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340 Biofuels for a More Sustainable Future
users to use interval numbers rather than the basketball numbers to establish
the comparison matrix was employed for determining the weights of the cri-
teria for sustainability assessment of biofuel production pathways, and the
interval GRA method was employed to determine the sustainability
sequence of alternative biofuel production pathways under uncertainties.
2 Interval multicriteria decision making method
Interval multicriteria decision making method is a series of MCDM adapting
interval numbers as criteria inputs and weights, which helps to deal with
complex decision-making cases with vagueness of language and uncertainty
of criteria values. The interval VIKOR raised by Sayadi et al. (2009) supports
decision-makers to rank the alternatives with regards to its performances
comparing to the best and the worst alternative. Giove (2002) and Jahan-
shahloo et al. (2006) have extended TOPSIS into interval TOPSIS, respec-
tively. The interval TOPSIS considers the balance between needs fulfillment
and lost compromise. Luo et al. (2015) developed an interval GRA method
based on the grey theory invented by Deng (1989). Xu and Da (2003) have
extended the AHP method into the interval analytic hierarchy process
(IAHP), which assistant to quantify the criteria values and weights according
to quality values. In addition, interval PROMETHEE (Le T eno and Mar-
eschal, 1998) and interval Best Worst Method (BWM) (Rezaei, 2016) are
methods for dealing qualified inputs as well. Among these, the IAHP is
one of the most commonly used weighting methods in MCDM for its
advantage of addressing the hesitations and ambiguity existing in human’s
judgments.
In this section, interval multicriteria decision making method for biofuel
production pathways selection is described. Criteria system establishment,
criteria weighting, and aggregating are three steps for MCDM method
whose methods are designed as criteria system establishment, interval
AHP, and interval GRA as shown in Fig. 12.1.
2.1 Interval numbers
The basic information of interval numbers was presented in this section
based on the work of He et al. (2017), Zhang et al. (2005), Bohlender
and Kulisch (2011), Moore (1966), Dymova et al. (2013), and Xu and Da
(2003).
Let x ¼ x , x½ + ¼ xx x x ,x x ,x , x 2 Rjf + + + g. Here
+
is called an interval number and is a positive interval number
x ¼ x , x½
