzy data, International Mathematical
Forum , 33, pp. 1607-1623.
[19] Kao, C., and Liu, T. S. (2003). A mathematical programming approach to fuzzy efficiency
ranking,International Journal of Production Economics , 86, pp. 145-154.
[20] Kao, C., and Liu, T. S. (2000). Fuzzy efficiency measures in data envelopment analysis,
Fuzzy Sets and Systems , 113, pp. 427-437.
[21] Kopp, R., Smith, V., (1980). Frontier production function estimates for steam electric
generation: a comparative analysis, South. Econ. J., 46(4),pp. 1049-1059.
[22] Land, K. C., Lovell, CAK., and Thore, S. (1993). Chance-constrained data envelopment
analysis,Managerial and Decision Economics, 14 (6), pp. 541-554.
[23] Land, K.C., Lovell, CAK., and Thore, S. (1994). Productivity and efficiency under capitalism
and state socialism: an empirical inquiry using chance-constrained Data Envelopment
Analysis.Technol Forecast Soc Change 46,pp. 139-152.
[24] Le´on,T., Liern. V., Ruiz, J.L., and Sirvent,I.(2003), A fuzzy mathematical programming
approach to the assessment of efficiency with DEA models, Fuzzy Sets and Systems 139
pp. 407-419.
[25] Lertworasirikul, S., Fang, S. C., Joines, J. A., and Nuttle, H.L. W. (2002).Fuzzy Data
Envelopment Analysis (Fuzzy DEA): A Credibility Approach , In J. L. Verdegay, and M.
Nachtegael, Fuzzy Sets Based Heuristics for Optimization.
[26] Lertworasirikul, S., Fang, S. C., Joines, J. A., and Nuttle, H.L. W. (2003). Fuzzy data
envelopment analysis (DEA): a possibility approach ,Fuzzy Sets and Systems , 139, pp.
379-394.
[27] Lertworasirikul, S., Fang, C. S., Nuttle, H.L.W., and Joines, A. J. (2003). Fuzzy BCC
Model for Data Envelopment Analysis,Fuzzy Optimization and Decision Making , 2, pp.
337-358.
[28] Olesen, B. O., and Petersen, C. N. (1995, Mar).Chance constrained efficiency evaluation
,Management Science, 41 (3), pp. 442-457.
[29] Olesen, O. B. (2006, OCT). Comparing and Combining Two Approaches for Chance Constrained
DEA,Journal of Productivity Analysis , 26 (2), pp. 103-119.
[30] Saati, M. S., Memariani, A., and Jahanshahloo, R. G. (2002). Efficiency analysis and
ranking of DMUs with fuzzy data,Fuzzy Optimization and Decision Making , 3, pp. 255-
267.
[31] Schmidt, P., and Lin, T. F. (1984). Simple tests of alternative specifications in stochastic
frontier models,Journal of Econometrics , 24. pp. 349-361
[32] Sengupta, J. K. (1987). Data Envelopment Analysis for Effciency Measurement in the
Stochastic Case,Computers in Operational Research, 14:2, 117-129.
[33] Sengupta, K. J. (1992). A fuzzy systems approach in data envelopment analysis, Computers
and Mathematics with Applications , 24, pp. 259-266.
[34] Shephard, R. W. (1970). Theory of Cost and Production Functions,Princeton University
Press ,Princeton, NJ.
[35] Simar, L. (2007). How to improve the performances of DEA/FDH estimators in the presence
of noise?,Journal of Productivity Analysis, 28 (3), pp. 183-201.
[36] Triantis, K., and Girod, O. (1998). A Mathematical Programming Approach for Measuring
Technical Efficiency in a Fuzzy Environment,Journal of Productivity Analysis , pp. 85-
112.
[37] Wang, Y. M., Greatbanks, R.,and Yang, J. B. (2005). Interval efficiency assessument using
data envelopment analysis, Fuzzy sets and systems, Vol. 153, 347-370.
[38] Zadeh, A. L. (1965). Fuzzy sets as a basis for a theory of possibility,Information and
Control , 9, pp. 338-353.
[39] Zimmermann, J. H. (1976). Description and optimization of fuzzy system,International
Journal of General System , 2, pp. 209-216.