Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 60

Then we calculate the scores of all the alternatives:

S ( b 1 ) = 0 . 6982 , S ( b 2 ) = 0 . 7459 , S ( b 3 ) = 0 . 6810

S ( b 4 ) = 0 . 7435 , S ( b 5 ) = 0 . 6962

Since

S ( b 2 )> S ( b 4 )> S ( b 1 )> S ( b 5 )> S ( b 3 )

then

y 2 y 4 y 1 y 5 y 3

It can be seen that as the values of the parameters p and q change according
to the experts' subjective preferences, the rankings of the alternatives are slightly
different, which can reflect the experts' risk preferences. If we use the weighted
intuitionistic fuzzy Bonferroni mean (WIFBM) given by Xu and Yager (2011) to
aggregate the alternative performances, different results can be obtained. To give a
detail comparison, we express the scores of alternatives by Figs. 1.2 , 1.3 , 1.4 , 1.5 ,
1.6 , 1.7 , 1.8 , 1.9 , 1.10 and 1.11 (Xia et al. 2012a) as the parameters p and q change
between 0 and 10.
Figures 1.2 , 1.3 , 1.4 , 1.5 and 1.6 describe the scores of alternatives obtained by
Xia et al. (2012a)'s method, and Figs. 1.7 , 1.8 , 1.9 , 1.10 and 1.11 describe the scores
obtained byXu andYager (2011)'smethod. It is noted that most of the scores obtained
by Xia et al. (2012a)'s method are bigger than 0 and most of the ones obtained by Xu

The scores for the alternative y 1 obtained by the WlFGBM

Fig. 1.2 Thescoresforthealternative y 1 obtained by the WIFGBM