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A multicriteria intuitionistic fuzzy group decision-making method 363

1
(13.12)
ραðÞ ¼
0:51 + π α Þ 1 μð α Þ
ð
1
(13.13)
0:51 + π β 1 μ β
ρβðÞ ¼
(1) α¼(μ α ,υ α ,π α ) is superior to β¼(μ β ,υ β ,π β ) when ρ(α)>ρ(β).
(2) α¼(μ α ,υ α ,π α ) is equivalent to β¼(μ β ,υ β ,π β ) when ρ(α)¼ρ(β).
(3) α¼(μ α ,υ α ,π α ) is inferior to β¼(μ β ,υ β ,π β ) when ρ(α)<ρ(β).
Definition 5 Distance between two intuitionistic fuzzy numbers (Xu and
Yager, 2008)
Suppose α¼(μ α ,υ α ,π α ) and β¼(μ β ,υ β ,π β ), the distance between α and β
can be determined by Eq. (13.14).

1

μ μ + υ α υ β + π α π β (13.14)

ð
d α, βÞ ¼ α β
2
Definition 6 Similarity between two intuitionistic fuzzy sets (Xu, 2007b)
Assume that X¼{α 1 ,α 2 , …,α n } be a universe of discourse, the similarity
between two intuitionistic fuzzy sets A¼{hα j ,μ A (α j ),υ A (α j )ijα j 2X} and
B¼{hβ j ,μ A (β j ),υ A (β j )ijβ j 2X} can be determined by Eq. (13.15).
SA, BÞ ¼ 1
ð
3 1
n 2
2
X 2 2 2
μ α j μ

j
j
j

A B β + υ A α j υ B β + π A α j π B β
6 7
j¼1
6 7
6 7
n
6 2 2
X 2 7
μ α j + μ

4 5
j
j
j

A B β + υ A α j + υ B β + π A α j + π B β
j¼1
(13.15)
2.2 Similarity measure-based multicriteria
decision-making method
The multicriteria intuitionistic fuzzy group decision-making (MCIFGDM)
method for sustainability ranking of biofuel production pathways was devel-
oped in this section, and the MCIFGDM method was based on the similarity
measure. Let {A 1 ,A 2 , …,A m } be a discrete set of alternative biofuel produc-
tion pathways, {C 1 ,C 2 , …,C n } be a set of criteria for sustainability assess-
ment of biofuel production pathways, the developed MCIFGDM method
was presented in the following steps: