A combined evaluation method to rank alternatives based on VIKOR and DEA with BELIEF structure under uncertainty
Subject Areas : Operation Research
امیر
امینی
1
(MSc. Graduate of Industrial Engineering, Alghadir institute of higher education, Tabriz, Iran)
علیرضا
علینژاد
2
(Associate Professor, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran.)
Keywords: DEA, VIKOR, MCDM, BELIEF STRUCTURE,
Abstract :
This paper processes a combined method, based on VIKOR and Data Envelopment Analysis (DEA) to select the units with most efficiency. We utilize the VIKOR as compromise solution method. This research is a two-stage model designed to fully rank the alternatives, where each alternative has multiple inputs and outputs. The problem involves BELIEF parameters in the solution procedure. First, the alternative evaluation problem is formulated by Data Envelopment Analysis (DEA) and in the second stage; we use the opinion of experts with belief parameter to be applied into a model of group Decision-Making (DM) called the aggregated fuzzy belief decision matrix. . In this method weight of efficiency witch obtained from VIKOR is multiply with weight of CCR model of data envelopment analysis. Finally, to illustrate the proposed method, an illustrative example is provided.
Abo-Sinna, M. A., & Amer, A. H. (2005). Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems. Applied Mathematics and Computation, 162(1), 243–256.
Abo-Sinna, M.A. (2000). Extensions of the TOPSIS for multi-objective dynamic programming problems under fuzziness. Journal of Advances in Modeling and Analysis, 43 (4), 1–24.
Charnes, A., Cooper, W.W., & Rhodes, E. (1978). ‘Measuring the efficiency of decision making units’. Eur.J.Oper, 2,429-444.
Charnes, A., Cooper, W.W., & Rhodes, E., (1978). Measuring the efficiency of decision making units. Eur.J.Oper, 2, 429-444.
Cheng, E.W.L., Chiang, Y. H., & Tang, B.S. (2007). ‘Alternative approach to credit scoring by DEA: Evaluating borrowers with respect to PFI projects’. Building and Environment, 42, 1752– 1760.
Cheng, E.W.L., Chiang, Y. H., & Tang, B.S. (2007). Alternative approach to credit scoring by DEA: Evaluating borrowers with respect to PFI projects. Building and Environment,42, 1752– 1760.
Daneshvar Rouyendegh, B., (2011). The DEA and Intuitionistic Fuzzy TOPSIS Approach to epartments’ Performances:A Pilot Study. Journal of Applied Mathematics, Article ID 712194, 16 pages.
De Koster, M. B. M., Balk, B. M., & Van Nus, W. T. I. (2009). On using DEA for benchmarking container terminals. International Journal of Operations & Production Management, 29(11),1140-1155.
De,S.K.S, Biswas,R., & Roy,A.R. (2001).“An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, 117(2), 209–213.
Ebrahimnejad, S., Mousavi, S.M., & Seyrafianpour, H. (2010). Risk identification and assessment for build-operate-transfer projects: a fuzzy multi attribute deci- sion making model. Expert Syst. Appl, 37, 575–586.
Ebrahimnejad, S., Mousavi, S.M., Tavakkoli-Moghaddam, R., Hashemi, H., & Vahdani, B. (2012).A novel two-phase group decision making approach for construction project selection in a fuzzy environment. Appl. Math. Modell, 36 (9), 4197–4217.
Fu, C., & Yang C-L (2010) the group consensus based evidential reasoning approach for multiple attributive group decision analysis. European Journal of Operational Research, 206 601–608.
Ganley, j. A., & J.S. Cubbin, (1992). ‘Public Sector Efficiency Measurement: Applications of Data Envelopment Analysis. Elsevier Science Publishers.
Golany, B. (1988). “An interactive MOLP procedure for the extension of data envelopment analysis to effectiveness analysis.” Journal of the Operational Research Society, vol. 39, no. 8, pp. 725–734.
Huang, J.J., Tzeng, G.H., & Lio, H.H. (2009). A Revised VIKOR Model for Multiple Criteria Decision \Making- The perspective of Regret Theory. In: Proceedings of the 20th International Conference on Communications in Computer and Information Science (CCIS).
Jafarian-Moghaddam, A. R., & Ghoseiri, K. (2011). ‘Fuzzy dynamic multi-objective Data Envelopment Analysis model’.Expert Systems with Applications, 38, 850–855.
Jiang, J., Chen, Y.W., Chen, Y.W., & Yang, K.W. (2011). Topsis whit fuzzy belief structure for group belief multiple criteria decision making. Expert system whit applications, 38, 9400–9406.
Jolai, F., Yazdian, S.A., Shahanaghi, K., & Azari-Khojasteh, M. (2011). Integrating fuzzy TOPSIS and multi-period goal programming for purchasing multiple products from multiple suppliers. Journal of Purchasing & Supply Management, 17, 42–53.
Liua, H. C., Youa, J. J., Youb, X.Y., & Shan, M. M. (2014). A novel approach for failure mode and effects analysis using combination weighting and fuzzy VIKOR method, Applied Soft Computing (accepted paper).
Lozano, S., & Villa, G. (2004). ‘Centralized resource allocation using Data Envelopment Analysis’. Journal of Productivity Analysis, 22, 143–161.
Mandal, S., Singh, K., Behera, R. K., Sahu, S.K., Raj, N., & Maiti, J. (2015). Human error identification and risk prioritization in overhead crane operations using HTA, SHERPA and fuzzy VIKOR method. Expert Systems with Applications ,42 ,7195–7206.
Mehdiabadi, A., Rohani, A., & Amirabdollahiyan, S. (2013), Ranking industries using a hybrid of DEA-TOPSIS. Decision Science Letters, 2, 251–256.
Mohaghar, A., Fathi, M. R., Zarchi, M. K., & Omidian, A. A. (2012). Combined VIKOR- Fuzzy AHP. Approach to marketing strategy selection. Bus. Manage Strat, 3 (1).
Mousavi, S.M., Jolai, F., & Tavakkoli-Moghaddam, R. (2011). A fuzzy stochastic multi- attribute group decision-making approach for selection problems. Group Decis. Negot. http://dx.doi.org/10.1007/s10726-011-9259-1.
Opricovic, S. (1998). Multicriteria optimization of civil engineering systems. Faculty Civil Eng. Belgrade, 2, 5–21.
Opricovic, S., & Tzeng, G. H. (2002). Multicriteria planning of post-earthquake sustainable reconstruction. Comput. Aid. Civil Infrastruct. Eng. 17, 211–220.
Opricovic, S., & Tzeng, G. H. (2004). The Compromise solution by MCDM methods. A comparative analysis of VIKOR and TOPSIS. Eur. J. Operat. Res. 156, 445–455.
Opricovic, S., & Tzeng, G.H. (2007). Extended VIKOR method in comparison with outranking methods. Eur. J. Operat. Res. 178, 514–529.
Qin, J., Liu, X., & Pedrycz, W. (2015). An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment. Knowledge-Based Systems (accepted paper).
Ramanathan, R. (2007). ‘Supplier selection problem: Integrating DEA with the approaches of total cost of ownership an AHP’. Supply Chain Management, 12, 258-261.
Ramanathan, R. (2007). Supplier selection problem: Integrating DEA with the approaches of total cost of ownership an AHP. Supply Chain Management, 12, 258-261.
Rouyendegh, B. D., & Erol, S. (2010). The DEA—FUZZY ANP Department Ranking Model Applied in Iran Amirkabir University. Acta Polytechnica Hungarica, 7(4), 103–114.
Vahdani, B., Hadipour, H., Salehi Sadaghiani, J., & Amiri, M. (2010). Extension of VIKOR method based on interval-valued fuzzy sets. Int. J. Adv. Manuf. Technol, 47, 1231–1239.
Wang, T-C., Liang, J-L., Ho, C-Y., (2006), Multi-criteria decision analysis by using fuzzy VIKOR. Presented at The IEEE International Conference on Service Systems and Service Management Troyes, FRANCE.
Wei, S.H., & Chen, S.M. (2009) .A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Systems with Application, 36(1), 589–598.
Yang, J.B. (2001). Rule and utility based evidential reasoning approach for multi attribute decision analysis under uncertainties. European journal of operational research,131,31-61.
Yang, J.B., & Sen, P. (1994). A general multi-level evaluation process for hybrid MADM with uncertainty. IEEE Transactions on Systems,Man, and Cybernetics - Part A: Systems and Humans 24(10),1458–1473.
Yang, J.B., & Xu, D.L(2002). On the evidential reasoning algorithm for multi attribute decision analysis under uncertainty. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 32(3), 289–304.
Yang, J.B., & Xu, D.L. (2002). On the evidential reasoning algorithm for multi attribute decision analysis under uncertainty. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 32(3), 289–304.
Zhu, G. N., Hu, H., Qi, J., Gu, C. C., & Peng, Y. H. (2015). An integrated AHP and VIKOR for design concept evaluation based on rough number. Advanced Engineering Informatics (accepted paper).