RM approach for ranking of generalized trapezoidal fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).

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

[2]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads , 2009, Expert Syst. Appl..

[3]  Deng Yong,et al.  A TOPSIS-BASED CENTROID–INDEX RANKING METHOD OF FUZZY NUMBERS AND ITS APPLICATION IN DECISION-MAKING , 2005 .

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

[5]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[6]  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..

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

[8]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers , 2007, Applied Intelligence.

[9]  Qi Liu,et al.  A TOPSIS-BASED CENTROID–INDEX RANKING METHOD OF FUZZY NUMBERS AND ITS APPLICATION IN DECISION-MAKING , 2005, Cybern. Syst..

[10]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[11]  Jee-Hyong Lee,et al.  A method for ranking fuzzy numbers and its application to decision-making , 1999, IEEE Trans. Fuzzy Syst..

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

[13]  L. M. D. C. Ibáñez,et al.  A subjective approach for ranking fuzzy numbers , 1989 .

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

[15]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[16]  Changyong Liang,et al.  Ranking Indices and Rules for Fuzzy Numbers based on Gravity Center Point , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[17]  Ramesh Jain,et al.  DECISION MAKING IN THE PRESENCE OF FUZZY VARIABLES , 1976 .

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

[19]  Soheil Sadi-Nezhad,et al.  Ranking fuzzy numbers by preference ratio , 2001, Fuzzy Sets Syst..