A compositional approach to two-stage Data Envelopment Analysis in intuitionistic fuzzy environment

• Authors: JAVAHERIAN Nafiseh , HAMZEHEE Ali , SAYYADI TOORANLOO Hossein
• Languages of publication: EN

Abstracts

EN

Classical methods of data envelopment analysis operate by measuring the efficiency of decision-making units (DMUs) compared to similar units, without taking their internal structure into account. However, some DMUs consist of two stages, with the first stage producing an intermediate product, which is then consumed in the second stage to produce the final output. The efficiency of this type of DMU is often measured using two-stage network data envelopment analysis. In real world, most data are vague. Therefore, the inputs and outputs of systems with vagueness data create uncertainty challenges for DMUs. As a result, when uncertainty appears, intuitionistic fuzzy sets can show more information than classical fuzzy sets. This paper presents a model of two-stage Network Data Envelopment Analysis based on intuitionistic fuzzy data, which measures the efficiency of the first and second stages of each DMU, and the overall efficiency measures based on the stage efficiencies

Keywords

EN

data envelopment analysis; intuitionistic fuzzy; two-stage DEA; triangular numbers

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2021
• Volume: 31
• Issue: 1
• Pages: 21-39

Contributors

author

JAVAHERIAN Nafiseh

• Department of Applied Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

author

HAMZEHEE Ali

• Department of Applied Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

author

SAYYADI TOORANLOO Hossein

• Department of Management, Meybod University, Meybod, Iran

References

• AMERI Z., SANA S.S., SHEIKH R., Self-assessment of parallel network systems with intuitionistic fuzzy data: a case study, Soft. Comput., 2019, 1–12.
• AMIN G.R., TOLOO M., Finding the most efficient DMUs in DEA: An improved integrated model, Comp.Ind. Eng., 2007, 52 (1), 71–77.
• ANANDARAO S., DURAI S.R.S., GOYARI P., Efficiency decomposition in two-stage data envelopment analysis: an application to life insurance companies in India, J. Quant. Econ., 2019, 17 (2), 271–285.
• ATANASSOV K.T., On a second new generalization of the Fibonacci sequence, Fibon. Quart., 1986, 24 (4), 362–365.
• BAMAKAN S.M.H., GHOLAMI P., A novel feature selection method based on an integrated data envelopment analysis and entropy model, Proc. Comp. Sci., 2014, 31, 632–638.
• BORAN F.E., GENÇ S., KURT M., AKAY D., A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert. Syst. Appl., 2009, 36 (8), 11363–11368.
• CASTELLI A., PESENTI R., UKOVICH W., A classification of DEA models when the internal structure of the decision making units is considered, Ann. Oper. Res., 2008, 173, 207–235.
• CHARNES A., COOPER W.W., RHODES E., Measuring the efficiency of decision making units, Eur. J. Oper. Res., 1978, 2 (6), 429–444.
• CHEN Y., COOK W.D., LI N., ZHU J., Additive efficiency decomposition in two-stage DEA, Eur. J. Oper. Res., 2009, 196 (3), 1170–1176.
• CHEN S.H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets Syst., 1985, 17, 113–129.
• CHEN Y., ZHU J., Measuring information technology’s indirect impact on firm performance, Inform. Technol. Manage., 2004, 5 (1), 9–22.
• CHEN Y., LIANG L., YANG F., ZHU J., Evaluation of information technology investment: a data envelopment analysis approach, Comp. Oper. Res., 2006, 33 (5), 1368–1379.
• CHILINGERIAN J.A., SHERMAN H.D., Health-care applications: from hospitals to physicians, fromproductive efficiency to quality frontiers, Handbook on data envelopment analysis, Springer, 2004, 481–537.
• COOK W.D., ZHU J., BI G., YANG F., Network DEA: Additive efficiency decomposition, Eur. J. Oper. Res., 2010, 207 (2), 1122–1129.
• DANESHVAR ROUYENDEGH B., The DEA and intuitionistic fuzzy TOPSIS approach to departmentsʼperformances: a pilot study, J. Appl. Math., 2011, 2011.
• DESPOTIS D.K., KORONAKOS G., SOTIROS D., Composition versus decomposition in two-stage network DEA: a reverse approach, J. Prod. Anal., 2016, 45 (1), 71–87.
• EMROUZNEJAD A., YANG G.L., A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016, Socio-Econ. Plan. Sci., 2018, 61, 4–8.
• FARE R., GROSSKOPF S., Intertemporal production frontiers with dynamic DEA, Kluwer Academic, Boston 1996.
• FÄRE R., GROSSKOPF S., DEA Network, Socio-Econ. Plan. Sci., 2000, 34 (1), 35–49.
• FÄRE R., Measuring Farrell efficiency for a firm with intermediate inputs, Acad. Econ. Pap., 1991, 19 (2), 329–340.
• FARRELL M.J., The measurement of productive efficiency, J. R. Stat. Soc. Ser. A, 1957, 120 (3), 253–281.
• GRZEGORZEWSKI P., Distances and orderings in a family of intuitionistic fuzzy numbers, EUSFLAT Conf., Warsaw, Poland, 2003.
• GUO P., TANAKA H., Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets Syst., 2001, 119 (1), 149–160.
• KAO C., Efficiency decomposition in network data envelopment analysis: A relational model, Eur. J. Oper. Res., 2009, 192 (3), 949–962.
• KAO C., HWANG S.N., Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan, Eur. J. Oper. Res., 2008, 185 (1), 418–429.
• KAO C., Efficiency decomposition for parallel production systems, J. Oper. Res. Soc., 2012, 63 (1), 64–71.
• KAO C., Network data envelopment analysis: A review, Eur. J. Oper. Res., 2014, 239 (1), 1–16.
• KAO C., LIU S.T., Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets Syst., 2000, 113, 427–437.
• KAO C., LIU S.T., Efficiencies of two-stage systems with fuzzy data, Fuzzy Sets Syst., 2011, 176, 20–35.
• LEÓN T., LIERN V., RUIZ J.L., SIRVENT I., A fuzzy mathematical programming approach to the assessment of efficiency with DEA model, Fuzzy Sets Syst., 2003, 139 (2), 407–419.
• LEWIS H.F., SEXTON T.R., Network DEA: efficiency analysis of organizations with complex internal structure, Comp. Oper. Res., 2004, 31 (9), 1365–1410.
• LIANG L., YANG F., COOK W.D., ZHU J., DEA models for supply chain efficiency evaluation, Ann. Oper. Res., 2006, 145, 35–49.
• LIANG L., COOK W.D, ZHU J., DEA models for two-stage processes: Game approach and efficiency decomposition, Nav. Res. Log., 2008, 55, 643–653.
• LI Y., CHEN Y., LIANG L., XIE J., DEA models for extended two-stage network structures, Omega, 2012, 40 (5), 611–618.
• LI D.F.,CHEN G.H., HWANG Z.G., Linear programming method for multiattribute group decision making using IF sets, Inform. Sci., 2010, 180 (9), 1591–1609.
• LIM S., ZHU J., Primal-dual correspondence and frontier projections in two-stage network DEA models, Omega, 2019, 83, 236–248.
• LIU S.T., Restricting weight flexibility in fuzzy two-stage DEA, Comp. Ind. Eng., 2014, 74, 149–160.
• LIU J.S.,LU L.Y.Y., LU W.M.,LIN B.J.Y., A survey of DEA application, Omega, 2013, 41 (5), 893–902.
• LOZANO S.,Process efficiency of two-stage systems with fuzzy data, Fuzzy Sets Syst., 2014, 243, 36–49.
• MAGHBOULI M., AMIRTEIMOORI A., KORDROSTAMI S., Two-stage network structures with undesirable outputs: A DEA based approach, Measure., 2014, 48, 109–118.
• MAHAPATRA G.,ROY T., Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations, World Acad. Sci. Eng. Technol., 2009, 50, 574–581.
• NOSRAT A.,SANEI M.,PAYAN A.,HOSSENZADEH-LOTFI F.,RAZAVYAN S.H.,Using credibility theory to evaluatethe fuzzy two-stage DEA; sensitivityand stability analysis, J. Intell. Fuzzy Syst., 2019, 1–20.
• PURI J., YADAV S.P., Intuitionistic fuzzy data envelopment analysis: An application to the banking sector in India, Expert Syst., Appl., 2015, 42 (11), 4982–4998.
• SAATI S., MEMARIANI A., Reducing weight flexibility in fuzzy DEA, Appl. Math. Comp., 2005, 161 (2), 611–622.
• SENGUPTA J.K., A fuzzy systems approach in data envelopment analysis, Comp. Math. Appl., 1992, 24 (8–9), 259–266.
• SHAKOURI B., SHURESHJANI ABBASI R., DANESHIAN B., HOSSEINZADEH LOTFI F., A parametric method for ranking intuitionistic fuzzy numbers and its application to solve intuitionistic fuzzy network data envelopment analysis models, Complexity, 2020, 2020, 1–25.
• SHURESHJANI R.A., FOROUGHI A.A., Solving generalized fuzzy data envelopment analysis model: a parametric approach, Cent. Eur. J. Oper. Res., 2017, 25, 889–905.
• TAVANA M., KHALILI-DAMGHANI K.A., New two-stage Stackelberg fuzzy data envelopment analysis model, Measure., 2014, 53, 277–296.
• TONE K., TSUTSUI M., Network DEA: A slacks-based measure approach, Eur. J. Oper. Res., 2009, 197 (1), 243–252.
• TRIANTIS K., GIROD O., A mathematical programming approach for measuring technical efficiency in a fuzzy environment, J. Prod. Anal., 1998, 10 (1), 85–102.
• WANG Y.M., GREATBANKS R., YANG J.B., Interval efficiency assessment using data envelopment analysis, Fuzzy Sets Syst., 2005, 153 (3), 347–370.
• WEI G., ZHAO X., WANG H., An approach to multiple attribute group decision making with interval intuitionistic trapezoidal fuzzy information, Technol. Econ. Dev. Eco., 2012, 18 (2), 317–330.
• ZADEH L.A., Fuzzy sets, Inform. Control., 1965, 8 (3), 338–353.
• ZIMMERMANN H.J., Applications of fuzzy set theory to mathematical programming, Inform. Sci., 1985, 36 (1–2), 29–58.

Identifiers

DOI

10.37190/ord210102