Page 366 - Biofuels for a More Sustainable Future

(11.8)
(11.4)
(11.7)
(11.9)
(11.5)
(11.6)
(11.3)
a 3 b 1 Þ
+ b 3 Þ
a 3
a 3 = b 1
a 2 b 2 ,
+ b 2 ,
a 3 b 3 Þ
a 3 b 3 Þ 2 i 1=2
a 2 = b 2,
a 2
a 2 b 2 ,
a 1 b 3 ,
+ b 1 ,
0<b 1 b 2 b 3
a 1 = b 2,
a 1 b 1 ,
a 1
+ ð
b 3 Þ ¼
b 3 Þ ¼ ð
b 3 Þ ¼ ð
b 3 Þ ¼ ð
λa 3 Þ
a 2 b 2 Þ 2
fuzzy numbers λ2R λ>0, and numbers, fuzzy triangular two are b 1 , b 2 , b 3 Þ Fuzzy MCDM for ranking the biofuels production pathways 323
λa 2 ,
b 2 ,
b 2 ,
triangular e ¼ ð b 2 , b 1 , b 1 , b 2 , b 1 , λa 1 , b 1 , 1 a 1 a 2 , + ð and
the B and a 3 Þ + ð a 2 , a 3 Þ ð a 2 , a 3 Þ
ð a 3 Þ ¼ ð a 3 Þ ð a 2 , 1 1 a 3 , a 1 b 1 Þ 2 0<a 1 a 2 a 3
between a 1 , a 2 , a 3 Þ e a 1 , e a 1 , a 2 , a 1 , a 2 , a 1 , e a 1 , 1 , a 3 Þ ¼ a 1 , a 2 h e ¼ ð B
operations e ¼ ð A e + B ¼ ð A e B ¼ ð A e A
e ¼ ð B λ e ¼ λð A e B ¼ ð A 1 e ¼ ð A e A, d where
arithmetic
The distance
11.1 Subtraction Multiplication
Table Addition Scalar Division Reciprocal Euclidean