Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Các thước đo mờ cho hiệu quả chéo mờ trong mô hình phân tích dữ liệu
Tóm tắt
Đánh giá hiệu quả chéo đo lường hiệu quả của các đơn vị ra quyết định (DMUs) thông qua cả phương pháp tự đánh giá và đánh giá đồng nghiệp. Vì hiệu quả chéo có hiệu quả trong việc phân biệt giữa các DMUs, kỹ thuật đánh giá này đã được ứng dụng rộng rãi trong nhiều lĩnh vực. Trong thực tế, có những trường hợp mà các quan sát rất khó để đo lường chính xác. Các phương pháp đánh giá hiệu quả chéo mờ hiện có sử dụng phương pháp mục tiêu thứ cấp để xác định trọng số cho việc đo lường hiệu quả chéo mờ. Tuy nhiên, các phương pháp khác nhau để xác định trọng số có thể tạo ra những hiệu quả chéo mờ khác nhau. Trong bài báo này, chúng tôi đề xuất một phương pháp mới xem xét tất cả các trọng số có thể của tất cả các DMUs cùng một lúc để tính toán hiệu quả chéo mờ trực tiếp mà không cần xác định trọng số. Vì phương pháp dựa trên mức α là một trong những phương pháp phổ biến nhất để phát triển các mô hình phân tích dữ liệu mờ, nên phương pháp này được sử dụng để xây dựng quy trình đánh giá hiệu quả chéo mờ được đề xuất. Một cặp chương trình tuyến tính được phát triển để tính toán hiệu quả chéo mờ. Ở một mức α cụ thể, việc giải quyết cặp chương trình tuyến tính tạo ra giới hạn dưới và giới hạn trên của điểm số hiệu quả mờ. Các ví dụ minh họa cho thấy phương pháp đánh giá hiệu quả chéo mờ được đề xuất trong bài viết này có khả năng phân biệt cao trong việc xếp hạng các DMUs khi dữ liệu là các số mờ.
Từ khóa
#hiệu quả chéo #phân tích dữ liệu mờ #đơn vị ra quyết định #chương trình tuyến tính #trọng số mờTài liệu tham khảo
Abbasbandy, S., & Hahhari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers & Mathematics with Applications, 57, 413–419.
Adler, N., Friedman, L., & Sinuany-Stern, Z. (2002). Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research, 140, 249–265.
Alcaraz, J., Ramόn, N., Ruiz, J. L., & Sirvent, I. (2013). Ranking ranges in cross-efficiency evaluations. European Journal of Operational Research, 226, 516–521.
Al-Siyabi, M., Amin, G. R., Bose, S., et al. (2018). Peer-judgment risk minimization using DEA cross-evaluation with an application in fishery. Annals of Operations Research. https://doi.org/10.1007/s10479-018-2858-3.
Boulmakoul, A., Laarabi, M. H., Sacile, R., & Garbolino, E. (2017). An original approach to ranking fuzzy numbers by inclusion index and Biset Encoding. Fuzzy Optimization and Decision Making, 16, 23–49.
Boussofiane, A., Dyson, R. G., & Thanassoulis, E. (1991). Applied data envelopment analysis. European Journal of Operational Research, 52, 1–15.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Chen, S. J., Hwang, C. L., & Hwang, F. P. (1992). Fuzzy multiple attribute decision making method and applications. Berlin: Springer-Verlag.
Chen, C. B., & Klein, C. M. (1997). A simple approach to ranking a group of aggregated utilities. IEEE Transactions on System, Man, and Cybernetics-Part B, 27, 6–35.
Chen, L., & Wang, Y. M. (2016). Data envelopment analysis cross-efficiency model in fuzzy environments. Journal of Intelligent & Fuzzy Systems, 30(5), 2601–2609.
Chu, T. C., & Tsao, C. T. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers & Mathematics with Applications, 43, 111–117.
Dimitris, K. D., & Yiannis, G. S. (2002). Data envelopment analysis with imprecise data. European Journal of Operational Research, 140, 24–36.
Dotoli, M., Epicoco, N., Falagario, M., & Sciancalepore, F. (2015). A cross-efficiency fuzzy data envelopment analysis technique for performance evaluation of decision making units under uncertainty. Computers & Industrial Engineering, 79, 103–114.
Doyle, J. R., & Green, R. H. (1994). Efficiency and cross efficiency in DEA: derivations, meanings and uses. Journal of the Operational Research Society, 45, 567–578.
Du, F., Cook, E. D., Liang, L., & Zhu, J. (2014). Fixed cost and resource allocation based on DEA cross-efficiency. European Journal of Operational Research, 235, 206–214.
Emrouznejad, A., & Tavana, M. (2014). Performance measurement with fuzzy data Envelopment Analysis. Heidelberg: Springer.
Falagario, M., Sciancalepore, F., Costaniyo, N., & Pietroforte, R. (2012). Using a DEA-cross efficiency approach in public procurement tenders. European Journal of Operational Research, 218, 523–529.
Guo, P., & Tanaka, H. (2001). Fuzzy DEA: A perceptual evaluation method. Fuzzy Sets and Systems, 119, 149–160.
Hatami-Marbini, A., Emrouznejad, A., & Tavana, M. (2011). A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making. European Journal of Operational Research, 214, 457–472.
Hatami-Marbini, A., Saati, S., & Tavana, M. (2010). An ideal-seeking fuzzy data envelopment analysis framework. Applied Soft Computing, 10, 1062–1070.
Jahanshahloo, G. R., Hosseinzadeh Lofti, F., Jafari, Y., & Maddahi, R. (2011). Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation. Applied Mathematical Modelling, 35, 544–549.
Jahanshahloo, G. R., Soleimani-Damaneh, M., & Nasrabadi, E. (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.
Kao, C., & Hung, H. T. (2005). Data envelopment analysis with common weights: The compromise solution approach. Journal of the Operational Research Society, 56, 1196–1203.
Kao, C., & Liu, S. T. (2000). Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets and Systems, 113, 427–437.
Karsak, E. E., & Ahiska, S. S. (2005). Practical common weight multi-criteria decision-making approach with an improved discriminating power for technology selection. International Journal of Production Research, 43, 1537–1554.
Lam, K. F. (2010). In the determination weight sets to compute cross-efficiency ratios in DEA. Journal of the Operational Research Society, 61, 134–143.
León, T., Liern, V., Ruiz, J. L., & Sirvent, I. (2003). A fuzzy mathematical programming approach to the assessment of efficiency with DEA models. Fuzzy Sets and Systems, 139, 407–419.
Lertworasirkul, S., Fang, S. C., Joines, J. A., & Nuttle, H. L. W. (2003). Fuzzy data envelopment analysis (DEA): A possibility approach. Fuzzy Sets and Systems, 139, 379–394.
Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008). The DEA game cross efficiency model and its Nash equilibrium. Operations Research, 56, 1278–1288.
Lim, S. (2012). Minimax and maximin formulations of cross-efficiency in DEA. Computers & Industrial Engineering, 62, 101–108.
Lim, S., Oh, K. W., & Zhu, J. (2014). Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market. European Journal of Operational Research, 236, 361–368.
Liu, S. T. (2008). A fuzzy DEA/AR approach to the selection of flexible manufacturing systems. Computers & Industrial Engineering, 54, 66–76.
Liu, S. T. (2018). A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio. Annals of Operations Research, 261, 207–232.
Liu, J. S., Lu, L. Y. Y., Lu, W. M., & Lin, B. J. Y. (2013). Data envelopment analysis 1978-2010: A citation-based literature survey. Omega, 41, 3–15.
Lu, W. M., & Lo, S. F. (2007). A closer look at the economic-environmental disparities for regional development in China. European Journal of Operational Research, 183, 882–894.
Oliveira, C., & Antunes, C. H. (2007). Multiple objective linear programming models with interval coefficients- an illustrative overview. European Journal of Operational Research, 181, 1434–1463.
Oral, M., Amin, G. R., & Oukil, A. (2015). Cross-efficiency in DEA: A maximum resonated appreciative model. Measurement, 63, 159–167.
Oral, M., Oukil, A., Malouin, J.-L., & Kettani, O. (2014). The appreciative democratic voice of DEA: A case of faculty academic performance evaluation. Socio-Economic Planning Sciences, 48, 20–28.
Örkcü, H. H., & Bal, H. (2011). Goal programming approaches for data envelopment analysis cross efficiency evaluation. Applied Mathematics and Computation, 218, 346–356.
Örkcü, H. H., Ünsal, M. G., & Bal, H. (2015). A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity. Annals of Operations Research, 235, 599–623.
Oukil, A. (2018). Ranking via composite weighting schemes under a DEA cross-evaluation framework. Computers & Industrial Engineering, 117, 217–224.
Oukil, A., & Amin, G. R. (2015). Maximum appreciative cross-efficiency in DEA: A new ranking method. Computers & Industrial Engineering, 81, 14–21.
Ramón, N., Ruiz, J. L., & Sirvent, I. (2010). On the choice of weights profiles in cross-efficiency evaluations. European Journal of Operational Research, 207, 1564–1572.
Ramόn, N., Ruiz, J. L., & Sirvent, I. (2014). Dominance relations and ranking of units by using interval number ordering with cross-efficiency intervals. Journal of the Operational Research Society, 65, 1336–1343.
Ruiz, J. L., & Sirvent, I. (2017). Fuzzy cross-efficiency evaluation: a possibility approach. Fuzzy Optimization and Decision Making, 16, 111–126.
Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. In R. H. Silkman (Ed.), Measuring efficiency: An assessment of data envelopment analysis. San Francisco, CA: Jossey-Bass.
Shang, J., & Sueyoshi, T. (1995). A unified frame work for the selection of a flexible manufacturing system. European Journal of Operational Research, 85, 297–315.
Shi, H. L., Wang, Y. M., Chen, S. Q., & Lan, Y. X. (2017). An approach to two-sided M&A fits based on a cross-efficiency evaluation with contrasting attitudes. Journal of the Operational Research, 68, 41–52.
Shokouhi, A. H., Hatami-Marbini, A., Tavana, M., & Satti, S. (2010). A robust optimization approach for imprecise data envelopment analysis. Computers & Industrial Engineering, 59, 387–397.
Sirvent, I., & León, T. (2014). Cross-efficiency in fuzzy data envelopment analysis (FDEA): Some proposals. In A. Emrouznejad & M. Tavana (Eds.), Performance measurement with fuzzy data envelopment analysis (pp. 101–116). Berlin: Springer.
Sun, S. (2002). Assessing computer numerical control machines using data envelopment analysis. International Journal of Production Research, 40, 2011–2039.
Talluri, S., & Yoon, K. P. (2000). A cone-ratio DEA approach for AMT justification. International Journal of Production Economics, 66, 119–129.
Wang, Y. M., & Chin, K. S. (2010). A neural DEA model for cross-efficiency evaluation and its extension. Expert Systems with Applications, 37, 3666–3675.
Wang, Y. M., Chin, K. S., & Wang, S. (2012). DEA models for minimizing weight disparity in cross-efficiency evaluation. Journal of the Operational Research Society, 63, 1079–1088.
Wang, Z. X., Liu, Y. J., Fan, Z. P., & Feng, B. (2009). Ranking L-R fuzzy number based on deviation degree. Information Sciences, 179, 2070–2077.
Wu, J., Chu, J., Sun, J., Zhu, Q., & Liang, L. (2016). Extended secondary goal models for weights selection in DEA cross-efficiency evaluation. Computers & Industrial Engineering, 93, 143–151.
Wu, J., Sun, J. S., & Liang, L. (2012). Cross efficiency evaluation method based on weight-balanced data envelopment analysis model. Computers & Industrial Engineering, 63, 513–519.
Yang, F., Ang, S., Xia, Q., & Yang, C. (2012). Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis. European Journal of Operational Research, 223, 483–488.
Yu, M. M., Ting, S. C., & Chen, M. (2010). Evaluating the cross efficiency of information sharing in supply chains. Expert Systems with Applications, 37, 2891–2897.
Zerafat Angiz, L. M., Emrouznejad, A., & Mustafa, A. (2010). Fuzzy assessment of performance of a decision making units using DEA: A non-radial approach. Expert Systems with Applications, 37, 5153–5157.
Zimmermann, H. Z. (1996). Fuzzy set theory and its applications (3rd ed.). Boston: Kluwer-Nijhoff.