Page 180 - Materials Chemistry, Second Edition

178 9. Life cycle decision support framework: Method and case study

Some studies realized that uncertainties generated by fluctuation of data regarding time
change, and human judgment buffer left because of knowledge limitations, impacted the re-
sults of decision making. To illustrate the uncertainties of values, the interval numbers, fuzzy
numbers, and rough numbers were adapted in the MCDM methods. The extended methods

l
u
revised the crisp number (x ij ) in decision-making matrix into interval number (e x ij ¼ x , x ,
l
u
where x is the lower limit and x is the upper limit of this interval number), triangular fuzzy
l m u
u
l
m
number (e x ij ¼ x , x , x , where x is the lower limit, x is the most possible number, and x is
the upper limit of this interval number), and other numbers that can express uncertainties.
Similarly, the criteria weights can be revised to use fuzzy numbers or rough numbers to
involve uncertainties.
9.2.3 Criteria weighting
Criteria weighting is one of the important steps of MCDM to determine the weights of
criteria according to different preferences from decision makers. Many studies have been car-
ried out to develop MCDM and to adapt MCDM to LCSA analysis based on real-life case
studies. Summarized from the literature, the criteria weighting methods adapted in the com-
bination of MCDM and LCSA method in 2005–2019 are shown in Table 9.1.
As observed from Table 9.1, analytical hierarchy analysis (AHP) raised by Saaty (1987)
is the classic but most popular weighting method. Furthermore, some adaptions have
been made from original version AHP to make it suitable in more situations. In addition,
some studies have extended MCDM to be applied in interval number, fuzzy number,
rough number, and other types of number to take reservations of decision makers into
consideration.

TABLE 9.1 Weighting methods used in sustainability analysis.
Method Reference
Crisp number
AHP Alwaer and Clements-Croome (2010), Castillo and Pitfield (2010), San-Jos e Lombera and
Cuadrado Rojo (2010), Awasthi and Chauhan (2011), Turskis and Zavadskas (2011),
Awasthi and Chauhan (2012), Dai and Blackhurst (2012), Del Can ˜o et al. (2012), Zavadskas
ˇ
et al. (2012), Jones et al. (2013), Palevi cius et al. (2013), Raslanas et al. (2013), Sioz ˇinyt_ e et al.
(2014), Akhtar et al. (2015), Ren et al. (2015), Bari c et al. (2016), De La Fuente et al. (2016),
Entezaminia et al. (2016), Al Garni and Awasthi (2017), B€ uy€ uk€ ozkan and Karabulut (2017),
Das and Shaw (2017), de la Fuente et al. (2017), Gao et al. (2017), Inti and Tandon (2017),
Luthra et al. (2017a), Rashid et al. (2017), Xu et al. (2017), Alhumaid et al. (2018), De Luca
et al. (2018), Dı ´az-Cuevas et al. (2018), Mirjat et al. (2018), Opher et al. (2018b), Tang et al.
(2018), Yazdani et al. (2018), Zheng et al. (2019)
BWM Rezaei et al. (2016), Kusi-Sarpong et al. (2018), Liu et al. (2018)
ANP Tsai et al. (2013), Ozcan-Deniz and Zhu (2015), Zhang et al. (2015)