Ranking Indices and Rules for Fuzzy Numbers based on Gravity Center Point

Cheng's paper (1998) proposed the method for ranking of fuzzy numbers by distance index (R
0
) and CV index based on the calculation of centroid point [see equation in pdf file]. But, CV index may be inconsistent with distance index R
0
in some circumstances. This paper proposes ranking of fuzzy numbers by distance index (R
*
) and RV index based on gravity center point [see equation in pdf file]. Furthermore, we build the rules for choosing the main ranking index between distance index (R
*
) and RV index. Finally, five numerical examples are presented to illustrate that our proposed ranking indices and rules are able to resolve the inconsistency in Cheng's paper.