Ranking Fuzzy Numbers by Centroid Method

Fateen Najwa Azman, Lazim Abdullah

Abstract


Ranking fuzzy numbers are one of the important tools in decision process. There are many methods that have been proposed by a number of researchers but most of the methods are nondiscriminating and counterintuitive. Thus, proposing a new method for ranking fuzzy numbers are very prominent. The main objective of this paper is to get better ranking results to rank generalized fuzzy numbers than existing method. This paper reviews the centroid method in ranking fuzzy numbers by several researchers. A new calculation of centroid method will be proposed in this paper. At the end of the paper, a numerical calculation and a comparison of centroid method between the proposed method and other researchers’ method will be showed to check on its consistency.

Keywords


Ranking Fuzzy Numbers; Centroid; Circumcenter of Centroids;

Full Text:

PDF

References


S,J.Chen and C.L. Hwang, Fuzzy Multiple Attribute Decision Making, Methods and Applications, Springer, Berlin, 1992.

J.H. Lee and K.H. You, A fuzzy ranking method for fuzzy numbers. IEICE Trans Fundam Electrom Commun Comput Sci, Vol. E86-A, No.10, 2003, pp. 2650-2658.

P.P. Bushan Rao and N.R.Shankar, Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and Index of Modality. Advances in Fuzzy Systems. Vol. 2011.

R. Jain. Decision-making in the presence of fuzzy variables, IEEE Transactions on Systems, Man. and Cybernatics. Vol. 6, No. 10,1976, pp. 698-703.[5]

G. Bortolan and R. Degani, A review of some methods for ranking fuzzy subsets, Fuzzy Sets and Systems, Vol. 15, No.1, 1985, pp. 1-19.

S. H. Chen. Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems, Vol. 17, No. 2, 1985, pp. 113-129.

M. Delgado, J.L. Verdegay and M.A. Vila. A procedure for ranking fuzzy numbers using fuzzy relations, Fuzzy Sets and Systems, Vol. 26, No. 1, 1988, pp. 49-62.

K. Kim and K. S. Park. Ranking fuzzy numbers with index of optimism, Fuzzy Sets and Systems, Vol. 35, No. 2, 1990, pp. 143-150.

Y. Yuan. Criteria for evaluating fuzzy ranking methods, Fuzzy Sets and Systems, Vol. 43, No. 2, 1991, pp. 139-157.

F. Choobineh and H. Li. An index for ordering fuzzy numbers, Fuzzy Sets and Systems, Vol. 54, No. 3, 1993, pp. 287-294.

C.H. Cheng. A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, Vol. 95, No. 3, 1998, pp. 307-317.

L.-H. Chen and H.-W. Lu. An approximate approach for ranking fuzzy numbers based on left and right dominance, Computers and Mathematics with Applications, Vol.41, No. 12, 2001, pp. 1589-1602.

Y. Deng, Z. Zhenfu and L. Qi. Ranking fuzzy numbers with an area method using radius of gyration, Computers and Mathematics with Applications, Vol. 51, No. 6-7, 2006, pp. 1127-1136.

A.M. Nejad and M.Mashinchi. Ranking fuzzy numbers based on the areas on the left and the right sides of fuzzy number, Computers and Mathematics with Applications, 2010, pp. 1-12.

R.R. Yager. Fuzzy decision making including unequal objectives, Fuzzy Sets and Systems, Vol. 1, Issue 2, April 1978, 1981, pp. 87-95.

T.C. Chu and C.T. Tsao. Ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications, Vol. 43, 2002, pp. 111-117.

C. Liang, J. Wu and J. Zhang. Ranking indices and rules for fuzzy numbers based on gravity center point. Paper presented at the 6th World Congress on Intelligent Control and Automation, Dalian, China.

Y.J. Wang and H.S.Lee. The revised method of ranking fuzzy numbers with an area between the centroid and original points, Computers and Mathematics with Applications, Vol. 55, 2008, pp. 2033-2042.

S.H. Chen. Operations on fuzzy numbers with function principal, Tamkang J. Management Science, Vol. 6, No. 1, 1985, pp. 13-25.

A. Kaufmann and M.M. Gupta. Introduction to fuzzy arithmetics : Theory and applications, Van Nostrand Reinhold, New York, 1985.




DOI: https://doi.org/10.11113/mjfas.v8n3.134

Refbacks

  • There are currently no refbacks.


Copyright (c) 2014 Fateen Najwa Azman, Lazim Abdullah

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Copyright © 2005-2019 Penerbit UTM Press, Universiti Teknologi Malaysia. Disclaimer: This website has been updated to the best of our knowledge to be accurate. However, Universiti Teknologi Malaysia shall not be liable for any loss or damage caused by the usage of any information obtained from this website.