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

                   Except for the uncertainty considered in MCDM, MCDM used in further analysis of alter-
                 natives based on LCSA results has adapted the group decision making concept. The group
                 MCDM can acquire all preferences from multiple stakeholders and reflect them in the
                 decision-making results. For example, group interval BWM and interval TOPDIM have been
                 adapted in hydrogen production technique selection (Ren et al., 2018), group interval AHP
                 has been proposed in sustainability assessment framework (Ren et al., 2017), and group
                 GRA has been raised for hydrogen technologies selections as well (Manzardo et al., 2012).
                   To illustrate better the process of MCDM based on LCSA, a case study regarding oil man-
                 agement is studied by a group fuzzy MCDM method in the next section.



                                                 9.3 Methodology

                   In this section, a new group MCDM method is introduced. In order to deal with hesitations
                 happened during the judgment process by decision makers, the ZBWM (Aboutorab et al.,
                 2018) was adapted and revised as the weighting method to transform the linguistic prefer-
                 ences of criteria with respect to different decision makers into numerical fuzzy criteria
                 weights. In this revised version, group opinions were considered with various opinions from
                 multiple stakeholders. Thereafter, the goal programming method was adapted as the aggre-
                 gating method to help aggregate integrated criteria preference and the actual performance of
                 each option. Those options can be ranked according to the scores generated from the pro-
                 posed method. The detailed methodology, calculation process, and result discussions were
                 provided accordingly below.



                 9.3.1 Step 1. Determine the criteria system
                   The first step is to select criteria from LCSA indicators that can better describe the options.
                 Criteria in environmental, economic, and social perspectives are selected from LCA, LCC, and
                 LCSA, respectively, and the hierarchical structure of the criteria system is built in this step. The
                 selection of criteria depends on the situation of industry and the knowledge from experts.


                 9.3.2 Step 2. Determine the decision-making matrix
                   As for all alternatives (a 1 , a 2 , …, a n ), the decision-making matrix (X) contains the informa-
                 tion of data (x ij )of ith criterion with respect to jth alternative where i¼1, 2, …, m, and j¼1,
                 2, …, n, as shown by Eq. (9.1).
                   The data x ij of criteria are collected from scientific and reliable information resources, for
                 instance, the LCA, LCC, and SLCA results with the same research boundary. The criteria
                 weights indicate the importance of each criterion in the analysis. To avoid large changes in
                 scores due to the unit of weights; the weights (w i )of ith criterion, as shown in Eq. (9.1), should
                 satisfy Eq. (9.2).
                                                     X
                                                         w j ¼ 1                              (9.2)
                                                       i
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