Subsequently, the fuzzy ANP method was used to calculate the weights of the criteria in each aspect, whose evaluation network structure was illustrated in Fig. 9.6. In this study, the interactive and interdependent relationships among the criteria are based on a focus group meeting carried out in Chongqing University in China, and a total of seven experts including three processors in Chemical Engineering, two chemical engineers who has abundant experience in cleaner production, and two Ph.D. students whose research focuses on Sustainability Engineering. The relationships among the criteria were presented in Table 9.13. If the element of cell (i,j) in Table 9.13 is 1, it means that the jth criterion affects the ith criterion, while 0 means that the jth criterion does not affect the ith criterion. For instance, the elements of cell (8,1) and cell (11,1) in Table 9.13 are equal to 1, indicating that the criteria of C₈ (maturity) and C₁₁ (technology innovation) affect C₁ (capital cost). The interactions and interdependencies among the criteria as well as their intensity vary with the preferences of the users and the actual conditions of the studied industrial system as they are incorporated in the developed method.

Afterward, the local priority vectors were obtained by executing the fuzzy pairwise comparisons and entered in the appropriate column of the supermatrix. Taking the criterion of O&M cost (C₂) in the economic aspect as an example, four criteria (C₈, C₉, C₁₀, and C₁₁) in the technological aspect affect the O&M cost, the pairwise comparison can be established as showed in Table 9.14. The local priorities of C₈, C₉, C₁₀, and C₁₁ in the first cluster (economic aspect) were obtained to be 0.4437, 0.2973, 0.1846, and 0.0744, respectively, which were entered in the appropriate place of the second column of the unweighted supermatrix (Table 9.15). Similarly, the other elements in the unweighted supermatrix could also be determined and the corresponding element is equal to 0 if the two criteria do not affect each other.

Table 9.14

Comparison Matrix for Calculating the Weights of the Criteria in the Technological Aspect Affecting the Criterion of “O&M Cost”

	C8	C9	C10	C11	Weight
Maturity (C8)	(1,1,1)	(1,3/2,2)	(3/2,2,5/2)	(3/2,2,5/2)	0.4437
Energy efficiency (C9)	(1/2,2/3,1)	(1,1,1)	(1,3/2,2)	(1,3/2,2)	0.2973
Exergy efficiency (C10)	(2/5,1/2,2/3)	(1/2,2/3,1)	(1,1,1)	(1,3/2,2)	0.1846
Technology innovation (C11)	(2/5,1/2,2/3)	(1/2,2/3,1)	(1/2,2/3,1)	(1,1,1)	0.0744
${\lambda }_{\max }=4.0104$, $\mathrm{CI}=0.0035$, $\mathrm{CR}=0.0038<0.1$

Meanwhile, it was assumed that the four aspects of the sustainability assessment are interactive and interdependent, the influences of each corresponding cluster on the other clusters with respect to the evaluation criteria were hence determined. Taking the “economic” cluster as an example, by assuming that the four clusters of economic, environmental, technological, and social–political aspects affect the “economic” cluster, the comparison matrix for calculating the weights of the four aspects affecting the economic aspect can be calculated according to the fuzzy AHP method (Table 9.16). Then, the weights of these four clusters in term of their effect on the “economic” cluster can be determined according to Chang’s fuzzy AHP method (also see Table 9.16) (Chang, 1996). By following a similar procedure, the weights representing the influences of the other clusters on the “environmental,” “technological,” and “social–political” clusters can also be obtained (Table 9.17).

If the sum of the elements of any column in the composed supermatrix is greater than 1, the column will be normalized according to the relative weights in the weighted matrix determined by using the ANP method (see Table 9.18) (Dagdeviren and Yuksel, 2010; Saaty, 1996). Taking the third column (towards the criterion of “feedstock cost (C₃)” in the economic cluster in Table 9.15 as an example, the sum of the elements of the column is greater than 1, and five criteria including one criterion in the “economic” cluster and four criteria in the “technological” cluster affect the criterion. The weight of the “economic” cluster and “technological” cluster on the “economic” cluster is 0.2203 and 0.5121 according to Table 9.16; thus, the relative weights of the two clusters can be determined: 0.2203/(0.2203+0.5121)=0.3008 and 0.5121/(0.2203+0.5121)=0.6992. Then, the studied column can be weighted by multiplying the elements and the corresponding relative weights of the cluster to which these elements belong. Thus, cell (5,3) in Table 9.5 should multiply by 0.3008, cell (8,3), cell (10,3), and cell (11,3) should multiply by 0.6992. Similarly, all the columns in the unweighted supermatrix can be weighted, and the weighted supermatrix was obtained as showed in Table 9.18. Subsequently, the limit supermatrix was calculated as showed in Table 9.19. After the normalization, the weights of the 14 criteria are W=[0.0196, 0.0122, 0.0065, 0.0163, 0.0310, 0.0436, 0.0401, 0.1045, 0.0667, 0.0564, 0.2511, 0.0432, 0.0505, 0.2583].

After the decision-making matrix of the 5 technologies regarding all the 14 criteria was obtained (Table 9.20), the PROMETHEE method was used to determine the sustainability sequence of the five scenarios by calculating the positive flow, the negative flow, and the net flow according to Eqs. (9.15)– (9.18). The obtained priority sequence in Table 9.21 shows that the pathway of BG was assessed as the most sustainable technology for hydrogen production, followed by WEL, PVEL, SMR, and CG. This result agrees well with the actual conditions. The pathway of BG has the highest energy efficiency and exergy efficiency, and the second best performance on “policy applicability,” which is the most important criterion according to its weight. Meanwhile, it also has a medium performance on the other criteria. WEL was regarded as the second best pathways as its corresponding net flow is close to that with respect to BG. On the other side, although the technology of “PVEL” emerges as an innovative technology for hydrogen production due to its excellent environmental and social performance, its development in large scales is still being dragged by the problems of low energy efficiency, low exergy efficiency, and high capital cost. As for the conventional hydrogen production pathways of SMR and CG, the negative values of the net flows clearly demonstrate the low sustainability of the two technologies.

It needs to be clarified that the result of this case study is based on the current status of these technologies; the priority sequence would surely change with the technological development as well as the variation of resource reserves (Gim and Kim, 2014). Moreover, the relative priorities (performances) of the soft criteria determined by using the fuzzy AHP method and the weights of the criteria determined by using the fuzzy ANP method were only based on the knowledge and preferences of the authors and a limited amount of experts, the users of this methodology can calculate them via a more thorough investigation of the preference/willingness of the decision-makers/stakeholder and experts.

In order to investigate the robustness of the prioritization results, especially the effect of the interactions and interdependencies among the criterion on the final ranking, the sensitivity analysis method presented in Section 9.2.5 was employed to determine the most critical criterion. The results were presented in Tables 9.22 and 9.23, in which the alternative pathways of CG, SMR, BG, PVEL, and WEL were denoted as A₁, A₂, A₃, A₄, and A₅, respectively. Tables 9.22 and 9.23 demonstrate the change of the criteria weights for achieving the rank reversal of each pair of alternatives in absolute and percentage values, respectively. According to Definitions 1 and 2, Feedstock cost (C₃) was recognized as both the PT critical criterion and the PA critical criterion. Table 9.24 presents the CD and the SC of each criterion determined according to Definitions 3 and 4. It is apparent that the 14 criteria can be categorized into three groups according to their relative criticality and sensitivity: most critical and sensitive group, moderately critical and sensitive group, and less critical and sensitive group. The most critical and sensitive group consists of feedstock cost (C₃), acidification potential (C₇), and O&M cost (C₂). The criteria of production cost (C₄), energy efficiency (C₉), and exergy efficiency (C₁₀) belong to the moderately critical and sensitive group. The other criteria belong to the less critical and sensitive group. Consequently, the accurate determination of the weights of feedstock cost (C₃), acidification potential (C₇), and O&M cost (C₂) is crucial for ranking the alternatives correctly and accurately. Thus, the sensitivity analysis of the interactions and interdependencies associated to these three criteria was conducted by changing the corresponding weights in the weighted supermatrix (see Table 9.18). Moreover, it is worth pointing out that the high criticality and sensitivity does not mean high importance as the importance of the criteria can only be reflected by their weights.

Taking C₃ as an example, it can be affected by four criteria, i.e., C₅, C₈, C₁₀, and C₁₁, and the corresponding weights are 0.3008, 0.3143, 0.1449, and 0.2400, respectively (see Table 9.18). When applying sensitivity analysis, the weight of the investigated criterion is varied while the relative ratio between the weights of the other criteria remains constant. Then, when the sensitivity of ${\omega }_{53}$ that represents the effect of C₅ on C₃ is investigated, we changed ${\omega }_{53}$ from 0 to 1 with a step size of 0.1, while keeping the relative ratio between ${\omega }_{83}$, ${\omega }_{103}$, and ${\omega }_{113}$ to be constant. When ${\omega }_{53}=0.1$, we could obtain:

${\omega }_{83}=\frac{(1-0.1)\times 0.3143}{(0.3143+0.1449+0.2400)}=0.4046,$

${\omega }_{103}=\frac{(1-0.1)\times 0.1449}{(0.3143+0.1449+0.2400)}=0.1865,$

${\omega }_{113}=\frac{(1-0.1)\times 0.2400}{(0.3143+0.1449+0.2400)}=0.3089.$

Then, the new weighted supermatrix can be obtained by replacing the corresponding elements in the original weighted supermatrix (Table 9.18) with the four new weights. The net flows and the ranking of the five alternative pathways was then recalculated by running PROMETHEE with the new weights. Consequently, the net flow of the alternative hydrogen production pathways at different ${\omega }_{53}$ values can be determined as presented in Table 9.25.

Table 9.25

Sensitivity Analysis of ${\omega }_{53}$ in the Weighted Supermatrix on the Net Flow of Different Pathways

${\omega }_{53}$	CG	SMR	BG	PVEL	WEL
0	−1.7508	−1.1773	1.1540	0.6972	1.0769
0.1	−1.7532	−1.1797	1.1548	0.6994	1.0787
0.2	−1.7555	−1.1821	1.1556	0.7016	1.0805
0.3	−1.7578	−1.1845	1.1564	0.7038	1.0822
0.4	−1.7602	−1.1870	1.1572	0.7060	1.0840
0.5	−1.7625	−1.1894	1.1580	0.7082	1.0857
0.6	−1.7648	−1.1918	1.1587	0.7104	1.0875
0.7	−1.7672	−1.1942	1.1595	0.7126	1.0892
0.8	−1.7695	−1.1967	1.1603	0.7148	1.0910
0.9	−1.7718	−1.1991	1.1611	0.7171	1.0927
1.0	−1.7742	−1.2015	1.1619	0.7193	1.0945

The results of the sensitivity analysis by changing the weights of C₅, C₈, C₁₀, and C₁₁ with respect to C₃ on the final ranking of the alternative hydrogen production pathways were summarized in Fig. 9.7 by varying the values of ${\omega }_{53}$, ${\omega }_{83}$, ${\omega }_{10,3}$, and ${\omega }_{11,3}$ from 0 to 1 with a step size of 0.1, respectively. Fig. 9.7 clearly shows that the net flow of each alternative pathway changes slightly with the variation of the weights of C₅, C₈, C₁₀, and C₁₁ with respect to C₃ (Table 9.18), while the priority sequence keeps invariant. Therefore, the final ranking is not sensitive to the interactions and interdependencies between the other criteria with C₃ though it is the most critical and sensitive criterion in the decision-making. The sensitivity analysis of the weight of C₈, C₉, C₁₀, and C₁₁ with respect to C₂ on the final ranking was also employed, and a similar conclusion was drawn according to the results presented in Fig. 9.8.

However, the sensitivity analysis of the weights of C₈, C₉, C₁₀, and C₁₁ with respect to C₇ demonstrated a different conclusion. The results of the sensitivity analysis in Fig. 9.9 show that the variation of the weights of C₈ and C₁₁ with respect to C₇ can alter the priority order between BG and WEL. Therefore, the final ranking is sensitive to the interactions and interdependencies between the other criteria with C₇. Therefore, it can be concluded that only the interactions and interdependencies between the other criteria with C₇ have a significant impact on the final ranking.

In order to verify the advantages of the developed method, including the significance of employing the fuzzy ANP method to determine the weights of the criteria, the advantages of using the fuzzy AHP method to quantify the performances of the alternatives with respect to the soft criteria, and the accuracy of PROMETHEE for decision-making, the following three cases were studied to compare the final ranking of the alternative hydrogen production pathways determined by using the developed method with that by using the previous methods.

Case 1: PROMETHEE was used to rank the hydrogen production alternatives based on the obtained decision-making matrix, in which the weights of the criteria for sustainability assessment were determined by using the conventional AHP method instead of the fuzzy ANP method and the performance of the alternative pathways with respect to the soft criteria was quantified by using the fuzzy AHP method. This case aims to prove the necessity for considering the interactions and interdependencies among the criteria when calculating the weights of the criteria. The weight of the four macroaspects was first determined (Table 9.26). Similarly, the local weight of the criteria in each of the four aspects was also determined, and the results were presented in Table 9.27. Then, the global weight of each criterion (Table 9.27) can be determined by calculating the product of the local weight of the criterion and the weight of the aspect to which the criterion belongs to. For instance, the global weight of “capital cost (C₁)” is the product of its local weight (0.1443) and the weight of the economic aspect (0.4717) as 0.1443×0.4717=0.0681. Fig. 9.10 compared the weights determined by using the fuzzy ANP method with those determined by using the conventional AHP method. It is apparent that the weights of the criteria determined by using the two methods are different; the conventional AHP method gives high priorities to the criteria of “feedstock cost (C₃)” and “production cost (C₄),” while the fuzzy ANP method gives high priorities to the criteria of “technology innovation (C₁₁)” and “policy applicability (C₁₄).” The result obtained by using the fuzzy ANP method with the consideration of the interactions and interdependencies among the criteria is considered to be more accurate than that determined by using the conventional AHP method as “technology innovation (C₁₁)” and “policy applicability (C₁₄)” can significantly affect some other criteria or be affected by some other criteria, and therefore, both of them play a key role in the complex cause–effect relationships among the 14 criteria. On the contrary, the users of the conventional AHP method consider that the criteria of “feedstock cost (C₃)” and “production cost (C₄)” have significant direct effects on people’s preferences to the alternative hydrogen production pathways, while the indirect effects due to the interactions and interdependencies among the criteria cannot been incorporated. Therefore, it is natural that higher weights were assigned to the criteria of “feedstock cost (C₃)” and “production cost (C₄)” by the conventional AHP method.

According to the weights determined by using the conventional AHP method, the final ranking of the alternatives hydrogen production pathways was presented in Table 9.28, and the result is quite different from that determined by using the developed method in this study. The result is considered to be unreasonable as PVEL was ranked as the most sustainable scenario for hydrogen production, while it still faces many severe problems, e.g., low energy efficiency, low exergy efficiency, and high capital cost. Therefore, this case verified the advantage to determine weights of the criteria by using the fuzzy ANP method over the conventional AHP method due to the incorporation of the interactions and interdependencies among the criteria in the fuzzy ANP method.

Case 2: PROMETHEE was used to rank the alternatives based on the obtained decision-making matrix, in which the weights of the criteria for sustainability assessment were determined by using the fuzzy ANP method, while only the performance of the alternative pathways with respect to the hard criteria was assessed. This case aims to investigate the advantages of incorporating the soft criteria into the sustainability prioritization. In this case study, the weights of the hard criteria were recalculated according to their relative ratio in Table 9.20 by ignoring the soft criteria. The obtained sustainability sequence in Table 9.29 is slightly different from that determined by using the proposed method with the consideration of soft criteria, in which the pathway of SMR was ranked before PVEL. Moreover, the data of the net flow indicate that the sustainability of BG seems much better than that of WEL, which does not conform with the fact that the two technologies are two comparable pathways for the hydrogen production if neglecting the soft criteria.

Case 3: Three different MCDM methods, i.e., sum-weighted model (SWM), TOPSIS method, and VIKOR (Viekriterijumsko Kompromisno Rangiranje) method, were used to rank the sustainability sequence of the five alternative hydrogen production pathways based on the decision-making matrix presented in Table 9.20. This case aims to test the effectiveness of PROMETHEE in the sustainability prioritization of alternative industrial systems.

The sustainability sequences ranked by the SWM, TOPSIS, and VIKOR methods are same (Table 9.30), and the only difference with that obtained by the PROMETHEE method is that the priority order between BG and WEL is reversed. As discussed above, the result determined by using the PROMETHEE method conforms better with the actual conditions as it is rational to consider that BG is superior to wind turbine according to the current conditions. Therefore, ROMETHEE is more suitable for the sustainability prioritization of alternative industrial systems than SWM, TOPSISI, and GRA.

4 Conclusion and Discussion

Sustainability assessment and prioritization of various industrial systems is of vital importance for the stakeholders/decision-makers to select the most sustainable scenario. Accordingly, this paper proposed a MCDM methodology for sustainability assessment of industrial systems that can consider both hard and soft criteria, as well as the interdependencies and interactions among these criteria. The methodology incorporates a fuzzy AHP method to quantify the soft criteria, which allows the decision-makers to assess the performances of various scenarios with respect to the soft criteria by using linguistic terms. A fuzzy ANP method is employed to calculate the weight of each criterion, which cannot only reflect the preference and willingness of the stakeholders but also incorporate the interdependencies and interactions among the criteria. The final priority sequence of various technologies is ranked by using the PROMETHEE method according to their net outranking flow. Moreover, a sensitivity analysis method was developed to identify the most critical and sensitive criteria that have significant effects on the sustainability sequence of alternative industrial systems, and to analyze the effects of the interactions and interdependencies among the criteria on the final priority ranking.

The developed methodology was illustrated by a case study to rank the sustainability of five alternative hydrogen production technologies (CG, SMR, BG, PVEL, and WEL). The results demonstrated that the proposed methodology is feasible to find the most sustainable scenario for hydrogen production among various alternatives. The proposed method is object oriented and has the ability to determine the priority sequence of alternative industrial systems according to the preferences of the decision-makers/stakeholders and the actual conditions. Finally, the advantages of the developed methodology were verified by the other three case studies. The necessity for considering the interactions and interdependencies among the criteria when calculating the criteria weights, the advantages of incorporating the soft criteria into the sustainability assessment, and the effectiveness of PROMETHEE to prioritize the sustainability of alternative industrial systems, was proved, respectively.

Acknowledgment

The chapter is reprinted from AIChE Journal, 62(1), Jingzheng Ren, Di Xu, Huan Cao, Shun’an Wei, Michael Evan Goodsite, Lichun Dong. Sustainability decision support framework for industrial system prioritization, Pages No. 108–130, (2016), with permission from John Wiley and Sons.