Asian Journal of Managerial Science (AJMS)
An Assessment of Objectivity Convergence of Fuzzy TOPSIS Method Extended With Rank Order Weights in Group Decision Making
Author : Ayan Chattopadhyay and Upasana BoseVolume 7 No.3 October-December 2018 pp 26-33
Abstract
Group decision making in a multi criteria environment is a familiar business situation where the decision makers identify an ideal choice, among many. The situation gets complex when decision makers do not have crisp data to deal with. The fuzzy TOPSIS method, and its likes, provides solution to such problems and the criteria weight plays a determinant role in the overall priority estimation. This paper presents an extended fuzzy TOPSIS approach by incorporating criteria weights derived from rank order. It considers three criteria weights; the rank order centroid, rank sum and rank reciprocal weights. The criteria weights are calculated separately and integrated with fuzzy TOPSIS method to rank choices. Finally, objectivity convergence of the alternative rankings is tested. The proposed method yields a fairly uniform and consistent result in the case of supply chain management and anticipates wide application in multi criteria environment, concomitant with uncertainty and vagueness.
Keywords
MCDM, Fuzzy TOPSIS, Rank Order Centroid, Rank Sum, Rank Reciprocal
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References
[1] Barron, F., & Barrett, B.E. (1996b). Decision Quality Using Ranked Attribute Weights. Management Science, 42, 1515-1523.
[2] Barron, F.H. (1992). Selecting a Best Multiattribute Alternative with Partial Information about Attribute Weights. Acta Psychologica, 80, 91-103.
[3] Barron, F.H. & Barrett, B.E. (1996a). The Efficacy of SMARTER: Simple Multiattribute Rating Technique Extended to Ranking. Acta Psychologica, 93(1–3), 23–36.
[4] Boer, L.D., Labro, E., & Morlacchi, P. (2001). A review of methods supporting supplier selection. European Journal of Purchasing & Supply Management, 7, 75–89.
[5] Chan, F.T.S., & Kumar, N. (2007). Global supplier development considering risk factors using fuzzy extended AHP-based approach. OMEGA – International Journal of Management Science, 35(4), 417-431.
[6] Chen, M.F., Tzeng, G.H., & Ding, C.G. (2003). Fuzzy MCDM Approach to select service provider. Proceedings of the IEEE international conference on fuzzy systems, 572-577.
[7] Chen, S.H. (1985). Operations on fuzzy numbers with function principle. Tamkang Journal of Management Sciences, 6(1), 13-26.
[8] Cheong, C.W., Jie, L.H., Meng, M.C., & Lan. A.L.H. (2008). Design and Development of Decision Making System Using Fuzzy Analytic Hierarchy Process. American Journal of Applied Sciences, 5(7), 783-787.
[9] Dahel, N.E. (2003). Vendor selection and order quantity allocation in volume discount environments. Supply Chain Management: An International Journal, 8(4), 335-342.
[10] Dale, E. (1960). The great organizers. McGraw Hill, New York.
[11] Ding, J.F. (2011). An intergrated fuzzy TOPSIS method for ranking alternatives and its application. Journal of Marine Science and Technology, 19(4), 341-352.
[12] Dyer, J.S., Fishburn, P.C., Steuer, R.E., Wallenius, J., & Zionts, S. (1992). Multiple criteria decision making, multiattribute utility theory: the next ten years. Management Science, 38(5), 645–654.
[13] Feng, C.M., & Wang, R.T. (2000). Performance evaluation for airlines including the consideration of financial ratios. Journal of Air Transport Management, 6, 133–142.
[14] Gani, A.N., & Assarudeen, S.N.M. (2012). A New Operation on Triangular Fuzzy Number for Solving Fuzzy Linear Programming Problem. Applied Mathematical Sciences, 6(11), 525–532.
[15] Ghazanfari, M., Rouhani, S., & Jafari, M. (2014). A fuzzy TOPSIS model to evaluate the Business Intelligence competencies of Port Community Systems. Polish Maritime Research, 2(82), 86-96.
[16] Ghodsypour, S.H., & O’Brin, C. (1998). A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming. International Journal of Production Economics, 56-57(1-3), 199-212.
[17] Hwang, C.L., & Yoon, K. (1981). Multiple Attribute Decision Making Methods and Applications. Springer, Berlin Heidelberg.
[18] Jahanshahloo, G.R., Lotfi, F.H., & Izadikhah, M. (2006). Extension of the TOPSIS method for decision-making problems with fuzzy data. Applied Mathematics and Computation, 181, 1544–1551.
[19] Kumar, S., Kumar, S., & Barman, A.G. (2018). Supplier selection using fuzzy TOPSIS multi criteria model for a small scale steel manufacturing unit. Procedia Computer Science, 133, 905–912.
[20] Lai, Y.J., Liu, T.Y., & Hwang, C.L. (1992). Fuzzy mathematical programming, methods and applications. Springer, Berlin, Heidelberg.
[21] Liu, F.H., & Hai, H.L. (2005). The voting analytic hierarchy process method for selecting supplier. International Journal of Production Economics, 97(3), 308-317.
[22] Mehralian, G., Gatari, A.R., Morakabati, M., & Vatanpour, H. (2012). Developing a suitable model for supplier selection based on
supply chain risks: an empirical study from Iranian Pharmaceutical Companies. Iranian Journal of Pharmaceutical Research, 11(1), 209-219.
[23] Nadaban, S., Dzitac, S., & Dzitac, I. (2016). Fuzzy Topsis: A general view. Procedia Computer Science, 91, 823-831.
[24] Saghafian, S., & Hejazi, S.R. (2005). Multi-criteria Group Decision Making Using a Modified Fuzzy TOPSIS Procedure. Proceedings of the IEEE Conference, 215-221. Retrieved from http://j.mp/2t5AtIS.
[25] Sarkis, J., & Talluri, S. (2002). A Model for Strategic Supplier Selection. The Journal of Supply Chain Management, 38(1), 18-28.
[26] Shemshadi, A., Shirazi, H., Toreihi, M., & Tarokh, M. (2011). A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Systems with Applications, 38, 12160–12167.
[27] Solymosi. T., & Dompi J. (1985). Method for Determining the Weights of Criteria: the Centralized Weights. European Journal of Operational Research, 26, 35-41.
[28] Stillwell, W.G., Seaver D.A., & Edwards, W. (1981). A comparison of weight approximation techniques in multi attribute utility decision making. Organizational Behavior and Human Performance, 28, 62-77.
[29] Sun, C.C., & Lin, G.T.R. (2009). Using fuzzy TOPSIS method for evaluating the competitive advantages of shopping websites. Expert Systems with Applications, 36, 11764–11771.
[30] Wang, Y.M., & Elhag, T. (2006). Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Systems with Applications, 31(2), 309-319.
[31] Wang, T.C., & Lee, H.D. (2009). Developing a Fuzzy TOPSIS Approach based on Subjective Weights and Objective Weights. Expert Systems with Applications, 36, 8980–8985.
[32] Wang, Y. J., & Lee, H.S. (2007). Generalizing TOPSIS for fuzzy multiple-criteria group decision-making. Computers and Mathematics with Applications, 53, 1762–1772.
[33] Wang, Y.J., Lee, H.S., & Lin, K. (2003). Fuzzy TOPSIS for multi-criteria decision making. International Mathematical Journal, 3, 367–379.
[34] Weber, C.A. (1996). A data envelopment analysis approach to measuring vendor performance. Supply Chain Management, 1(1), 28-39.
[35] Zadeh, L.A. (1970). The concept of a linguistic variable and its application to approximate reasoning – I. Information Sciences, 8, 199–249.