Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31435
A Centroid Ranking Approach Based Fuzzy MCDM Model

Authors: T. C. Chu, S.H. Wu


This paper suggests ranking alternatives under fuzzy MCDM (multiple criteria decision making) via an centroid based ranking approach, where criteria are classified to benefit qualitative, benefit quantitative and cost quantitative ones. The ratings of alternatives versus qualitative criteria and the importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. The membership function for the final fuzzy evaluation value of each alternative can be developed through α-cuts and interval arithmetic of fuzzy numbers. The distance between the original point and the relative centroid is applied to defuzzify the final fuzzy evaluation values in order to rank alternatives. Finally a numerical example demonstrates the computation procedure of the proposed model.

Keywords: Fuzzy MCDM, Criteria, Fuzzy number, Ranking, Relative centroid.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1380


[1] S. Abbasbandy and T. Hajjari, “A new approach for ranking of trapezoidal fuzzy numbers,”Computers and Mathematics with Applications,vol.57,pp.413-419, 2009.
[2] L. Afkham, F. Abdi, and A. Rashidi, “Evaluation of service quality by using fuzzy MCDM: A case study in Iranian health-care centers,”Management Science Letters. vol.2, no.1,pp.291-300, 2012.
[3] B. Asady, “The revised method of ranking LR fuzzy number based on deviation degree,”Expert Systems with Applications, vol.37, pp.5056-5060, 2010.
[4] G. Büyüközkan, O. Feyzioglu, and G. Çifçi, “Fuzzy multi-criteria evaluation of knowledge management tools,” International Journal of Computational Intelligence Systems,vol.4, no.2, pp.184-195, 2011.
[5] C. Carlssonand R. Fullér, “Fuzzy multiple criteria decision making: Recent developments,”Fuzzy Sets and System, vol.78, no.2,pp.139-153, 1996.
[6] S.J. Chen and C.L. Hwang,Fuzzy Multiple Attribute Decision Making.Berlin: Springer, 1992.
[7] C.C.Chou, “A fuzzy MCDM method for solving marine transshipment container port selection problems,” Applied Mathematics and Computation, vol.186, no.1, pp.435-444, 2007.
[8] T.C. Chu and Y. Lin, “An Extension to Fuzzy MCDM,” Computers and Mathematics with Applications, vol.57, no.3, pp.445-454, 2009.
[9] G. Çifçi, and G. Büyüközkan, “A fuzzy MCDM approach to evaluate green suppliers,”International Journal of Computational Intelligence Systems, vol.4, no.5, pp.894-909, 2011.
[10] D. Dubois and H. Prade, “Operations on fuzzy numbers,”International Journal of Systems Science, vol.9, no.6, pp.613-626, 1978.
[11] R. Ezzati,T.Allahviranloo, S. Khezerloo, and M. Khezerloo, “An approach for ranking of fuzzy number,”Expert Systems with Applications, vol.39, no.1, pp.690-695, 2012.
[12] Z. Hu,Z. Chen, Z. Pei, X. Ma, and W. Liu, “An improved ranking strategy for fuzzy multiple attribute group decision making,” International Journal of Computational Intelligence Systems, vol.6, no.1, pp.38-46, 2013.
[13] E. Jafarian and M.A. Rezvani, “A valuation-based method for ranking the intuitionistic fuzzy numbers,” Journal of Intelligent & Fuzzy Systems, vol.24, pp.133-144, 2013.
[14] A. Kaufmann and M.M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Application. New York: Van Nostrand Reinhold, 1991.
[15] H.M. Nehi, “A new ranking method for intuitionistic fuzzy numbers,”International Journal of Fuzzy Systems, vol.12, no.1, pp.80-86, 2010.
[16] S. Önüt, S.S. Kara,and E. I┼čik, “Long term supplier selection using a combined fuzzy MCDM approach: A case study for a telecommunication company,” Expert Systems with Applications, vol.36 pp.3887-3895, 2009.
[17] Y.L.P. Thorani, P. PhaniBushanRao, and N. Ravi Shankar, “Ordering generalized trapezoidal fuzzy numbers,”International Journal of Contemporary Mathematical Science, vol.7, no.12, pp.555–573, 2012.
[18] X. Wang and E.E. Kerre, “Reasonable properties for the ordering of fuzzy quantities (I)& (II),”Fuzzy Sets and Systems, vol.118, no.3, pp.375-385 and pp.387-405, 2001.
[19] Y.J. Wang and H.S. Lee, “The revised method of ranking fuzzy numbers with an area between the centroid and original points,”Computers & Mathematics with Applications,vol.55, no.9,pp.2033-2042, 2008.
[20] Y.M. Wang, J.B. Yang, and D.L. Xu, “On the centroids of fuzzy numbers,” Fuzzy Sets and Systems,vol.157,pp.919-926, 2006.
[21] H.Y. Wu, G.H. Tzeng, and Y.H. Chen, “A fuzzy MCDM approach for evaluating banking performance based on balanced scorecard,”Expert Systems with Applicationsvol.36,no.6, pp.10135-10147, 2009.
[22] L.A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning, part 1,2 and 3,” Information Science, vol.8, no.3, pp.199-249, pp.301-357, 1975.
[23] L.A. Zadeh, “Fuzzy sets,”Information and Control, vol.8, no.3, pp.338-35, 1965.