Efficiency Evaluation of Two-Stage Data Envelopment Analysis Model Based on Triangular Intuitionistic Fuzzy numbers andslack variables

Subject Areas : Statistics

nafiseh  javaherian ¹ (Department of applied mathematics, Islamic Azad university, Kerman Branch, Kerman, Iran)
Ali  Hamzehee ² (Assistant Professor in applied mathematics, Department of applied mathematics, Kerman Branch, Islamic Azad university, Kerman, Iran)
Hossein  sayyadi Tooranloo ³ (Associate Professor in Industrial Management, Department of Management, Meybod University, Meybod, Iran)
Reza  Soleymani-Damaneh ⁴ (Assistant Professor in Management, Department of Management, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran)

Received: 2019-10-23 Accepted : 2020-07-08 Published : 2022-01-21

Keywords: متغیرهای کمکی, اعداد مثلثی فازی شهودی, تحلیل پوششی داده ها, تحلیل پوششی داده های دو مرحله ای فازی شهودی,

Abstract :

Data Envelopment Analysis (DEA) is one of the best tools for evaluating the performance of decision-making units. Traditional DEA fails to measure efficient and inefficient units and evaluate the performance of network systems, and traditional models of DEA do not pay attention to internal structures and intermediate values. For this reason, in recent years, DEA model, known as network Data Envelopment Analysis models, have been introduced, this models eliminated this deficiency by considering intermediate values. In this paper, DEA based on network two-stage and slack variables and triangular intuitionistic fuzzy data is used to identify the efficiency of units. At first, the two-stage DEA model is introduced and then the model is transformed based on intuitionistic fuzzy coefficients and variables and finally it is converted to crisp two-stage structures by arithmetic operators on intuitionistic fuzzy data. The importance of this model is to measure the values of slack variables, which based on the Tone and Tsutsui model optimizes the intermediate values for inefficient units and ultimately shows better inefficiency. Finally, the optimized intermediate values are considered in the proposed model and thus are improved the overall efficiency of the system.

References:

]1[ ج. گرامی، ارائه یک روش دو مرحله ای برای تعیین الگوی مناسب و بازده به مقیاس (مطالعه موردی: دبیرستان­های دخترانه ناحیه یک شهرستان شیراز)، پژوهش­های نوین در ریاضی، س. پنجم، ش. هجدهم، (1398)

]2[ س. ه. ناصری، ا. غلامی، ع. ابراهیم نژاد، م. فلاح جلودار، یک رویکرد جدید مبتنی بر آلفا برش­ها برای حل مدل تحلیل پوششی داده­ها با ورودی­ها  و خروجی­های تصادفی فازی، پژوهش­های نوین در ریاضی، س. دوم، ش. پنجم، (1395)

 [3] R. D. Banker, A. Charnes, W. W. Cooper, Some models for estimating technical and scale inefficiencies in

data envelopment analysis, Management science, 30 (1984), 1078-1092.

[4] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European journal of operational research, 2 (1978), 429-444.

[5] M. J, Farrell, The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General), 120 (1957), 253-281.

 

[6] A. Barzegarinegad G. R. Jahanshahloo,, M. Rostamy-Malkhalifeh, A full ranking for decision making units using ideal and anti-ideal points in DEA, The Scientific World Journal, 2014 (2014), 1-8.

[7] F. Hosseinzadeh lotfi,  M. Navabakhs, A. Tehranian, M. Rostamy-Malkhalifeh, R. Shahverdi, Ranking bank branches with interval data the application of DEA, International Mathematical Forum, 2 (9), (2007), 429-440.

[8]H. Nikfarjam, M. Rostamy-Malkhalifeh, S. Mamizadeh-Chatghayeh, Measuring supply chain efficiency based on a hybrid approach, Transportation Research Part D: Transport and Environment, 39 (2015), 141-150.

[9] R. Fare, S. Grosskopf, Intertemporal production frontiers, dynamic DEA, Kluwer Academic, In collaboration Boston, (1996).

[10] R. Färe,  S. Grosskopf, Network DEA, Socio-Econ, Plan. Sci, 34 (2000), 35-49.

[11] H. F. Lewis, T. R. Sexton. Network DEA: efficiency analysis of organizations with complex internal structure. Computers and Operations Research 2004, 31: 1365-1410.

[12] T. R. Sexton, H. F. Lewis, Two-stage DEA: An application to major league baseball, Journal of Productivity Analysis, 19 (2003), 227-249.

[13] A. M Prieto, J. L. Zofio, Network DEA efficiency in input–output models: with an application to OECD countries, European journal of operational research, 178 (2007), 292-304.

[14] K. Tone, A slacks-based measure of efficiency in data envelopment analysis, European journal of operational research 130 (2001), 498-509.

[15] A. Ashrafi, A. Jaafar, L. S Lee, A. Bakar, Efficiency decomposition for two-process production systems with shared inputs in data envelopment analysis, Applied Mathematical Sciences, 5 (2011), 2593-2602.

[16] M. Rostamy-Malkhalifeh, E.  Mollaeian, S. Mamizadeh-Chatghayeh, A new non-radial network DEA model for evaluating performance supply chain, Indian Journal of Science and Technology, 6 (3), (2013), 4188-4192.

[17] E. Khamseh, Ranking Efficient DMUs in Two-stage Network DEA with Common Weights method, Journal of New Researches in Mathematics, 3(2017), 5-18.

[18] K. Tone, M. Tsutsui, Network DEA: A slacks-based measure approach, European journal of operational research, 197 (2009), 243-252.

[19] K. Tone, M. Tsutsui, Dynamic DEA: A slacks-based measure approach. Omega 38 (2010), 145-156.

[20] K. Tone, M. Tsutsui, Dynamic DEA with network structure. In, Workshop on DNDEA 2013, 2013, 1-10.

[21] L. A. Zadeh, Fuzzy sets, Information and control 8 (1965), 338-353.

[22] M. Tavana, K. Khalili-Damghani, A new two-stage Stackelberg fuzzy data envelopment analysis model,  Measurement, 53 (2014), 277-296.

[23] A. Hatami-Marbini, M. Tavana, A. Emrouznejad, Productivity growth and efficiency measurements in fuzzy environments with an application to health care, International Journal of Fuzzy System Applications (IJFSA) 2 (2012), 1-35.

[24] P. Peykani, E. Mohammadi, A.  Emrouznejad, M. S Pishvaee, M. Rostamy-Malkhalifeh, Fuzzy data envelopment analysis: an adjustable approach, Expert Systems with Applications, 136 (2019), 439-452.

[25] P. Peykani, E. Mohammadi, M. S Pishvaee, M. Rostamy-Malkhalifeh, A. Jabbarzadeh, A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches, RAIRO-Operation, 52 (2018) 1445–1463.

 [26] P. Peykani, E. Mohammadi, M. Rostamy-Malkhalifeh, F. Hosseinzadeh Lotfi, Fuzzy data envelopment analysis approach for ranking of stocks with an application to Tehran stock exchange, Advances in Mathematical Finance and Applications 4 (1), (2019), 31-43.

 [27] A. Rahmani, F. Hosseinzadeh lotfi, M. Rostamy-Malkhalifeh, T. Allahviranloo, A new method for defuzzification and ranking of fuzzy numbers based on the statistical beta distribution, Advances in Fuzzy Systems, 2016 (2016), 1-8.

[28] A. Ebrahimnejad, Cost efficiency measures with trapezoidal fuzzy numbers in data envelopment analysis based on ranking functions: application in insurance organization and hospital, International Journal of Fuzzy System Applications (IJFSA) 2 (2012), 51-68.

 [29] C. Kao, S. T. Liu, Fuzzy efficiency measures in data envelopment analysis, Fuzzy sets and systems, 113 (2000), 427-437.

[30] P. Guo, H. Tanaka, Fuzzy DEA: a perceptual evaluation method, Fuzzy sets and systems, 119 (2001), 149-160.

[31] S. Lertworasirikul, S. C. Fang, H. L. Nuttle, J. A. Joines, Fuzzy BCC model for data envelopment analysis, Fuzzy Optimization and Decision Making, 2 (2003), 337-358.

[32] S. Saati, A. Memariani, G. R. Jahanshahloo, Efficiency analysis and ranking of DMUs with fuzzy data, Fuzzy Optimization and Decision Making, 1 (2002), 255-267.

[33] S. Saati, N. Imani, Classifying Flexible Factors Using Fuzzy Concept, Journal of New Researches in Mathematics, 1(2), (2015), 36-46.

[34] G. R. Jahanshahloo, M. Sanei, M. Rostamy-Malkhalifeh, H. Saleh, A comment on “A fuzzy DEA/AR approach to the selection of flexible manufacturing systems”, Computers and Industrial Engineering, 56 (4), (2009), 1713-1714

[35] M. Rostamy-Malkhalifeh, E.  Mollaeian, Evaluating performance supply chain by a new non-radial network DEA model with fuzzy data, Journal of Data Envelopment Analysis and Decision, 9  (2012), 1-9.

[36] K. T. Atanassov, Intuitionistic fuzzy sets, fuzzy sets ans systems, 20 (1), (1986), 87-96.

[37] E. Szmidt, J. Kacprzyk, Intuitionistic fuzzy sets in group decision making, Notes on IFS, 2 (1996).

[38] X. Zhang, P. Liu, Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making, Technological and economic development of economy 16 (2010), 280-290.

[39] A. Arya, S. P. Yadav, Development of intuitionistic fuzzy data envelopment analysis models and intuitionistic fuzzy input–output targets, Soft Computing, (2018), 1-19.

 [40] J. Puri, S. P. Yadav, Intuitionistic fuzzy data envelopment analysis: An application to the banking sector in India, Expert Systems with Applications, 42 (2015), 4982-4998.

[41] İ. Otay, B. Oztaysi, S. C. Onar, C. Kahraman, Multi-expert performance evaluation of healthcare institutions using an integrated intuitionistic fuzzy AHP and DEA methodology, Knowledge-Based Systems, 133 (2017), 90-106.

[42] M. E. Dotoli, N. Falagario, M. Sciancalepore, A Cross-Efficiency Fuzzy Data Envelopment Analysis Technique For Performance Evaluation of Decision Making Units Under Uncertainty,

Computers & Industrial Engineering, 79 (2015), 103-114.

[43] S. H. R. Hajiagha, H. Akrami, E. Kazimieras Zavadskas, S. S. Hashemi, An intuitionistic fuzzy data envelopment analysis for efficiency evaluation under ucertainty: case of a finance and credit institution, (2013).

[44] A. Arya, S. P. Yadav, Development of intuitionistic fuzzy super-efficiency slack based measure with an application to health sector, Computers and Industrial Engineering, 115 (2018), 368-380.

[45] G. Mahapatra, T. Roy, Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations, World Academy of Science, Engineering and Technology, 50 (2009), 574-581.

[46] C. Tofallis, Input efficiency profiling: an application to airlines, Computers and Operations Research, 24 (1997), 253-258.

 [47] B. Daneshvar Rouyendegh, The DEA and intuitionistic fuzzy TOPSIS approach to departments performances: a pilot study, Journal of Applied Mathematics (2011).

[48] G. Klir, B. Yuan, Fuzzy sets and fuzzy logic: theory and applications, Upper Saddle River, (1995).