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 (R0) and CV index based on the calculation of centroid point [see equation in pdf file]. But, CV index may be inconsistent with distance index R0in 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.