A Centroid Ranking Approach Based Fuzzy MCDM Model
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.
<p>[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. Işik, “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.</p>
<p>[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. Işik, “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.</p>
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:54373", author = "T. C. Chu and S.H. Wu", title = "A Centroid Ranking Approach Based Fuzzy MCDM Model", abstract = "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.", volume = "7", number = "7", pages = "1461-7", }
