Revision of distance minimization method for ranking of fuzzy numbers

Abstract Asady and Zendehnam employed “distance minimization” to ranking fuzzy numbers in Ref [1] . Then Abbasbandy and Hajjari in [2] found a problem of its. To overcome it problem, they proposed magnitude method to ranking fuzzy numbers. Unfortunately, their method can not to overcome this problem. In this paper, we want to indicate this problem and then propose a revise method of distance minimization method which can avoid problem for ranking fuzzy numbers. Since the revised method is based on the distance minimization method, it is easy to rank fuzzy numbers in a way similar to the original method.

[1]  Ching-Hsue Cheng,et al.  A new approach for ranking fuzzy numbers by distance method , 1998, Fuzzy Sets Syst..

[2]  José L. Verdegay,et al.  Automatic ranking of fuzzy numbers with the criterion of a decision-maker learnt by an artificial neural network , 1994 .

[3]  Saeid Abbasbandy,et al.  Ranking of fuzzy numbers by sign distance , 2006, Inf. Sci..

[4]  Saeid Abbasbandy,et al.  A new approach for ranking of trapezoidal fuzzy numbers , 2009, Comput. Math. Appl..

[5]  Miao-Ling Wang,et al.  Ranking Fuzzy Number Based on Lexicographic Screening Procedure , 2005, Int. J. Inf. Technol. Decis. Mak..

[6]  Huijun Sun,et al.  A new approach for ranking fuzzy numbers based on fuzzy simulation analysis method , 2006, Appl. Math. Comput..

[7]  Hsuan-Shih Lee,et al.  The revised method of ranking fuzzy numbers with an area between the centroid and original points , 2008, Comput. Math. Appl..

[8]  O. P. Dias,et al.  Ranking alternatives using fuzzy numbers: a computational approach , 1993 .

[9]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[10]  Marc Roubens,et al.  Ranking and defuzzification methods based on area compensation , 1996, Fuzzy Sets Syst..

[11]  K. Kim,et al.  Ranking fuzzy numbers with index of optimism , 1990 .

[12]  Jian-Bo Yang,et al.  On the centroids of fuzzy numbers , 2006, Fuzzy Sets Syst..

[13]  Etienne E. Kerre,et al.  Reasonable properties for the ordering of fuzzy quantities (II) , 2001, Fuzzy Sets Syst..

[14]  Caro Lucas,et al.  A NEW METHOD FOR RANKING OF FUZZY NUMBERS THROUGH USING DISTANCE METHOD , 2003 .

[15]  G. Bortolan,et al.  A review of some methods for ranking fuzzy subsets , 1985 .

[16]  Shigeaki Mabuchi,et al.  An approach to the comparison of fuzzy subsets with an α-cut dependent index , 1988, IEEE Trans. Syst. Man Cybern..

[17]  Przemyslaw Grzegorzewski,et al.  Nearest interval approximation of a fuzzy number , 2002, Fuzzy Sets Syst..

[18]  Bo Feng,et al.  Ranking L-R fuzzy number based on deviation degree , 2009, Inf. Sci..

[19]  H. Lee-Kwang,et al.  Ranking fuzzy values with satisfaction function , 1994 .

[20]  Shan-Huo Chen.  Ranking fuzzy numbers with maximizing set and minimizing set , 1985 .

[21]  T. Chu,et al.  Ranking fuzzy numbers with an area between the centroid point and original point , 2002 .

[22]  B. Asady,et al.  RANKING FUZZY NUMBERS BY DISTANCE MINIMIZATION , 2007 .

[23]  E. Lee,et al.  Comparison of fuzzy numbers based on the probability measure of fuzzy events , 1988 .

[24]  F. Choobineh,et al.  An index for ordering fuzzy numbers , 1993 .

[25]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[26]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

[27]  Mao-Jiun J. Wang,et al.  Ranking fuzzy numbers with integral value , 1992 .

[28]  B. Asady,et al.  The revised method of ranking LR fuzzy number based on deviation degree , 2010, Expert Syst. Appl..

[29]  Liang-Hsuan Chen,et al.  An approximate approach for ranking fuzzy numbers based on left and right dominance , 2001 .