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Prioritization of biofuels production pathways under uncertainties 349
The interval AHP was then employed to determine the interval weights
of the three dimensions (environmental, economic, and social aspects) and
the local interval weights of the criteria in each dimension. Taking the
weights of the three dimensions as an example, the interval comparison
matrix was first determined, as presented in Eq. (12.26).
Environmental Economic Social
Environmental 1 ½ 3 5 ½ 24
1 1
Economic 1 ½ 1 2 (12.26)
5 3
1 1 1
Social 1 1
4 2 2
The interval pair-wise comparison matrix (presented in Eq. 12.26) into
two crisp nonnegative matrices, as presented in Eqs. (12.27), (12.28),
respectively.
Environmental Economic Social
Environmental 1 3 2
1
Economic 1 1 (12.27)
5
1 1
Social 1
4 2
Environmental Economic Social
Environmental 1 5 4
1
Economic 1 2 (12.28)
3
1
Social 1 1
2
According to the geometric mean method, W L and W U can be deter-
mined, and the results are presented in Eqs. (12.29), (12.30), respectively.
(12.29)
W L ¼ 0:6262 0:2015 0:1723½
(12.30)
W U ¼ 0:6195 0:1994 0:1811½
According to Eqs. (12.14), (12.15), the values of m and k can be deter-
mined, and m¼1.0779, and k¼0.9117. It can satisfy 0<k 1 m, thus, the
interval weights of the three dimensions can be determined by Eq.(12.16),
and the results are presented in Eq. (12.31).
(12.31)
½
W ¼ 0:5709 0:6678½½ ,0:1837 0:2149,0:1571 0:1953
½
