×

A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. (English) Zbl 1219.90199

Summary: Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. In this study, we provide a taxonomy and review of the fuzzy DEA methods. We present a classification scheme with four primary categories, namely, the tolerance approach, the \(\alpha \)-level based approach, the fuzzy ranking approach and the possibility approach. We discuss each classification scheme and group the fuzzy DEA papers published in the literature over the past 20 years. To the best of our knowledge, this paper appears to be the only review and complete source of references on fuzzy DEA.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90B50 Management decision making, including multiple objectives
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Allahviranloo, T.; Hosseinzade Lotfi, F.; Adabitabar, M. Firozja, Fuzzy efficiency measure with fuzzy production possibility set, Applications and Applied Mathematics: An International Journal, 2, 2, 152-166 (2007) · Zbl 1175.90434
[2] Asady, B.; Zendehnam, A., Ranking fuzzy numbers by distance minimization, Applied Mathematical Modelling, 11, 2589-2598 (2007) · Zbl 1211.03069
[3] Azadeh, A.; Alem, S. M., A flexible deterministic, stochastic and fuzzy data envelopment analysis approach for supply chain risk and vendor selection problem: simulation analysis, Expert Systems with Applications, 37, 12, 7438-7448 (2010)
[4] Azadeh, A.; Ghaderi, S. F.; Javaheri, Z.; Saberi, M., A fuzzy mathematical programming approach to DEA models, American Journal of Applied Sciences, 5, 10, 1352-1357 (2008)
[5] Azadeh, M. A.; Anvari, M.; Izadbakhsh, H., An integrated FDEA-PCA method as decision making model and computer simulation for system optimization, (Proceedings of the Computer Simulation Conference (2007), Society for Computer Simulation International San Diego: Society for Computer Simulation International San Diego CA, USA), 09-616
[6] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiency in data envelopment analysis, Management Science, 30, 1078-1092 (1984) · Zbl 0552.90055
[7] Bagherzadeh valami, H., Cost efficiency with triangular fuzzy number input prices: an application of DEA, Chaos, Solitons and Fractals, 42, 1631-1637 (2009) · Zbl 1198.90423
[8] Bass, S.; Kwakernaak, H., Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, 13, 1, 47-58 (1977) · Zbl 0363.90010
[9] Bellman, R. E.; Zadeh, L. A., Decision making in a fuzzy environment, Management Science, 17, 4, 141-164 (1970) · Zbl 0224.90032
[10] Bojadziev, G.; Bojadziev, M., Fuzzy Logic for Business, Finance, and Management (1997), World Scientific: World Scientific Singapore · Zbl 1050.91500
[11] Carlsson, C.; Korhonen, P., A parametric approach to fuzzy linear programming, Fuzzy Sets and Systems, 20, 17-30 (1986) · Zbl 0603.90093
[12] Charnes, A.; Cooper, W. W.; Rhodes, E. L., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 6, 429-444 (1978) · Zbl 0416.90080
[13] Chen, C. B.; Klein, C. M., A simple approach to ranking a group of aggregated fuzzy utilities, IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics, 27, 26-35 (1997)
[14] Chen, C.-T., A fuzzy approach to select the location of the distribution center, Fuzzy Sets and Systems, 118, 1, 65-73 (2001) · Zbl 1151.90453
[15] Chen, M. F.; Tzeng, G. H., Combining grey relation and TOPSIS concepts for selecting an expatriate host country, Mathematical and Computer Modelling, 40, 13, 1473-1490 (2004) · Zbl 1099.90549
[16] Chen, S. H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, 17, 113-129 (1985) · Zbl 0618.90047
[17] Chen, S. J.; Hwang, C. L., Fuzzy Multi-attribute Decision-making: Methods and Applications (1992), Springer: Springer Berlin
[18] Chiang, T. Z.; Che, Z. H., A fuzzy robust evaluation model for selecting and ranking NPD projects using Bayesian belief network and weight-restricted DEA, Expert Systems with Applications, 37, 1111, 7408-7418 (2010)
[19] Chiou, H. K.; Tzeng, G. H.; Cheng, D. C., Evaluating sustainable fishing development strategies using fuzzy MCDM approach, Omega, 33, 3, 223-234 (2005)
[20] Cook, W. D.; Kress, M.; Seiford, L. M., Data envelopment analysis in the presence of both quantitative and qualitative factors, Journal of Operational Research Society, 47, 945-953 (1996) · Zbl 0863.90002
[21] Cook, W. D.; Seiford, L. M., Data envelopment analysis (DEA) - Thirty years on, European Journal of Operational Research, 192, 1, 1-17 (2009) · Zbl 1180.90151
[22] Cooper, W. W.; Deng, H.; Huang, Z. M.; Li, S. X., Satisfying DEA models under chance constraints, The Annals of Operations Research, 66, 279-295 (1996) · Zbl 0864.90003
[23] Cooper, W. W.; Shanling, L.; Tone, L. M.; Thrall, R. M.; Zhu, J., Sensitivity and stability analysis in DEA: some recent development, Journal of Productivity Analysis, 15, 3, 217-246 (2001)
[24] Dia, M., A model of fuzzy data envelopment analysis, INFOR, 42, 4, 267-279 (2004) · Zbl 07682334
[25] Ding, J. F.; Liang, G. S., Using fuzzy MCDM to select partners of strategic alliances for liner shipping, Information Sciences, 173, 1-3, 197-225 (2005) · Zbl 1104.91015
[26] Dubois, D.; Prade, H., Possibility Theory: An Approach to Computerized Processing of Uncertainty (1988), Plenum Press: Plenum Press New York
[27] Emrouznejad, A.; De Witte, K., COOPER-framework: a unified process for non-parametric projects, European Journal of Operational Research, 207, 3, 1573-1586 (2010)
[28] Emrouznejad, A.; Parker, B. R.; Tavares, G., Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA, Socio-Economic Planning Sciences, 42, 3, 151-157 (2008)
[29] Entani, T.; Maeda, Y.; Tanaka, H., Dual models of interval DEA and its extension to interval data, European Journal of Operational Research, 136, 1, 32-45 (2002) · Zbl 1087.90513
[30] (Figueira, J.; Greco, S.; Ehrgott, M., Multiple Criteria Decision Analysis: State of the Art Surveys (2004), Springer: Springer New York) · Zbl 1060.90002
[31] Garcia, P. A.A.; Schirru, R.; Melo, P. F.F. E., A fuzzy data envelopment analysis approach for FMEA, Progress in Nuclear Energy, 46, 3-4, 359-373 (2005)
[32] Gattoufi, S.; Oral, M.; Reisman, A., A taxonomy for data envelopment analysis, Socio-Economic Planning Sciences, 38, 2-3, 141-158 (2004)
[33] Geldermann, J.; Spengler, T.; Rentz, O., Fuzzy outranking for environmental assessment. Case study: Iron and steel making industry, Fuzzy Sets and Systems, 115, 1, 45-65 (2000) · Zbl 1073.91619
[34] Ghapanchi, A.; Jafarzadeh, M. H.; Khakbaz, M. H., Fuzzy-Data envelopment analysis approach to enterprise resource planning system analysis and selection, International Journal of Information Systems and Change Management, 3, 2, 157-170 (2008)
[35] Girod, O. A.; Triantis, K. P., The evaluation of productive efficiency using a fuzzy mathematical programming approach: the case of the newspaper preprint insertion process, IEEE Transactions on Engineering Management, 46, 4, 429-443 (1999)
[36] Girod, O., 1996. Measuring technical efficiency in a fuzzy environment, Ph.D. Dissertation, Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University.; Girod, O., 1996. Measuring technical efficiency in a fuzzy environment, Ph.D. Dissertation, Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University.
[37] Guh, Y. Y., Data envelopment analysis in fuzzy environment, International Journal of Information and Management Sciences, 12, 2, 51-65 (2001) · Zbl 0983.90083
[38] Guo, P.; Tanaka, H., Decision making based on fuzzy data envelopment analysis, to appear in Intelligent Decision and Policy Making Support Systems, (Ruan, D.; Meer, K. (2008), Springer: Springer Berlin/Heidelberg), 39-54
[39] Guo, P., Fuzzy data envelopment analysis and its application to location problems, Information Sciences, 179, 6, 820-829 (2009) · Zbl 1156.90467
[40] Guo, P.; Tanaka, H., Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets and Systems, 119, 1, 149-160 (2001)
[41] Guo, P.; Tanaka, H.; Inuiguchi, M., Self-organizing fuzzy aggregation models to rank the objects with multiple attributes, IEEE Transactions on Systems, Man and Cybernetics, Part A - Systems and Humans, 30, 5, 573-580 (2000)
[42] Hatami-Marbini, A.; Saati, S., Stability of RTS of efficient DMUs in DEA with fuzzy under fuzzy data, Applied Mathematical Sciences, 3, 44, 2157-2166 (2009) · Zbl 1189.90217
[43] Hatami-Marbini, A.; Saati, S.; Makui, A., An application of fuzzy numbers ranking in performance analysis, Journal of Applied Sciences, 9, 9, 1770-1775 (2009)
[44] Hatami-Marbini, A.; Saati, S.; Tavana, M., An ideal-seeking fuzzy data envelopment analysis framework, Applied Soft Computing, 10, 4, 1062-1070 (2010)
[45] Hatami-Marbini, A.; Saati, S.; Makui, A., Ideal and anti-ideal decision making units: a fuzzy DEA approach, Journal of Industrial Engineering International, 6, 10, 31-41 (2010)
[46] Hatami-Marbini, A., Tavana, M., Ebrahimi, A., in pressc. A fully fuzzified data envelopment analysis model. International Journal of Information and Decision Sciences.; Hatami-Marbini, A., Tavana, M., Ebrahimi, A., in pressc. A fully fuzzified data envelopment analysis model. International Journal of Information and Decision Sciences.
[47] Hatami-Marbini, A., Tavana, M., Emrouznejad, A., Saati, S., in pressd. Efficiency measurement in fuzzy additive data envelopment analysis. International Journal of Industrial and Systems Engineering.; Hatami-Marbini, A., Tavana, M., Emrouznejad, A., Saati, S., in pressd. Efficiency measurement in fuzzy additive data envelopment analysis. International Journal of Industrial and Systems Engineering. · Zbl 1219.90199
[48] Hatami-Marbini, A., Saati, S., Tavana, M., in presse. Data envelopment analysis with fuzzy parameters: an interactive approach. International Journal of Operations Research and Information Systems.; Hatami-Marbini, A., Saati, S., Tavana, M., in presse. Data envelopment analysis with fuzzy parameters: an interactive approach. International Journal of Operations Research and Information Systems. · Zbl 1325.68228
[49] Ho, W.; Xu, X.; Dey, P. K., Multi-criteria decision making approaches for supplier evaluation and selection: a literature review, European Journal of Operational Research, 202, 1, 16-24 (2010) · Zbl 1175.90223
[50] Hosseinzadeh Lotfi, F.; Adabitabar Firozja, M.; Erfani, V., Efficiency measures in data envelopment analysis with fuzzy and ordinal data, International Mathematical Forum, 4, 20, 995-1006 (2009) · Zbl 1172.90420
[51] Hosseinzadeh Lotfi, F.; Allahviranloo, T.; Mozaffari, M. R.; Gerami, J., Basic DEA models in the full fuzzy position, International Mathematical Forum, 4, 20, 983-993 (2009) · Zbl 1172.90520
[52] Hosseinzadeh Lotfi, F.; Jahanshahloo, G. R.; Allahviranloo, T.; Noroozi, E.; Hosseinzadeh Lotfi, A. A., Equitable allocation of shared costs on fuzzy environment, International Mathematical Forum, 2, 65, 3199-3210 (2007) · Zbl 1153.91611
[53] Hosseinzadeh Lotfi, F.; Jahanshahloo, G. R.; Alimardani, M., A new approach for efficiency measures by fuzzy linear programming and Application in Insurance Organization, Applied Mathematical Sciences, 1, 14, 647-663 (2007) · Zbl 1200.90174
[54] Hosseinzadeh Lotfi, F.; Jahanshahloo, G. R.; Rezai Balf, F.; Zhiani Rezai, H., Discriminant analysis of imprecise data, Applied Mathematical Sciences, 1, 15, 723-737 (2007) · Zbl 1157.91423
[55] Hosseinzadeh Lotfi, F.; Jahanshahloo, G. R.; Vahidi, A. R.; Dalirian, A., Efficiency and effectiveness in multi-activity network DEA model with fuzzy data, Applied Mathematical Sciences, 3, 52, 2603-2618 (2009) · Zbl 1184.90079
[56] Hosseinzadeh Lotfi, F.; Mansouri, B., The extended data envelopment analysis/discriminant analysis approach of fuzzy models, Applied Mathematical Sciences, 2, 30, 1465-1477 (2008) · Zbl 1153.90459
[57] Hougaard, J. L., Fuzzy scores of technical efficiency, European Journal of Operational Research, 115, 3, 529-541 (1999) · Zbl 0946.91002
[58] Hougaard, J. L., A simple approximation of productivity scores of fuzzy production plans, Fuzzy Sets and Systems, 152, 3, 455-465 (2005) · Zbl 1142.90384
[59] Hsu, K. H., Using balanced scorecard and fuzzy data envelopment analysis for multinational R & D project performance assessment, Journal of American Academy of Business, Cambridge, 7, 1, 189-196 (2005)
[60] Inuiguchi, M.; Ichihashi, H.; Tanaka, H., Fuzzy programming: a survey of recent developments, (Slowinski, R.; Teghem, J., Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty (1990), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 45-68 · Zbl 0728.90091
[61] Jahanshahloo, G. R.; Soleimani-Damaneh, M.; Nasrabadi, E., 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, 1, 175-187 (2004) · Zbl 1134.90444
[62] Jahanshahloo, G. R.; Hosseienzadeh Lotfi, F.; Shoja, N.; Sanei, M., An alternative approach for equitable allocation of shared costs by using DEA, Applied Mathematics and computation, 153, 1, 267-274 (2004) · Zbl 1049.90029
[63] Jahanshahloo, G. R.; Hosseinzade Lotfi, F.; Shoja, N.; Tohidi, G.; Razavian, S., Ranking by \(l_1\)−norm in data envelopment analysis, Applied Mathematics and Computation, 153, 1, 215-224 (2004) · Zbl 1080.62503
[64] Jahanshahloo, G. R.; Hosseinzadeh Lotfi, F.; Nikoomaram, H.; Alimardani, M., Using a certain linear ranking function to measure the Malmquist productivity index with fuzzy data and application in insurance organization, Applied Mathematical Sciences, 1, 14, 665-680 (2007) · Zbl 1200.90175
[65] Jahanshahloo, G. R.; Hosseinzadeh Lotfi, F.; Adabitabar Firozja, M.; Allahviranloo, T., Ranking DMUs with fuzzy data in DEA, International Journal Contemporary Mathematical Sciences, 2, 5, 203-211 (2007) · Zbl 1245.90156
[66] Jahanshahloo, G. R.; Hosseinzadeh Lotfi, F.; Alimardani Jondabeh, M.; Banihashemi, Sh.; Lakzaie, L., Cost efficiency measurement with certain price on fuzzy data and application in insurance organization, Applied Mathematical Sciences, 2, 1, 1-18 (2008) · Zbl 1142.90519
[67] Jahanshahloo, G. R.; Sanei, M.; Rostamy-Malkhalifeh, M.; Saleh, H., A comment on a fuzzy DEA/AR approach to the selection of flexible manufacturing systems, Computers and Industrial Engineering, 56, 4, 1713-1714 (2009)
[68] Jahanshahloo, G. R.; Hosseinzadeh Lotfi, F.; Shahverdi, R.; Adabitabar, M.; Rostamy-Malkhalifeh, M.; Sohraiee, S., Ranking DMUs by \(l_1\)−normwith fuzzy data in DEA, Chaos, Solitons and Fractals, 39, 2294-2302 (2009) · Zbl 1197.90356
[69] Jiang, N.; Yang, Y., A fuzzy chance-constrained DEA model based on Cr measure, International Journal of Business and Management, 2, 2, 17-21 (2007)
[70] Jiménez, M., Ranking fuzzy numbers through the comparison of its expected intervals, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4, 4, 379-388 (1996) · Zbl 1232.03040
[71] Juan, Y. K., A hybrid approach using data envelopment analysis and case-based reasoning for housing refurbishment contractors selection and performance improvement, Expert Systems with Applications, 36, 3, 5702-5710 (2009)
[72] Kahraman, C., Tolga, E. 1998. Data envelopment analysis using fuzzy concept. 28th International Symposium on Multiple-Valued Logic, pp. 338-343.; Kahraman, C., Tolga, E. 1998. Data envelopment analysis using fuzzy concept. 28th International Symposium on Multiple-Valued Logic, pp. 338-343.
[73] Kao, C., A mathematical programming approach to fuzzy efficiency ranking, (Proceedings of the International Conference on Fuzzy Systems, vol. 1 (2001), Institute of Electrical and Electronics Engineers Inc.: Institute of Electrical and Electronics Engineers Inc. Melbourne, Australia), 216-219
[74] Kao, C., Interval efficiency measures in data envelopment analysis with imprecise data, European Journal of Operational Research, 174, 1087-1099 (2006) · Zbl 1103.90356
[75] Kao, C.; Liu, S. T., Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems, 113, 3, 427-437 (2000) · Zbl 0965.90025
[76] Kao, C.; Liu, S. T., Data envelopment analysis with missing data: an application to University libraries in Taiwan, Journal of Operational Research Society, 51, 8, 897-905 (2000) · Zbl 1107.90374
[77] Kao, C.; Liu, S. T., A mathematical programming approach to fuzzy efficiency ranking, International Journal of Production Economics, 86, 2, 145-154 (2003)
[78] Kao, C.; Liu, S. T., Data envelopment analysis with imprecise data: an application of Taiwan machinery firms, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13, 2, 225-240 (2005)
[79] Kao, C.; Liu, S. T., Data envelopment analysis with missing data: a reliable solution method, to appear, (Zhu, J.; Cook, W. D., Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis (2007), Springer), 292-304
[80] Karsak, E. E., Using data envelopment analysis for evaluating flexible manufacturing systems in the presence of imprecise data, The International Journal of Advanced Manufacturing Technology, 35, 9-10, 867-874 (2008)
[81] Khodabakhshi, M.; Gholami, Y.; Kheirollahi, H., An additive model approach for estimating returns to scale in imprecise data envelopment analysis, Applied Mathematical Modelling, 34, 5, 1247-1257 (2010) · Zbl 1186.90072
[82] Kuo, H.C., Wang, L.H., 2007. Operating performance by the development of efficiency measurement based on fuzzy DEA. Second International Conference on Innovative Computing, Information and Control, p. 196.; Kuo, H.C., Wang, L.H., 2007. Operating performance by the development of efficiency measurement based on fuzzy DEA. Second International Conference on Innovative Computing, Information and Control, p. 196.
[83] Lai, Y. J.; Hwang, C. L., A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49, 2, 121-133 (1992)
[84] Lee, H.S., 2004. A fuzzy data envelopment analysis model based on dual program. Conference Proceedings - 27th edition of the Annual German Conference on Artificial Intelligence, pp. 31-39.; Lee, H.S., 2004. A fuzzy data envelopment analysis model based on dual program. Conference Proceedings - 27th edition of the Annual German Conference on Artificial Intelligence, pp. 31-39.
[85] Lee, H. S.; Shen, P. D.; Chyr, W. L., A fuzzy method for measuring efficiency under fuzzy environment, (Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3682 (2005), Springer Verlag: Springer Verlag Melbourne, Australia, Heidelberg, Germany), 343-349, D-69121
[86] Leon, T.; Liern, V.; Ruiz, J. L.; Sirvent, I., A fuzzy mathematical programming approach to the assessment of efficiency with DEA models, Fuzzy Sets and Systems, 139, 2, 407-419 (2003) · Zbl 1044.90096
[87] Lertworasirikul, S., 2002. Fuzzy Data Envelopment Analysis (DEA), Ph.D. Dissertation, Dept. of Industrial Engineering, North Carolina State University.; Lertworasirikul, S., 2002. Fuzzy Data Envelopment Analysis (DEA), Ph.D. Dissertation, Dept. of Industrial Engineering, North Carolina State University.
[88] Lertworasirikul, S., Fang, S.C., Nuttle, H.L.W., Joines, J.A., 2002a. Fuzzy data envelopment analysis, Proceedings of the 9th Bellman Continuum, Beijing, p. 342.; Lertworasirikul, S., Fang, S.C., Nuttle, H.L.W., Joines, J.A., 2002a. Fuzzy data envelopment analysis, Proceedings of the 9th Bellman Continuum, Beijing, p. 342. · Zbl 1051.90040
[89] Lertworasirikul, S.; Fang, S. C.; Joines, J. A.; Nuttle, H. L.W., A possibility approach to fuzzy data envelopment analysis, (Proceedings of the joint conference on information sciences, vol. 6 (2002), Duke University/Association for Intelligent Machinery: Duke University/Association for Intelligent Machinery Durham, US), 176-179
[90] Lertworasirikul, S.; Fang, S. C.; Joines, J. A.; Nuttle, H. L.W., Fuzzy data envelopment analysis (DEA): a possibility approach, Fuzzy Sets and Systems, 139, 2, 379-394 (2003) · Zbl 1047.90080
[91] Lertworasirikul, S.; Fang, S. C.; Nuttle, H. L.W.; Joines, J. A., Fuzzy BCC model for data envelopment analysis, Fuzzy Optimization and Decision Making, 2, 4, 337-358 (2003) · Zbl 1178.90184
[92] Lertworasirikul, S.; Fang, S. C.; Joines, J. A.; Nuttle, H. L.W., Fuzzy data envelopment analysis (fuzzy DEA): a credibility approach, (Verdegay, J. L., Fuzzy Sets Based Heuristics for Optimization (2003), Physica Verlag), 141-158 · Zbl 1051.90040
[93] Li, N., Yang, Y., 2008. FDEA-DA: discriminant analysis method for grouping observations with fuzzy data based on DEA-DA. Chinese Control and Decision Conference, art. no. 4597688, pp. 2060-2065.; Li, N., Yang, Y., 2008. FDEA-DA: discriminant analysis method for grouping observations with fuzzy data based on DEA-DA. Chinese Control and Decision Conference, art. no. 4597688, pp. 2060-2065.
[94] Liu, B., Uncertainty Theory: An Introduction to its Axiomatic Foundations (2004), Springer-Verlag: Springer-Verlag Berlin · Zbl 1072.28012
[95] Liu, S. T., A fuzzy DEA/AR approach to the selection of flexible manufacturing system, Computer and Industrial Engineering, 54, 66-76 (2008)
[96] Liu, S. T.; Chuang, M., Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries, Expert Systems with Applications, 36, 2, 1105-1113 (2009)
[97] Liu, Y. P.; Gao, X. L.; Shen, Z. Y., Product design schemes evaluation based on fuzzy DEA, Computer Integrated Manufacturing Systems, 13, 11, 2099-2104 (2007)
[98] Luban, F., Measuring efficiency of a hierarchical organization with fuzzy DEA method, Economia, Seria Management, 12, 1, 87-97 (2009)
[99] Mahdavi-Amiri, N.; Nasseri, S. H., Duality in fuzzy number linear programming by use of a certain linear ranking function, Applied Mathematics and Computation, 180, 206-216 (2006) · Zbl 1102.90080
[100] Maleki, H. R., Ranking functions and their applications to fuzzy linear programming, Far East Journal of Mathematical Sciences, 4, 3, 283-301 (2002) · Zbl 1006.90093
[101] Maleki, H. R.; Tata, M.; Mashinchi, M., Linear programming with fuzzy variables, Fuzzy Sets and Systems, 109, 21-33 (2000) · Zbl 0956.90068
[102] Meada, Y., Entani, T., Tanaka, H., 1998. Fuzzy DEA with interval efficiency. Proceedings of 6th European Congress on Intelligent Techniques and Soft Computing. EUFIT ’98. Aachen, Germany, Verlag Mainz. 2, pp. 1067-1071.; Meada, Y., Entani, T., Tanaka, H., 1998. Fuzzy DEA with interval efficiency. Proceedings of 6th European Congress on Intelligent Techniques and Soft Computing. EUFIT ’98. Aachen, Germany, Verlag Mainz. 2, pp. 1067-1071.
[103] Molavi, F.; Aryanezhad, M. B.; Shah Alizadeh, M., An efficiency measurement model in fuzzy environment, using data envelopment analysis, Journal of Industrial Engineering International, 1, 1, 50-58 (2005)
[104] Noora, A. A.; Karami, P., Ranking functions and its application to fuzzy DEA, International Mathematical Forum, 3, 30, 1469-1480 (2008) · Zbl 1157.90454
[105] Noura, A. A.; Saljooghi, F. H., Ranking decision making units in fuzzy-DEA using entropy, Applied Mathematical Sciences, 3, 6, 287-295 (2009) · Zbl 1178.90191
[106] Ölçer, A.İ.; Odabaşi, A. Y., A new fuzzy multiple attributive group decision making methodology and its application to propulsion/maneuvering system selection problem, European Journal of Operational Research, 166, 1, 93-114 (2005) · Zbl 1066.90536
[107] Pal, R.; Mitra, J.; Pal, M. N., Evaluation of relative performance of product designs: a fuzzy DEA approach to quality function deployment, Journal of the Operations Research Society of India, 44, 4, 322-336 (2007) · Zbl 1152.90492
[108] Qin, R.; Liu, Y.; Liu, Z.; Wang, G., Modeling fuzzy DEA with type-2 fuzzy variable coefficients, (Lecture Notes in Computer Science (2009), Springer: Springer Berlin/Heidelberg), 25-34
[109] Qin, R.; Liu, Y. K., A new data envelopment analysis model with fuzzy random inputs and outputs, Journal of Applied Mathematics and Computing (2009), 10.1007/s12190-009-0289-7
[110] Qin, R.; Liu, Y. K., Modeling data envelopment analysis by chance method in hybrid uncertain environments, Mathematics and Computers in Simulation, 80, 5, 922-950 (2010) · Zbl 1185.62095
[111] Ramezanzadeh, S.; Memariani, A.; Saati, S., Data envelopment analysis with fuzzy random inputs and outputs: a chance-constrained programming approach, Iranian Journal of Fuzzy Systems, 2, 2, 21-29 (2005) · Zbl 1131.90025
[112] Ramı´k, J.; Řı´mánek, J. T., Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems, 16, 123-138 (1985) · Zbl 0574.04005
[113] Saati, S.; Memariani, A., Reducing weight flexibility in fuzzy DEA, Applied Mathematics and Computation, 161, 2, 611-622 (2005) · Zbl 1084.62124
[114] Saati, S.; Memariani, A., A note on measure of efficiency in DEA with fuzzy input-output levels: a methodology for assessing, ranking and imposing of weights restrictions by Jahanshahloo et al, Journal of Science, Islamic Azad University, 16, 58/2, 15-18 (2006)
[115] Saati, S.; Memariani, A., SBM model with fuzzy input-output levels in DEA, Australian Journal of Basic and Applied Sciences, 3, 2, 352-357 (2009)
[116] Saati, S.; Memariani, A.; Jahanshahloo, G. R., Efficiency analysis and ranking of DMUs with fuzzy data, Fuzzy Optimization and Decision Making, 1, 255-267 (2002) · Zbl 1091.90536
[117] Sanei, M.; Noori, N.; Saleh, H., Sensitivity analysis with fuzzy Data in DEA, Applied Mathematical Sciences, 3, 25, 1235-1241 (2009)
[118] Saneifard, R.; Allahviranloo, T.; Hosseinzadeh Lotfi, F.; Mikaeilvand, N., Euclidean ranking DMUs with fuzzy data in DEA, Applied Mathematical Sciences, 1, 60, 2989-2998 (2007) · Zbl 1136.90378
[119] Seiford, L. M., Data envelopment analysis: the evolution of the state of the art (1978-1995), The Journal of Productivity Analysis, 7, 99-137 (1996)
[120] Sengupta, J. K., A fuzzy systems approach in data envelopment analysis, Computers and Mathematics with Applications, 24, 8-9, 259-266 (1992) · Zbl 0765.90004
[121] Sengupta, J. K., Measuring efficiency by a fuzzy statistical approach, Fuzzy Sets and Systems, 46, 1, 73-80 (1992)
[122] Sheth, N.; Triantis, K., Measuring and evaluating efficiency and effectiveness using goal programming and data envelopment analysis in a fuzzy environment, Yugoslav Journal of Operations Research, 13, 1, 35-60 (2003) · Zbl 1274.90525
[123] Soleimani-Damaneh, M., Fuzzy upper bounds and their applications, Chaos, Solitons and Fractals, 36, 217-225 (2008) · Zbl 1130.26026
[124] Soleimani-damaneh, M., Establishing the existence of a distance-based upper bound for a fuzzy DEA model using duality, Chaos, Solitons and Fractals, 41, 485-490 (2009) · Zbl 1198.90422
[125] Soleimani-damaneh, M.; Jahanshahloo, G. R.; Abbasbandy, S., Computational and theoretical pitfalls in some current performance measurement techniques and a new approach, Applied Mathematics and Computation, 181, 2, 1199-1207 (2006) · Zbl 1102.90031
[126] Sueyoshi, T., DEA-discriminant analysis in the view of goal programming, European Journal of Operational Research, 115, 564-582 (1999) · Zbl 0941.91059
[127] Sueyoshi, T., Extended DEA-discriminant analysis, European Journal of Operational Research, 131, 324-351 (2001) · Zbl 0991.91056
[128] Tanaka, H.; Ichihasi, H.; Asai, K., A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers, Control and Cybernetics, 13, 185-194 (1984) · Zbl 0551.90062
[129] Tlig, H.; Rebai, A., A mathematical approach to solve data envelopment analysis models when data are LR fuzzy numbers, Applied Mathematical Sciences, 3, 48, 2383-2396 (2009) · Zbl 1184.90013
[130] Tran, L.; Duckstein, L., Comparison of fuzzy numbers using a fuzzy distance measure, Fuzzy Sets and Systems, 130, 331-341 (2002) · Zbl 1023.03543
[131] Triantaphyllou, E., Multi-criteria Decision Making Methods: A Comparative Study (2000), Kluwer Academic Publishers: Kluwer Academic Publishers London · Zbl 0980.90032
[132] Triantis, K. P.; Girod, O., A mathematical programming approach for measuring technical efficiency in a fuzzy environment, Journal of Productivity Analysis, 10, 1, 85-102 (1998)
[133] Triantis, K., Fuzzy non-radial data envelopment analysis (DEA) measures of technical efficiency in support of an integrated performance measurement system, International Journal of Automotive Technology and Management, 3, 3-4, 328-353 (2003)
[134] Uemura, Y., Fuzzy satisfactory evaluation method for covering the ability comparison in the context of DEA efficiency, Control and Cybernetics, 35, 2, 487-495 (2006) · Zbl 1178.90213
[135] Wang, Y. M.; Luo, Y.; Liang, L., Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises, Expert Systems with Applications, 36, 5205-5211 (2009)
[136] Wang, C. H.; Chuang, C. C.; Tsai, C. C., A fuzzy DEA-neural approach to measuring design service performance in PCM projects, Automation in Construction, 18, 702-713 (2009)
[137] Wang, J.; Lin, Y. T., Fuzzy multicriteria group decision making approach to select configuration items for software development, Fuzzy Sets and Systems, 134, 3, 343-363 (2003) · Zbl 1031.91019
[138] Wang, J. J.; Jing, Y. Y.; Zhang, C. F.; Zhao, J. H., Review on multi-criteria decision analysis aid in sustainable energy decision-making, Renewable and Sustainable Energy Reviews, 13, 9, 2263-2278 (2009)
[139] Wang, Y. M.; Greatbanks, R.; Yang, J. B., Interval efficiency assessment using data envelopment analysis, Fuzzy Sets and Systems, 153, 3, 347-370 (2005) · Zbl 1122.91339
[140] Wen, M.; Li, H., Fuzzy data envelopment analysis (DEA): model and ranking method, Journal of Computational and Applied Mathematics, 223, 872-878 (2009) · Zbl 1159.90533
[141] Wen, M.; You, C.; Kang, R., A new ranking method to fuzzy data envelopment analysis, Computers & Mathematics with Applications, 59, 11, 3398-3404 (2010) · Zbl 1197.90305
[142] Wu, D.; Olson, D. L., Supply chain risk, simulation, and vendor selection, International Journal of Production Economics, 114, 2, 646-655 (2008)
[143] Wu, D.; Yang, Z.; Liang, L., Efficiency analysis of cross-region bank branches using fuzzy data envelopment analysis, Applied Mathematics and Computation, 181, 271-281 (2006) · Zbl 1142.91702
[144] Wu, R.; Yong, J.; Zhang, Z.; Liu, L.; Dai, K., A game model for selection of purchasing bids in consideration of fuzzy values, (Proceedings of the international conference on services systems and services management, vol. 1 (2005), IEEE: IEEE New York), 254-258
[145] Xu, Z.-S.; Chen, J., An interactive method for fuzzy multiple attribute group decision making, Information Sciences, 177, 1, 248-263 (2007) · Zbl 1142.68556
[146] Yager, R. R.; Basson, D., Decision making with fuzzy sets, Decision Sciences, 6, 3, 590-600 (1975)
[147] Yao, J. S.; Wu, K., Ranking fuzzy numbers based on decomposition principle and signed distance, Fuzzy Sets and Systems, 116, 275-288 (2000) · Zbl 1179.62031
[148] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606
[149] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28 (1978) · Zbl 0377.04002
[150] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, 8, 3, 199-249 (1975) · Zbl 0397.68071
[151] Zhang, L.; Mannino, M.; Ghosh, B.; Scott, J., Data warehouse (DWH) efficiency evaluation using fuzzy data envelopment analysis (FDEA), Proceedings of the Americas Conference on Information Systems, 113, 1427-1436 (2005)
[152] Zerafat Angiz, L. M.; Saati, S.; Memariani, M. A.; Movahedi, M., Solving possibilistic linear programming problem considering membership function of the coefficients, Advances in Fuzzy Sets and Systems, 1, 2, 131-142 (2006) · Zbl 1278.90483
[153] Zerafat Angiz, L. M.; Emrouznejad, A.; Mustafa, A., Fuzzy assessment of performance of a decision making units using DEA: a non-radial approach, Expert Systems with Applications, 37, 7, 5153-5157 (2010)
[154] Zerafat Angiz, L. M.; Emrouznejad, A.; Mustafa, A.; al-Eraqi, A. S., Aggregating preference ranking with fuzzy data envelopment analysis, Knowledge-Based Systems, 23, 6, 512-519 (2010)
[155] Zhou, S.J., Zhang, Z.D., Li, Y.C., 2008. Research of real estate investment risk evaluation based on fuzzy data envelopment analysis method. Proceedings of the International Conference on Risk Management and Engineering Management, pp. 444-448.; Zhou, S.J., Zhang, Z.D., Li, Y.C., 2008. Research of real estate investment risk evaluation based on fuzzy data envelopment analysis method. Proceedings of the International Conference on Risk Management and Engineering Management, pp. 444-448.
[156] Zimmermann, H. J., Fuzzy Set Theory and Its Applications (1996), Boston, Kluwer-Nijhoff Publishing: Boston, Kluwer-Nijhoff Publishing Boston · Zbl 0845.04006
[157] Zimmermann, H. J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 1, 45-55 (1978) · Zbl 0364.90065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.