1. Introduction
The world is moving towards a low carbon economy, which has brought “green energy” an integral part of the future energy mix [
1]. Given the substantial dependence of many countries on fossil-fuel based electricity generation, substitution of fossil fuels with more CO
2-neutral sources of green energy will be challenging, but critical to accomplish in the near term. In past decades, nuclear energy became a well-established option making a prominent contribution to energy sustainability from the perspectives of economics, environment, and society [
2]. The use of nuclear power is still controversial due to huge public concern about potential accidents, risk of proliferation, and nuclear waste management issues. Even so, many countries have openly declared their willingness to start generating nuclear power or to expand the scale of existing civilian nuclear programs [
3].
Ultimate solution for completing an entire nuclear fuel cycle through an optimum transitional path towards sustainable development may one day be identified. Each nuclear country or newcomer interested in nuclear energy should carry out various and innovative Research and Development (R&D) programs in favor of their prevailing nuclear technologies and fuel cycle policy that may hasten that day. Therefore, it is significant to give the flexibility of the advanced nuclear fuel cycle under development, while addressing the nuclear waste management issues to support the development of the regional, national, and global energy strategies [
4,
5].
A complete and well-organized nuclear fuel cycle system is essential for nuclear sustainability, and also serves to exert considerable influence upon the decisions that must be made about distinctive energy strategies at a regional, national, or worldwide level [
6]. In any case, there is an urgency not only to assess the interrelated benefits and risks of future advanced nuclear energy systems, but also to recognize the trade-offs that may be required among development goals to achieve nuclear sustainability.
In our past studies, a simulation code was developed for modeling the material flows and analyzing system complexity based on physical equations and system dynamics. It provides a quantitative performance analysis of a case study in China, and contains four proposed nuclear fuel cycle transition options through 2100 [
7,
8]. However, with regard to the general comparison associated with environmental, economic, and social impacts presented previously, this approach was not conclusive in suggesting an optimum transitional path towards sustainability in the nuclear fuel cycle. Consequently, there is still need for decision support to develop superior nuclear energy strategies in the near future.
Decision making for developing national energy strategies is a complex deliberative process based on integrated system assessment [
9]. It is needed to consider extensive criteria and indicators to evaluate the different energy generation technologies, plans and policies. The Multi-Criteria Decision Making (MCDM) is a popular method for addressing the multi-dimensional and complex nature of sustainability encompassed the assessment of a finite number of sustainable energy options [
10,
11]. It enables conducting an integrated and operational evaluation for decision support that is applicable to solve complex problems featuring high uncertainty, conflicting objectives, a range of input data, and multiple interests and perspective. Given the broad range of processes involved in a complete nuclear fuel cycle, from cradle to grave, the MCDM study has become an important and convenient tool for the assessment of nuclear energy systems, nuclear facility site selection, and nuclear waste management issues. For instance, Keeney et al. [
12] initially analyzed the suitable additional future sites for 1984’s project of nuclear generating facilities in U.S. by using Multi-Attribute Utility Theory (MAUT) method. The same method was adopted in Keeney and Merkhofer’s study [
13], which was designed to aid the U.S. Department Of Energy (DOE) in its selection of three potential sites normalized for first geological repository of nuclear waste disposed of. An Evaluation and Screening Study (E&S Study) of nuclear fuel cycle options developed by U.S. DOE since 2011, which still selected MAUT as the basic analytical approach to provide the information about the potential benefits and challenges of a comprehensive set of nuclear fuel cycle options, as well as providing guidance for the R&D activities of fuel cycle technologies undertaken in U.S. [
14]. A. Schwenk-Ferrero’s studies [
15,
16,
17,
18] proposed a series of decision-making support work based on a complete MCDM framework for evaluating of nuclear waste management strategies and nuclear fuel cycle options in view of sustainability. They further applied the framework in the representative nuclear energy system studies previously investigated by International Atomic Energy Agency (IAEA) International Project on Innovative Nuclear Reactors and Fuel Cycles (INPRO) Collaborative project [
19] and Organization for Economic Cooperation and Development-Nuclear Energy Agency (OECD-NEA) [
20]. These studies have provided a broad range of background information as well as insights on the decision making analysis of nuclear fuel cycle system, which made great contribution to the method and conduct of this case study of nuclear sustainability in China.
The decision results obtained from MCDM analysis generally depend on the identified criteria and indicators on which the different candidate options are to be evaluated, the criteria weighting, and the adopted MCDM techniques based on specific ranking methods. However, this input information underlying MCDM study is always associated with uncertainties. Notably, different countries might select different but suitable evaluation criteria and indicators from specific points of view for sustainable development [
14,
19,
21]. Likewise, they might have opposite priorities relative to individual criteria owing to the country-specific primary context and national demands. Despite the importance of decision makers’ (DMs’) expertise and experiences in solving decision making problems for developing a national energy strategy, the subjective judgments should be combined with and supported by objective methods whenever possible [
22]. For reliable and robust decision making, it is necessary to explicitly address the accuracy of the weighting system, analyzing in great detail how the distinctive weighting methods impact the resultant decisions, and what weighting methods are best suited for a given situation. However, given a high sensitivity of criteria weighting in most MCDM studies of nuclear energy system analysis, few studies have explicitly discussed how the different weighting methods (subjective/objective) could be used simultaneously and be combined effectively in a group decision environment.
To bridge this gap, this study intends to stress on the uncertainties caused by applying any single type of weighting method. Instead, we are of interested in the improvement of an integrated weighting approach, along with the application in a country-specific decision making analysis about future nuclear energy development. The main contribution of our work is to present a preliminary evaluation of decision making for China’s future nuclear fuel cycle options from a sustainability perspective, with a particular emphasis on the strategic MCDM framework by adopting an improved integrated weighting method combined with the self-developed dynamic analysis model. Herein, a set of subjective and objective weighting methods were tested and compared against the weights of evaluation criteria for China-specific sustainability of nuclear energy. Then combined with the MCDM analysis, we provided a well-informed decision-making tool to support the development of national nuclear energy strategies. Particularly, we developed an improved integrated weighting method to effectively synthesize diverse weighting methods (subjective/objective) by which to evaluate conflicting criteria among the competing DMs at different levels of expertise and experience. This is the first time that this specifically tailored weighting method has been used in a nuclear fuel cycle evaluation study.
3. Description of MCDM Case Study in China
In our previous studies [
7,
8], we developed a dynamic model to analyze the quantitative performance of China’s future nuclear fuel cycle transition from the existing to future advanced energy systems through 2100. The MCDM case study herein is based on the previous performance data combined with an integrated evaluation of the most promising nuclear energy system option for sustainable development in China. The four candidate options of nuclear fuel cycle transition presented are: (1) direct disposal of spent fuel discharged from Pressurized Water Reactors (PWRs) without recycling (hereafter abbreviated as PWR-DD); (2) single-recycling of PWR spent fuel in PWRs fueled with Mixed Uranium-Plutonium Oxide (PWR-MOX) fuels (hereafter abbreviated as MOX-DD); (3) PWR-MOX followed by Fast Reactors (FRs) (hereafter abbreviated as PWR-MOX-FR); and (4) direct recycling of PWR spent fuel through FRs (hereafter abbreviated as PWR-FR). Each candidate option is therefore evaluated with respect to six criteria as follows: (1) resource utilization evaluated by Natural Uranium (NU) required per electricity generated; (2) nuclear waste management evaluated by accumulation of UO
2 spent fuel, High Level Waste (HLW) including spent fuel and reprocessing losses to be disposed, Low- and Intermediate-Level Waste (LILW) to be disposed, and Depleted Uranium (DU) per electricity generated; (3) economic competitiveness evaluated by levelized cost of electricity generation; (4) proliferation risk evaluated by plutonium inventory in the overall nuclear system and remaining separated plutonium in reprocessing facility per electricity generated; (5) environmental impact evaluated by land use, water use, and carbon emission per electricity generated; and (6) technological readiness evaluated by the deployment difficulty of First-Of-A-Kind (FOAK) commercial-scale facilities. These six criteria are associated with 12 detailed sub-criteria.
Table 1 lists the above criteria and the overall evaluation metrics.
It should be noted that the last criteria of technological readiness was the only one determined qualitatively, unlike the other 11 sub-criteria which were directly derived from the material flow modeling output results, expressed as a quantitative value of energy per unit. Herein, we simplified the concept of technological readiness by evaluating the time necessary to deploy the involved nuclear technologies underlying the technology-neutral and market-preference assumptions. Thus, to maintain consistency with the selected criteria and overall evaluation metrics, the same deployment years for the corresponding FOAK commercial-scale facilities associated with the four fuel cycle options were likewise adopted (2015, 2020, 2040, and 2030, respectively) [
7,
8].
The hierarchical structure of this MCDM case study is shown in
Figure 2. The overall hierarchy of preliminary evaluation of China’s sustainable nuclear energy system can be easily visualized from
Figure 2. From left to right, the problem objective is at the first level, the next level includes the criteria and sub-criteria affecting the decision making, and the four candidate options of nuclear fuel cycle transition are placed at the third level. Uncertainties analysis associated with the input data of the criteria and evaluation metrics, is not considered in the present study.
4. Results and Discussions
4.1. Fuzzy AHP Weights
In our study, the laborious work of random-sampling simulation, including consistency checking process are performed through a Matlab (R2015a, MathWorks, Natick, MA, USA) model. We finally stochastically selected 100 groups of simulated judgments and formulated them as 100 sets of valid pair-wise comparison matrices in line with the 12 sub-criteria at each individual hierarchy level. In principle, equal importance of the 100 simulated groups is unified. The corresponding 100 comparison matrices are well satisfied due to their high degree of consistency as well as to low repetition of diverse random elements.
Table 2 presents the aggregated results of pair-wise comparison matrices in TFNs for evaluating the six high-level criteria combined with 100 groups of simulated judgments. This is followed by the aggregated TFN matrices for evaluating Criterion 2 (nuclear waste management), Criterion 4 (proliferation risk), and Criterion 5 (environmental impact) in
Table 3,
Table 4 and
Table 5. Specifically, Criterion 4 is composed of only two sub-criteria, thus it is unnecessary to do the consistency checking on the related sampling data. For rationality, relative importance sampling was conducted based on the premise that Sub-criterion 4-1 (remaining separated plutonium in reprocessing facility) is more important than Sub-criterion 4-2 (plutonium inventory in the overall nuclear system).
Following Equations (1)–(6), the initial weights of individual criteria and sub-criteria at different levels were first calculated successively, and then were combined into the final overall weights.
Table 6 lists the comparative results of overall weights calculated by conventional AHP and Fuzzy AHP. Notably, a result of zero can be obtained using Chang’s Fuzzy AHP method (i.e., the weight of Sub-criterion 4-1), which means that the given criteria has an extremely small, or even a negligible influence, on the overall performance. It is largely a consequence of fuzzy synthetic extent logic for the defuzzification process to eliminate relatively nonessential criteria. For the conventional AHP method, by contrast, the related weighting value could be as low as near-zero, but nevertheless, reflecting a few individual opinions. It can be regarded that Fuzzy AHP is a natural result of the necessity for solving subjective uncertainties [
36].
4.2. Entropy and CRITIC Weights
As discussed above, before calculating the entropy or CRITIC weights, we applied a common linear min-max normalization method. This was done to normalize the original data of evaluation metrics measured in different units or scales (
Table 1) into a non-dimensional form with the unified monotonically decreasing utility. Then, the entropy, namely the degrees of diversity as well as the overall objective entropy weights (
Table 7), were obtained through Equations (7)–(9).
Table 8 shows the Pearson correlation coefficients among the 12 sub-criteria calculated via Equation (10). The CRITIC weights were calculated using Equation (11). In
Figure 3 are summarized the comparative results calculated by one subjective (Fuzzy AHP) and the two objective (Entropy and CRITIC) methods for illustrative purposes. However, it conceals large disparities among the calculated weighting results by using the individual subjective and objective methods. The variability in the results by adopting each of the weighting methods selected in this study (Fuzzy AHP, entropy and CRITIC) can be explained by the differences in the underlying factors respectively expressed in the above three typical methods: the subjective preference of decision makers, the level of diversity among a range of criteria, and the independency between criteria. Additionally, different normalization methods to pre-process the original input data of evaluation metrics as a common scale in the interval of “0–1” may also be one factor to result in weighting errors.
4.3. Integrated Weights
The original integrated weights equally assign the power for all the sets of weight and synthesize them by using a simple geometric mean. The above-mentioned weights (
Figure 3) are integrated as a whole, namely improved integrated weight, which can be calculated through Equation (13) for the present case study.
Given that the members of DM group might be from across sectors and industries with diverse levels of expertise/experiences in developing national energy strategies, as well as the complexity level of future nuclear energy system that the CDMs (Chief Decision Makers) would like to put forward, these could be reflected in the power assignment for the individual weighting methods. Herein, we proposed five potential cases underlying the roles of group composition and directly reflected the coefficient changes in the Equation (13), these DM cases are as follows.
Case 1: The DM group consists of the members from the nuclear-irrelevant fields; thus, they lack experience in giving credible subjective evaluation scores for nuclear projects. Hence, the CDMs have to select using only objective weights and assign equal power for each objective method, while discarding the subjective weights. Consequently, we have .
Case 2: All the DMs possess a high level of expertise in nuclear technologies and typically have rich experiences in decision making. In view of the high level confidence, the CDMs simply adopted the subjective weights as the final weights, completely accepting the professional judgments from DM group. In this case, , that is, the integrated weights are equal to the Fuzzy AHP weights.
Case 3: To maintain neutrality, the CDMs determined to adopt a relatively conservative approach. They assign an equal power to both objective and subjective weighting systems as follows: .
Case 4: The DMs can assign subjective weights in light of their expertise and background. Upon the consideration that objective weights are somewhat persuasive, the CMDs elected to assign larger power (from one to two) to the DM judgments (i.e., ).
Case 5: The CDMs adopt the most conservative method regardless of the distinctions of subjective and objective weighting methods. An equal power was given to all the weights considered, thereby obtaining more fair and accurate integrated weights (i.e.,).
The improvement in the integrated weighting method proposed here are therefore twofold: first, to flexibly adjust the preference coefficients on different weighting methods according to the practical application, and second, to directly reflect the real system complexity associated with the group decision support environments. The final integrated weighting results for the overall evaluation metrics in the five DM cases are listed in
Table 9.
Figure 4 shows the comparative integrative weights directly. Under different DM cases, the obtained sets of weights to Sub-criteria 1-1 (NU required), 3-1 (levelized cost of electricity), 4-2 (separated Pu in reprocessing facility) and 6-1 (deployment difficulty of FOAK commercial-scale facilities) are obviously higher than the others. The question “Which weighting method is most suitable and fair to evaluate the importance of each criteria” is essential for the final decision making, but different to answer. Herein, the integrated weighting method has played a subtle role in influencing the final decision making by merging perfectly some extremely biased subjective preferences with the statistical objective correlation coefficients.
4.4. Final Ranking Results of TOPSIS and PROMETHEE II
The resultant integrative weights (
Table 9) were then applied in the MCDM case study via the execution of both TOPSIS and PROMETHEE II methods, finally to obtain an overall ranking of the reference fuel cycle candidate options.
For the TOPSIS method, the TOPSIS scores, namely, the separation values of the four fuel cycle candidate options from both the positive and negative ideal solutions based on the five case assumptions, were calculated and are presented in
Table 10.
For the PROMETHEE II method, an outranking model was built to calculate the net flow and obtain the final rankings of the candidate options. First, we applied the level preference function to evaluate the qualitative criteria (C6), and the V-shaped function to evaluate the quantitative criteria (C1–5, respectively) [
45]. Second, in consideration that the values of the preference threshold in our study were not experimental values to be closely approximated, they might be somewhat arbitrarily specified for some specific values underlying the characteristics of individual criteria. Herein, we applied an objective method suggested by Rogers et al. [
46] instead subjective assumption for assessing the appropriateness of the evaluation criteria. Accordingly, the calculation results of the overall net ranking flows for each nuclear fuel cycle option are listed in
Table 10.
Figure 5 summarizes the comparative MCDM ranking results for China’s sustainable nuclear energy system transitional path with respect to the five DMs’ cases. The reference cases are located at the respective locations in the two-dimensional radar chart. This indicates that the overall ranking results using TOPSIS mostly agree well with the PROMETHEE II rankings regardless of the effects of different DM considerations. From a sustainability perspective, the first rank option is the PWR-FR fuel cycle while the last one is the PWR-DD fuel cycle, under the different DM cases. In addition, the rankings of the other reprocessing and recycling options (i.e., MOX-DD and PWR-MOX-FR) principally performed better than the PWR-DD option, the second-, or third-best option. The large exception noted was in Case 2: the rankings differ significantly from other cases in both TOPSIS and PROMETHEE II results. Case 2 was purely based on the subjective weights derived from the DM judgments. For enhancing the credibility and accuracy in subjective weights, we adopted a Fuzzy AHP application combined with random sampling method, which can reduce the subjective uncertainties caused by human perception, as well as of aggregating abundant conflicting opinions from the individual DMs. However, the methodological concerns could only help to strengthen the rationality of subjective weights consistently with the theoretical structure, rather than eliminating the inherent uncertainties of a certain technique. The large ranking variance in Case 2, on the other hand, is further proof of the importance of weighting system for decision making. The criteria weights directly influence the final ranking results of MCDM evaluation. It is necessary to stress the uncertainties caused by applying any single type of weighting method. Therefore, an integrated weighting method was recommended, to keep a balance between the subjective and objective weighting bias, and thereby increase the legitimacy of the outcome, as well as provide reliable and robust support for decision-making. Moreover, the proposed improved integrated weighting method based on the practical DM cases enabled us to assign more flexible powers to the specific objective/subjective weights, and to be more in line with the group decision support environments. Herein, we addressed the improvement of the integrated weighting approach, along with the application in a country-specific decision making analysis about future nuclear energy development.
However, overall, each MCDM method has distinctive advantages and disadvantages with respect to the pursuit of preferable solutions. In this investigation, the comparative ranking results of both TOPISIS and PROMETHEE II methods applied in the MCDM case study of China’s nuclear energy are proven robust and consistent. It is of great importance that various MCDM techniques are comparatively applied to evaluate and rank the transitional options of nuclear fuel cycle projects. The results of MCDM analysis are more rational and robust in the sustainable energy decision making.
5. Conclusions
While the prospects look bright for nuclear energy development in China, no consensus about an optimum transitional path towards sustainability in the nuclear fuel cycle has been achieved. The problem of decision analysis for national energy strategies can be characterized as dynamically complex, and which needs to anticipate the intended goal pursuits and unintended consequences of interventions in a dynamically evolving situation. A thorough set of decisions about China’s future nuclear energy systems has been proposed here based on the self-developed dynamic simulation code. It enables: (1) quantification of a range of tangible and intangible effects of four nuclear fuel cycle options and assessment of their consequential benefits and risks from a multidisciplinary viewpoint; (2) identification of sustainability evaluation metrics for nuclear energy in the Chinese context; and (3) provision of decision support for analyzing the trade-offs involved in selecting a promising transitional path of nuclear fuel cycle toward sustainable development. This study is innovative in that it incorporates currently available modeling techniques into a strategic MCDM framework to perform a preliminary integrated assessment on the critical sustainability issues of nuclear energy in China. Above all, an improved integrated weighting method for MCDM was applied for the first time in a nuclear fuel cycle evaluation study. This integrated method synthesizes diverse types of weighting methods to evaluate the conflicting criteria among competing DMs at different levels of expertise and experience. It makes some technical contributions to address the gaps in effectiveness and reliability of any single weighting system, while making it more adaptable to group decision support environments.
The results of the case study suggest that the PWR-FR fuel cycle is the most competitive candidate option while the PWR-DD fuel cycle is the least attractive option for China, from a sustainability perspective. This confirms the value of currently ongoing programs about reprocessing and recycling of spent nuclear fuel for sustainable nuclear energy development, and fully reflects the importance of the MCDM evaluation for developing national energy strategies as well. For R&D development in the long term, our study provides important support information for fuel cycle project prioritization. However, as the results showed, the promising transitional path of nuclear fuel cycle associated with FR recycling and the related reprocessing technologies could not meet all the evolving demands of nuclear energy development considering the country-specific dimensions. Likewise, such a preliminary study cannot conclude a determined decision on a certain preferred fuel cycle option at a national scale. There is still a long way for China to engage in the exploration of the nuclear energy R&D works for sustainability based on well-informed decision making.
In summary, the presented study provides a more reliable, effective, and systematic decision support tool based on an analytical MCDM framework. In a country-specific nuclear fuel cycle assessment study, the application of the integrated weighting method combined with the tangible case assumption of DMs, makes the overall evaluation more realistic and reliable. However, it should be noted that the MCDM study can only help the DMs to select a relatively preferable option from the existing candidate pool. The resultant option enables reflecting the DMs’ timely preference priorities, rather than ensuring providing an absolutely correct or permanent solution to the problem [
17]. Meanwhile, the input information of which MCDM study underlying is always associated with uncertainties (e.g., the identified evaluation criteria, the weights assigned to each criterion, and the selected MCDM techniques). Additionally, the limitation associated with each respective subjective or objective weighting method is perceived but inevitable. As a future direction, it should be added that the MCDM framework proposed herein is applied to a more appropriated sustainability evaluation metrics for assessing China’s nuclear energy system transition incorporating the experts’ judgment and DMs’ preference. In addition, the robustness of uncertainty modeling and agility in the decision-making process deserve more in-depth discussion. As another direction, further application of the dynamic performance modeling and integrated analysis of more potential nuclear fuel cycle options involving the various current ongoing nuclear technology programs for developing national energy strategies is worthwhile.