Risk Assessment of Offshore Wind–Solar–Current Energy Coupling Hydrogen Production Project Based on Hybrid Weighting Method and Aggregation Operator

Abstract

Under the dual pressures of global climate change and energy structure transition, the offshore wind–solar–current energy coupling hydrogen production (OCWPHP) system has emerged as a promising integrated energy solution. However, its complex multi-energy structure and harsh marine environment introduce systemic risks that are challenging to assess comprehensively using traditional methods. To address this, we develop a novel risk assessment framework based on hesitant fuzzy sets (HFS), establishing a multidimensional risk criteria system covering economic, technical, social, political, and environmental aspects. A hybrid weighting method integrating AHP, entropy weighting, and consensus adjustment is proposed to determine expert weights while minimizing risk information loss. Two aggregation operators—AHFOWA and AHFOWG—are applied to enhance uncertainty modeling. A case study of an OCWPHP project in the East China Sea is conducted, with the overall risk level assessed as “Medium.” Comparative analysis with the classical Cumulative Prospect Theory (CPT) method shows that our approach yields a risk value of 0.4764, closely aligning with the CPT result of 0.4745, thereby confirming the feasibility and credibility of the proposed framework. This study provides both theoretical support and practical guidance for early-stage risk assessment of OCWPHP projects.

1. Introduction

Under the dual pressures of global climate change and energy structure transformation, the need to advance the energy system toward cleanliness, low carbon emissions, and sustainability has become a global consensus. To achieve the carbon neutrality targets established by the Paris Agreement, countries worldwide are accelerating the green transformation of energy systems [1]. Renewable energy is increasingly replacing fossil fuels as the main source of global energy consumption, driving carbon reduction. Among renewable sources, wind and solar power have experienced rapid growth over the past decade due to abundant resources and mature technologies [2]. Meanwhile, marine energy—particularly ocean current energy—remains underdeveloped while has been increasingly recognized as a vital supplement for constructing highly reliable energy systems, owing to its stable flow direction and strong operational predictability [3].

In offshore regions with abundant wind, solar, and tidal resources, energy demand is often lower than the electricity generated, leading to wastage. Hydrogen energy, as a critical energy carrier for a future zero-carbon society, is increasingly recognized for its value. It offers advantages such as abundant sources, cleanliness, carbon-free characteristics, high energy density, and diverse application scenarios [4,5]. Among the various methods for converting energy into hydrogen, water electrolysis has emerged as the dominant technology for green hydrogen production due to its flexible process and direct utilization of renewable energy [6]. Based on this, the synergistic utilization of multiple renewable energy sources for water electrolysis can not only minimize energy losses from long-distance transmission but also enable efficient local conversion and utilization of resources. In this context, recent research on multi-energy systems with hydrogen integration has mainly focused on operational coordination and optimization. Jia et al. [7] developed a data-driven operation strategy for multi-energy microgrids integrating green hydrogen, ensuring secure and efficient coordination under uncertainty. Qi et al. [8] proposed a prediction-free optimization framework for the long-term energy management of microgrids with hybrid hydrogen–battery storage, effectively reducing operational costs. In addition to operational optimization, several studies have examined the comprehensive performance of hybrid renewable energy systems. Terlouw et al. [9] conducted a techno-economic and environmental assessment of island-based photovoltaic–wind–hydropower systems, confirming their feasibility and sustainability. Hasan et al. [10] analyzed a photovoltaic–wind-based microgrid in Australian island regions, demonstrating its operational efficiency and emission reduction potential. Zhang et al. [11] investigated N–1 contingency evaluation in integrated electricity–gas systems considering cyber–physical interdependence, providing valuable insights into the reliability and resilience assessment of coupled energy infrastructures. Yet these frameworks are largely confined to onshore or near-shore scenarios, lacking applicability to deep-sea multi-energy coupling environments with higher uncertainty and operational complexity.

Against this background, the ocean current–wind–photovoltaic–hydrogen production (OCWPHP) project has emerged as a new integrated energy application solution. By combining offshore wind, photovoltaic arrays, and ocean current turbines into a complementary platform, the OCWPHP system enhances renewable energy utilization and supply stability, thereby providing a stable and efficient power source for electrolyzers. This system constitutes a significant technical solution for the industrialization of green hydrogen energy. While the OCWPHP system has clear advantages in terms of technical pathways and resource utilization, its operational environment is highly complex. The system operates in an unpredictable and harsh marine environment, involving multiple energy types, diverse conversion equipment, and complex operational conditions. The boundary of system is extensive and highly interconnected, with numerous risk factors that are challenging to quantify comprehensively [12,13]. From project investment and system design to subsequent operation and maintenance, each stage faces potential technical, economic, social, political, and environmental risks.

The OCWPHP system includes multiple subsystems: offshore wind turbines, floating photovoltaic modules, ocean current turbines, energy storage devices, electrolytic hydrogen production systems, submarine cables, and hydrogen storage/transportation facilities [14,15]. These components operate continuously in harsh environments characterized by salt spray corrosion, high humidity, typhoons, and ocean current impacts, posing significant challenges to their reliability and service life [16]. Economically, the initial capital investment for such projects is substantial, with construction, operation, and maintenance costs considerably higher than regular onshore systems. The economic viability heavily depends on policy incentives and hydrogen market prices. Environmentally, socially, and politically, large-scale offshore engineering projects may cause irreversible damage to marine ecosystems and fishery resources, disrupt shipping channels and fishing activities, and threaten the livelihood security of coastal communities. Therefore, rigorous environmental impact assessments and social risk management are essential [17]. Moreover, the OCWPHP project’s deployment involves complex issues related to marine spatial-use rights allocation and multinational policy coordination, rendering its political sensitivity significantly greater than that of onshore renewable energy projects.

Despite its advantages in resource integration and carbon reduction, the OCWPHP system’s complex, multi-energy collaborative nature poses significant challenges for risk management. Most existing risk assessment methods are based on traditional single-energy system analyses and struggle to address the systemic complexity of OCWPHP projects, including structural hierarchy, policy disturbances, technical uncertainties, and environmental risks [18,19,20]. Existing risk assessment methods for hydrogen-related projects typically rely on traditional multi-criteria decision-making (MCDM) or probabilistic approaches such as analytic hierarchy process (AHP), failure mode and effects analysis (FMEA), and Bayesian networks [21,22,23]. While these tools can quantify individual risks, they often assume independence among factors and fail to capture cross-influences among technical, economic, and environmental subsystems. Furthermore, conventional frameworks usually depend on either subjective or objective weighting without integrating both, resulting in biased or unstable assessments. Expert evaluations also tend to vary widely due to background heterogeneity, and few studies have introduced effective mechanisms—such as consensus measurement or correction—to harmonize group judgments. Consequently, current methods struggle to model uncertainty propagation, hesitation, and nonlinear dependencies within multi-energy coupled hydrogen production systems. This limitation underscores the necessity of developing an adaptive and integrated risk assessment framework.

Overall, the existing research has obvious deficiencies in the following three aspects:

(1) There is a lack of a dedicated risk criteria system for the coupling characteristics of the OCWPHP system.

Currently, risk assessments predominantly focus on onshore and single-energy systems, such as risks associated with wind farm construction and investment return analyses of photovoltaic power stations. Existing criteria systems fail to adequately address the multi-energy coupling, cross-disciplinary risks, and deep-sea environmental challenges unique to OCWPHP projects. Environmental risks, such as accelerated equipment corrosion in deep and offshore areas, have often been overlooked, leading to significant operational and maintenance challenges Furthermore, key risk factors such as financing complexity and policy uncertainty arising from the coupling of multiple energy types remain insufficiently considered. These limitations in existing criteria systems constrain the comprehensiveness and relevance of risk assessments for OCWPHP projects.

(2) The existing weighting methods struggle to adapt to the multi-source information and expert variability present in OCWPHP system.

In the OCWPHP system, strong coupling exists among risk criteria, and the lack of comprehensive measured data makes expert judgment the primary information source. However, traditional studies predominantly employ either subjective or objective weighting methods, neglecting the complementarity of both, which leads to biased weighting outcomes. Additionally, experts from diverse backgrounds often differ significantly in their ranking of the same criteria’s importance. Current methods lack an effective mechanism to assess and regulate the consistency of group judgments, undermining the robustness and credibility of the evaluation model.

(3) Traditional aggregation methods are difficult to reveal the uncertainty coupling mechanism in the OCWPHP system.

In the OCWPHP system, risk factors such as technology, economy, and environment exhibit widespread cross-influences and path dependence, with transmission characterized by uncertainty, hesitation, and nonlinearity. Traditional methods typically employ linear weighting or independent aggregation strategies, which fail to capture the interdependencies among risk factors and struggle to reveal the linkage mechanisms between local disturbances and system responses.

To cope with these challenges, hesitant fuzzy set (HFS) theory is adopted in this study for the development of an uncertainty modeling tool capable of integrating subjective perception and objective evidence. Based on this framework, two weighted aggregation operators are employed: the adjusted hesitant fuzzy ordered weighted averaging (AHFOWA) and the adjusted hesitant fuzzy ordered weighted geometric (AHFOWG) operators. This approach not only manages hesitant evaluations from multiple experts but also considers the accuracy of importance ranking and risk perception during aggregation, thereby enhancing the explanatory power and decision-making relevance of the assessment within complicated systems. Furthermore, the approach introduces a hybrid weighting method combining AHP, entropy, and consensus adjustment within a HFS environment, enabling the management of multi-source uncertain information and expert hesitation. This methodological innovation provides a more robust and interpretable tool for assessing the risks of offshore multi-energy complementary hydrogen production systems. The primary research objectives include:

(1) Develop a multi-dimensional and hierarchical risk criteria system. Through literature review and expert consultation, the key risk factors faced by the OCWPHP project are identified and classified into five major dimensions: economy, technology, society, politics, and environment.

(2) Construct a dual weighting mechanism by combining the AHP with the entropy weight method, where AHP reflects experts’ subjective preferences and the entropy weight method identifies the information intensity embedded in the scoring data. Based on this, the Kendall’s coefficient of concordance (Kendall’s W) is introduced to adjust the consistency of expert opinions, thereby integrating subjective and objective information and enhancing expert group consensus.

(3) By integrating HFS theory and applying two aggregation operators, AHFOWA and AHFOWG, enhance the model’s capacity to process uncertain and hesitant information, thereby completing an integrated risk assessment model tailored for complex OCWPHP systems.

(4) Apply the proposed model in (3) to a typical OCWPHP project area to conduct a practical case study, verify the applicability and interpretability of the assessment framework and propose targeted risk prevention and control strategies.

2. Literature Review

The risk assessment of the OCWPHP project primarily focuses on identifying multidimensional risk factors and developing an adaptive assessment framework. This section reviews representative risk criteria and assessment methods from related research.

2.1. Identification of Risk Factors

Establishing a comprehensive risk criteria system is essential for accurately assessing the risk status of OCWPHP projects. Existing research has developed a relatively mature framework for risk assessment in renewable energy projects, typically encompassing dimensions such as economic feasibility, technical reliability, environmental compatibility, and social acceptance. For example, studies on offshore wind power projects primarily address equipment failure risks in harsh environments and the high costs associated with installation, operation, and maintenance [24,25,26]. Evaluations of independent electrolytic hydrogen production systems focus on technological maturity and the economics of hydrogen production [27,28]. Research on ocean current energy development emphasizes equipment reliability and uncertainties in resource assessment [29,30]. However, most of these studies concentrate on a single energy type or relatively simple technology combinations.

It is noteworthy that some existing studies also address hybrid energy systems or complex projects, offering valuable references for OCWPHP risk assessment. In evaluating offshore wind-solar hybrid projects, researchers commonly incorporate economic, technical, and environmental risk criteria [31,32,33]. The risk assessment framework for onshore wind-solar-storage hydrogen projects further includes factors such as social acceptance [34]. For offshore hydrogen production processes, research typically emphasizes specific safety risks, environmental impacts, and financing risks [35,36]. Recently, non-technical risks in large-scale energy projects, including social resistance, sea-use conflicts, and policy dependence, have garnered increased attention [37,38].

Although existing research on risk assessment for single energy projects and certain hybrid energy systems provides a valuable foundation for understanding basic risk dimensions (such as economic, technological, and environmental aspects) of OCWPHP projects, applying these criteria directly to highly integrated, multi-energy coupled systems operating in harsh environments still presents significant adaptation challenges. The current frameworks struggle to effectively capture and characterize the compound risk effects arising from the deep coupling characteristics of these systems.

Therefore, in Section 3 of this study, the literature review method [39] is employed to identify and analyze risk factors associated with integrated renewable energy systems, while the expert consultation method [40] is used to pinpoint specific risk factors of the OCWPHP project. Based on these findings, a customized risk assessment framework is developed to provide reliable guidance for stakeholders and investors in managing the complexities of multi-energy coupling projects.

2.2. Risk Assessment Framework

The risk assessment of OCWPHP projects involves a comprehensive analysis of multidimensional risk factors and requires the participation of multiple decision-makers (DMs), making it a typical MCDM problem. In addressing MCDM problems, three core issues typically arise: the representation of criteria information, the determination of criteria weights, and the selection of decision-making methods [41].

(1) Description of criteria information

In the risk assessment practice of the OCWPHP project, the primary challenge for decision-makers is accurately representing and managing the pervasive uncertainty inherent in the assessment process. Traditional risk assessment methods predominantly rely on deterministic values or simple fuzzy numbers to characterize risk criteria. However, this approach overlooks the intrinsic cognitive fuzziness and hesitation exhibited by decision-makers when confronted with complex technical systems [42,43]. This issue is particularly pronounced in innovative projects like OCWPHP, which operates at the technological frontier and lacks sufficient historical data. Consequently, decision-makers often struggle to provide a single definitive risk assessment value and instead tend to present a range of possible values to capture the uncertainty in their judgments.

To effectively address this uncertainty, fuzzy set theory and its extensions offer a theoretical foundation for representing risk information. Classical fuzzy set theory requires each element to correspond to a single membership degree value. However, in practical MCDM, decision-makers may assign multiple membership degrees of varying levels to the same risk factor [44]. The theory of HFS, first proposed by Torra in 2009, effectively resolves this limitation, it allows decision-makers to specify multiple possible membership values for a single evaluation object, thereby more accurately capturing the hesitation and diversity inherent in human decision-making processes [45].

Compared to traditional precise numerical evaluation methods, HFS offers significant theoretical advantages. HFS captures the natural responses of decision-makers to uncertainty, preventing information loss associated with mandatory single-value selections. Furthermore, HFS effectively integrates diverse perspectives from multiple decision-makers and reflects the degree of disagreement among expert groups through variations in hesitation levels. Finally, this method is particularly advantageous for emerging technology projects lacking historical data, as it fully leverages experts’ subjective judgments [46].

In recent years, HFS theory has been extensively applied and validated in risk assessment for energy projects. For example, in the technical risk assessment of offshore wind power projects, researchers have demonstrated that traditional deterministic methods often underestimate equipment failure probabilities under extreme sea conditions, whereas the HFS approach more effectively captures experts’ concerns regarding unknown risks [47]. Similarly, in the economic feasibility assessment of hydrogen energy projects, HFS effectively addresses challenges arising from hydrogen price fluctuations and policy uncertainties [48]. These empirical studies provide a robust theoretical foundation and practical support for applying HFS in the OCWPHP project.

Therefore, this study employs HFS theory to characterize hesitation and ambiguity in the risk assessment of the OCWPHP project, aiming to more accurately capture decision-makers’ true judgments and enhance the scientific rigor and credibility of the assessment.

(2) Determination of indicators’ weight

Traditional risk assessment research has methodological limitations in determining weights, mainly manifested as an excessive reliance on a single weighting path. Existing studies either rely entirely on subjective weighting methods such as the AHP or simply adopt objective weighting methods such as entropy weighting. This binary model often leads to a lack of comprehensiveness in the weighting results [49,50].

The primary limitation of subjective weighting methods is their heavy reliance on experts’ personal preferences and empirical judgments, which can be influenced by factors such as knowledge background and cognitive biases, leading to insufficient objective support for the resulting weights. Especially in complicated projects like OCWPHP that involves multiple disciplines, the judgment of experts in a single field often shows significant professional limitations. Relatively speaking, although objective weighting methods can extract information strength from the data itself and avoid subjective bias, they often ignore the professional knowledge of experts and the actual decision-making needs, and may produce weighting results that are contrary to the actual decision-making logic.

Based on the above issues, this study constructs a subjective and objective integrated weight determination mechanism of the AHP-entropy weight method. This mechanism fully exploits the professional judgment and decision-making preferences of experts through the AHP method, and constructs a hierarchical judgment matrix to quantify the relative importance among criteria. The entropy weighting approach derives its theoretical foundation from fundamental concepts in information theory. It objectively extracts the information carrying capacity of each criterion from the actual evaluation data, effectively avoiding the excessive influence of subjective preferences. The integration of the two methods has achieved an effective complementarity between subjective cognition and objective information, significantly enhancing the rigor and systematic nature of weight determination.

However, during the practical evaluation of the OCWPHP project, experts from different professional backgrounds often hold divergent perceptions regarding the importance of the same risk criterion. Such disagreements within the expert group may lead to instability in the weighting results. Given the critical influence of expert consensus on the final evaluation outcome, this study further introduces the Kendall’s W as a quantitative measure of group consensus [51]. When the level of consensus among experts falls below a predefined threshold, a structured feedback mechanism is employed to guide experts in re-examining the evaluation criteria, thereby progressively enhancing the consistency of group judgments. This dynamic adjustment mechanism effectively mitigates the instability in weighting results caused by excessive divergence in expert opinions.

In conclusion, the three-layer fusion weight determination method constructed in this study not only effectively integrates subjective and objective information, but also ensures the stability and reliability of the weight results through dynamic consensus adjustment.

(3) Selection of decision-making methods

On the basis of completing the representation of risk information and determining the weights, how to effectively aggregate multi-dimensional and multi-expert assessment information has become a key link in the risk assessment framework. Traditional information aggregation methods face several technical challenges when dealing with the complex risk information of OCWPHP projects.

Traditional multi-criteria decision-making methods such as Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) are mainly designed for scheme ranking and selection. Their linear aggregation mechanisms are difficult to effectively handle the nonlinear interaction and coupling effects among risk factors in OCWPHP projects. These methods assume that each risk factor is independent of each other, ignoring the complexity and path-dependent characteristics of risk transmission in multi-energy coupled systems. While current fuzzy aggregation operators demonstrate competence in processing uncertain data, conventional non-weighted methods fail to adequately account for variations in expert weighting during project risk evaluation [52,53]. This limitation often leads to assessment outcomes that lack both precision and contextual relevance.

To solve the above issues, Zhang et al. [54] proposed the ATS-WHFWA and ATS-WHFWG operators, Zeng et al. [55] proposed the WHFOWA and WHFOWG operators and other weighted hesitant fuzzy aggregation operators. However, though these weighting operators introduce expert weight mechanisms, they often involve complex calculation processes and redundant intermediate steps, resulting in an excessive computational burden when dealing with large-scale risk criteria systems. More crucially, these operators often lead to information distortion or offset when dealing with hesitant and fuzzy information, and tend to produce excessive smoothing effects when handling extreme value information, thereby weakening the effectiveness of the risk early warning function.

In response to the above-mentioned technical deficiencies, this study employs a novel aggregation operator system based on HFS, including the AHFOWA operator and the AHFOWG operator. The AHFOWA operator adopts a weighted average aggregation strategy and simplifies the calculation process through an optimized addition operation rule. It exhibits conservative decision-making characteristics in risk assessment and is suitable for robustness assessment fields such as economic risk and policy risk. The AHFOWG operator adopts a geometric mean aggregation strategy, showing higher sensitivity to extreme risk values and demonstrating cautious decision-making characteristics. It is suitable for assessment scenarios that require early warning functions, such as technical risks and environmental risks.

3. OCWPHP Risk Assessment Criteria Framework

The proposed criteria framework for risk assessment comprehensively captures potential risk factors associated with OCWPHP projects across various critical dimensions. This multidimensional approach provides substantial value for conducting thorough feasibility analyses and implementing effective risk mitigation strategies during project execution. As shown in

Table 1. Risk assessment criteria related to the OCWPHP project.

Criteria	References
	[25]	[27]	[28]	[29]	[30]	[31]	[35]	[56]	[57]
High initial Investment	√	√	√		√	√	√	√
High operation and maintenance costs	√		√		√	√	√
Annual rate of return		√	√		√	√	√
Financing risk	√				√		√	√
Technology maturity	√	√		√		√	√
Technological advancement			√
Operation and maintenance risk		√				√
Work safety risk	√			√			√
Social acceptance risk	√						√	√
Requisition risk	√								√
Public opinion risk				√		√	√
Policy fluctuation risk	√		√				√		√
Policy support risk	√	√				√		√
Bribery and corruption risk								√	√
Contract risk								√
Ecological and environmental risk	√		√	√	√	√	√
Natural environment risk	√			√	√	√	√		√

, this paper summarizes the general influencing factors based on a review of a large number of related studies. In combination with the engineering characteristics of the OCWPHP project, such as multi-energy integration and deep-sea deployment, a targeted risk assessment index system has been constructed, as shown in Figure 1. This system encompasses five aspects: economy, technology, society, politics and environment, comprehensively reflecting the main risks that the OCWPHP project may encounter during the actual implementation process.

3.1. Economic Risk

(1) High initial investment C11: The OCWPHP project requires the deployment of offshore wind power, photovoltaic platforms, and ocean current power generation devices, combined with a hydrogen production system. The overall system construction period is long, and the costs of equipment purchase and installation are high, resulting in significant initial investment pressure.

(2) High operation and maintenance costs C12: The project is located in a deep-sea area, equipment operation and maintenance involve high difficulty and cost, with expenses increasing over time due to equipment aging, environmental stress, and rising repair frequency throughout the project lifecycle.

(3) Annual rate of return C13: Despite the abundance of renewable resources at sea, the initial investment is large, the operating costs are high, and the hydrogen energy market is still unstable, which leads to considerable uncertainty in the annualized return.

(4) Financing risk C14: Due to the high difficulty of technical integration and the complexity of risk identification, financial institutions are cautious about investing in OCWPHP projects, and financing channels are restricted, which may affect the smooth progress of the project.

3.2. Technical Risk

(1) Technology maturity C21: Currently, there are no mature cases at the engineering level regarding the coordinated operation of wind, solar and ocean current energy sources and the integration of hydrogen production systems, and the overall system stability is uncertain.

(2) Technological advancement C22: This project requires efficient coupling and intelligent regulation of multiple energy sources. It is necessary to introduce high-tech intelligent control and hydrogen production equipment, and has high requirements for the technological advancement of the system.

(3) Operation and maintenance risk C23: The operation of the OCWPHP system is restricted by the marine environment. The equipment is vulnerable to salt spray corrosion, typhoons and other extreme weather conditions, and there is considerable operation and maintenance pressure on the stability and service life of the equipment operation.

(4) Risk of work safety C24: The offshore hydrogen production system operates under high pressure, with a high risk of flammability and explosion. The consequences of safety accidents occurring in the marine environment are relatively serious, and it is necessary to strengthen the design of risk prevention and control.

3.3. Social Risk

(1) Social acceptance risk C31: Hydrogen production facilities may be accompanied by problems such as noise, electromagnetic radiation or frequent transportation. If they are close to marine tourist areas or fish farms, they may encounter opposition from the public and local governments.

(2) Requisition risk C32: If the project deployment area is close to the exclusive economic zone, fishery or shipping passage, it is necessary to coordinate multiple resources. Also, there is a risk of difficulty in obtaining the right to use or legal disputes.

(3) Public opinion risk C33: If the project generates environmental or ecological disputes, or if safety accidents occur frequently, it may trigger public criticism and negative media reports, affecting the social image and policy support.

3.4. Political Risk

(1) Policy fluctuation risk C41: The policy adjustments made by the state in the hydrogen energy development strategy directly affects the project implementation pace, marketization path and energy trading mechanism, and there is uncertainty in policy changes.

(2) Policy support risk C42: The OCWPHP project belongs to a cutting-edge and cross-disciplinary field. If there is a lack of clear subsidy mechanism, demonstration project support policies or sea area resource allocation mechanisms, it may affect the feasibility of the project.

(3) The risk of bribery and corruption C43: In key links involving sea area approval, equipment procurement, project acceptance, etc., if supervision is not in place, it may lead to corrupt behavior by management personnel or local departments.

(4) Contract risk C44: In a joint development model involving multiple parties, the contract terms are complex. If the responsibilities are not clearly defined or there is a breach of contract, it may lead to legal risks such as project delays and litigation.

3.5. Environmental Risk

(1) Ecological and environmental risk C51: During the construction and operation of the project, there may be damage to the marine ecosystem and biodiversity, such as the laying of submarine cables and noise affecting marine mammals.

(2) Natural environment risk C52: The project is subject to extreme marine climate impacts such as storm surges, typhoons and freezing. Extreme events may cause equipment damage or even system paralysis, increasing the probability of environmental accidents.

4. Research Method

4.1. Hesitant Fuzzy Set

Since experts always describe the evaluation criteria with hesitant and vague language, HFS is widely employed to represent such linguistic variables. Proposed in 2009, HFS can effectively capture the hesitant nature of experts during assessments. This paper uses HFS to represent the evaluation information provided by experts regarding the criteria. Its definition is as follows:

Definition 1

([58]). Given a domain X, a HFS is defined which’s membership function h on X, and HFS is expressed as:

$$HFS=\{<x,h(x)>|x\in X\}$$

(1)

Among them, h(x) is called the hesitant fuzzy element (HFE), representing the membership degree of the set of possible values in [0,1] in x ∈ X.

Definition 2

([58]). Given three HFEs h₁, h₂ and h₃, and λ > 0, the operation rules for these three HFEs are as follows:

(1) $h^{\lambda }={\displaystyle {\cup }_{\partial \in h}\left\{{\partial }^{\lambda }\right\}}$

(2) $\lambda h={\displaystyle {\cup }_{\partial \in h}\{1-{(1-\partial )}^{\lambda }\}}$

(3) $h_1\oplus h_2={\displaystyle {\cup }_{{\partial }_1\in h_1,{\partial }_2\in h_2}\{{\partial }_1+{\partial }_2-{\partial }_1{\partial }_2\}}$

(4) $h_1\otimes h_2={\displaystyle {\cup }_{{\partial }_1\in h_1,{\partial }_2\in h_2}\left\{{\partial }_1{\partial }_2\right\}}$

Definition 3

([59]). Let h = {ξ₁, ξ₂, …, ξ_l} is HFE, then the score function S of HFE h is defined as follows:

$$S(h)={\displaystyle \frac{1}{l}}{\displaystyle {\sum }_{i=1}^l{\xi }_i}$$

(2)

Among them, l is the length of h.

Table 2. Comparison table of evaluation value and hesitation preference degree.

Language Variable	Preference Degree of Hesitation
EL (Extremely low)	[0,0.2]
VL (Very low)	[0.2,0.35]
L (Low)	[0.35,0.5]
M (Median)	[0.5,0.65]
H (High)	[0.65,0.8]
VH (Very high)	[0.8,0.9]
EH (Extremely high)	[0.9,1]

shows the correspondence between the evaluation values and the hesitant fuzzy element:

4.2. Determination of Expert Weights

For risk assessment, the evaluation of criteria by experts has a decisive impact on the outcome of project risk assessment. Therefore, in the research of risk assessment, the weight of experts is an indispensable part. This paper proposes a hybrid weighting method combining AHP, entropy weight method and consensus degree adjustment to determine the weights of each expert. The calculation steps of this hybrid weighting method are as follows:

Step 1: An observation group composed of 3 interpersonal relationship experts and 2 psychology experts observed the group discussion of the expert group throughout the process, and compared the experts pairwise in terms of knowledge, experience and professional title according to

Table 3. 1–9 scaling method [59].

Scale	Meaning
1	Both factors are equally important
3	The former is slightly more important than the latter
5	The former is obviously more important than the latter
7	The former is more important than the latter
9	The former is extremely important than the latter
2, 4, 6, 8	Between adjacent scales
Reciprocal	alk = 1/akl

to construct the judgment matrix A = [a_kl]_K×K among the experts [60].

$$A=\left[\begin{array}{ccc}{a}_{11}& \dots & a_{1K}\\ ⋮& \ddots & ⋮\\ 1/a_{K1}& \dots & a_{KK}\end{array}\right]$$

(3)

Among them, K is the number of factors; k, l = 1, 2, …, K; when k = l, a_kl =1.

Step 2: Consistency test. Calculate the consistency ratio CR [60].

$$\begin{array}{cc}CI={\displaystyle \frac{{\lambda }_{\max }-K}{K-1}},& CR={\displaystyle \frac{CI}{RI}}\end{array}$$

(4)

Among them, CR < 0.1; CI is a consistency indicator; λ_max is the maximum eigenvalue of A.

Step 3: Calculate the weights of the experts. Normalize expert weights w^a.

$$\begin{array}{cc}{w}^a={\displaystyle \frac{v}{{\displaystyle {\sum }_{k=1}^K{v}_k}}},& Av={\lambda }_{\max }v\end{array}$$

(5)

Among them, v is the eigenvector of A.

Step 4: Calculate the objective weights of experts using the entropy weight method. First, normalize the expert’s scoring matrix for the criteria by column to obtain matrix P = [p_ij].

$$p_{ij}={\displaystyle \frac{x_{ij}}{{\displaystyle {\sum }_{i=1}^n{x}_{ij}}+\epsilon }}$$

(6)

Among them, X = [x_ij]_n×m is the scoring matrix of the expert for the criteria system, and m is the number of criteria; ε is a minimal quantity, used to prevent the denominator from being zero.

Step 5: Calculate the entropy value E_j and entropy weight w_j^m.

$$\begin{array}{cc}{E}_j=-k{\displaystyle {\sum }_{i=1}^n{p}_{ij}\ln p_{ij},}& k=1/\ln n\end{array}$$

(7)

$$w_j^m={\displaystyle \frac{1-E_j}{{\displaystyle {\sum }_{j=1}^m(1-E_j)}}}$$

(8)

Step 6: Calculate the objective weight w_i^e of the expert.

$$w_i^e={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^m{p}_{ij}{w}_j^m}}{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{p}_{ij}{w}_j^m}}}}$$

(9)

Step 7: Calculate the expert rank matrix R = [r_ij] and the coordination Kendall’s W, and adjust the consensus degree.

$$\begin{array}{l}\begin{array}{cc}& \end{array}\\ \begin{array}{ccc}W={\displaystyle \frac{12S}{n^2(m^3-m)}},& S={\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{(r_{ij}-{\tilde{r}}_j)}^2}},& {\tilde{r}}_j={\displaystyle \frac{1}{n}}{\displaystyle {\sum }_{i=1}^n{r}_{ij}}\end{array}\end{array}$$

(10)

Here, S represents the sum of squares of the rank deviation; r_ij represents the rank of the jth criterion by the ith expert. R represents the average of all expert ranks on the jth criterion.

Step 8: Calculate the penalty for outlier experts.

When W < 0.5, calculate the deviation degree and adjust the weights:

$$\begin{array}{cc}deviatio{n}_i=\sqrt{{\displaystyle {\sum }_{j=1}^m{(x_{ij}-{\mu }_j)}^2}},& {\mu }_j={\displaystyle \frac{1}{n}}{\displaystyle {\sum }_{i=1}^n{x}_{ij}}\end{array}$$

(11)

$$w_i^c={\displaystyle \frac{\exp (-deviatio{n}_i)}{{\displaystyle \sum (\exp (-deviatio{n}_i))}}}$$

(12)

Among them, deviation_i represents the Euclidean distance between the opinion of expert i and the average group.

Step 9: Calculate the comprehensive weight of the experts w_i.

$$w_i={\displaystyle \frac{(\alpha w_i^a+(1-\alpha )w_i^e)\cdot w_i^c}{{\displaystyle {\sum }_{i=1}^n(\alpha w_i^a+(1-\alpha )w_i^e)\cdot w_i^c}}}$$

(13)

Among them, $\alpha \in [0,1]$ is the principal and objective equilibrium coefficient.

4.3. Risk Aggregation Method

This paper analyzes the OCWPHP project by using the method of aggregation operators. The risk criteria in formation of OCWPHP is aggregated to obtain the risk level of the project.

In 2020, Mo et al. [53] introduced the AHFOWA and AHFOWG operators, which effectively reduced the computational complexity of aggregation operators for hesitant fuzzy sets and were applied to aggregate citizen life satisfaction. Building on this, the proposed AHFOWA and AHFOWG operators are also employed in this study to aggregate project risks. These operators have a computational complexity of $O\left(\mathrm{mn}\right)$, where m represents the length of the HFE and n represents the number of participants. This is comparable to traditional hesitant fuzzy operators, but the adjusted operators reduce redundancy, improving computational efficiency for large-scale decision-making problems. In terms of stability, these operators maintain convergence through normalization and parameter adjustment processes, ensuring stability when applied to complex decision-making scenarios involving uncertainty and hesitation. Moreover, the proposed operators perform effectively in MCDM and risk assessment problems, particularly in large-scale group decision-making (LSGDM) contexts. Their robustness makes them well-suited for the systemic risk assessment of multi-energy complementary hydrogen production systems, especially when dealing with uncertainty and expert diversity.

(1) For a given set of HFEs h₁, h₂, …, h_n, the definitions of the AHFOWA operators are as follows:

$$AHFOWA(h_1,h_2,\dots ,h_n)=\underset{i=1}{\overset{n}{{\displaystyle \oplus }}}({\omega }_i{h}_{\sigma (i)})={\displaystyle \underset{k=1}{\overset{m}{\cup }}\{1-{\displaystyle \prod _{i=1}^n{(1-{\xi }_{\sigma (i)(k)})}^{{\omega }_i}}\}}$$

(14)

Here, m represents the length of HFE; n represents the number of criteria; h_σ(i) is the ith minimum HFE based on the score function, and ξ_σ(i)(k) represents the kth minimum value in h_σ(i). ω = (ω₁, ω₂, …, ω_n)^T is h_σ(i) (i = 1, 2, …, n), the weight of n, and ${\omega }_i\in (0,1),{\displaystyle {\sum }_{i=1}^n{\omega }_i}=1$.

(2) For a given set of HFEs h₁, h₂, …, h_n, the definitions of the AHFOWG operators are as follows:

$$AHFOWG(h_1,h_2,\dots ,h_n)={\otimes }_{i=1}^n{h}_{\sigma (i)}^{{\omega }_i}={\displaystyle {\cup }_{k=1}^m\{{\displaystyle {\prod }_{i=1}^n{\xi }_{\sigma (i)(k)}^{{\omega }_i}}\}}$$

(15)

5. The Risk Assessment Framework of the OCWPHP Project

This paper proposes a risk assessment framework based on a hybrid weighting method. Based on an in-depth understanding of decision-making methods such as AHP, entropy weighting method, and consensus adjustment, combined with hesitant fuzzy theory and aggregation operators, a three-stage risk assessment framework for OCWPHP projects is presented.

5.1. Phase One—Establish a Risk Assessment Criteria System and Collect Expert Evaluation Information

It is necessary to establish the OCWPHP project risk assessment criteria system and use the HFS theory to describe the evaluation information of experts on the criteria. The specific steps are as follows:

Step 1: Establish an expert panel and auxiliary working groups. The expert panel comprises five members, including two full professors in risk assessment, one associate professor in risk assessment, and two senior engineers each with over five years of experience in offshore energy development projects. The auxiliary working group is composed of over twenty employees from the risk assessment company and mainly engages in literature research and information statistics.

Step 2: Collect the risk factors of the OCWPHP project. The auxiliary working group statistically analyzes the risk factors related to the pyrolysis recovery project through literature review methods, then classifies and organizes them.

Step 3: Establish a criteria system. The expert committee discusses the risk factors collected in Step 2 and makes appropriate additions and deletions. Finally, the risk assessment criteria system for the OCWPHP project is determined in Figure 1.

Step 4: Set the expert group as E = {E₁, E₂, E₃, E₄, E₅}, and have the expert group conduct group discussions to score the risk criteria based on Table 3, and construct the expert-criterion scoring matrix.

Step 5: Since the sum of multiple weights may be greater than 1, normalization processing of {w_j} is required.

5.2. Phase Two—Determination of Expert Weights

This section uses the AHP-entropy weight method along with the consensus degree adjustment method to assign weights to each expert. For specific calculation steps, please refer to Section 4.2.

5.3. Phase Three—Comprehensive Assessment of Project Risks

To account for the weights of both the criteria and the experts, a two-stage aggregation method is employed in this paper to aggregate the project’s risk information.

Step 1: Apply the AHFOWA operator to each criterion (see Section 4.3 for details), aggregate the evaluations of all experts on this criterion, and obtain a comprehensive HFE.

Step 2: For the comprehensive HFE obtained in Step 1, the AHFOWG operator (see Section 4.3 for details) is used to aggregate the risk information according to the criteria’s weights, thereby obtaining the project’s risk value.

6. Case Study

The risk assessment framework proposed in Section 5 is applied to the case study in this section, and sensitivity and comparative analyses of the results are conducted to verify the effectiveness of the framework.

6.1. Case Description

A company plans to invest and build an OCWPHP project in the East China Sea. As this project is relatively cutting-edge, there is no approximate risk value for reference. Therefore, a risk assessment of this project is necessary.

6.2. Collection of Criteria Information

The expert group is set as E = {E₁, E₂, E₃, E₄, E₅}, and the expert committee scores the risk values of each criterion. The scoring situation is shown in

Table 4. The scoring situation of the criteria by the expert group.

	E1	E2	E3	E4	E5
C11	0.5	0.6	0.65	0.5	0.6
C12	0.55	0.6	0.55	0.65	0.6
C13	0.3	0.45	0.35	0.3	0.35
C14	0.7	0.7	0.65	0.6	0.65
C21	0.6	0.55	0.4	0.65	0.6
C22	0.4	0.4	0.35	0.4	0.4
C23	0.65	0.55	0.6	0.7	0.55
C24	0.25	0.15	0.3	0.2	0.25
C31	0.6	0.55	0.6	0.55	0.65
C32	0.7	0.75	0.7	0.65	0.7
C33	0.7	0.75	0.8	0.8	0.75
C41	0.3	0.65	0.45	0.6	0.5
C42	0.75	0.45	0.4	0.7	0.45
C43	0.35	0.25	0.4	0.4	0.3
C44	0.15	0.2	0.35	0.2	0.5
C51	0.2	0.3	0.2	0.25	0.2
C52	0.65	0.55	0.45	0.65	0.7

.

6.3. Calculate the Weights of the Experts

The judgment matrix A = [a_kl]_K×K among the experts is constructed by the observation group as shown in Equation (16), and the weights of the expert groups are calculated as w = {0.0026, 0.5246, 0.0207, 0.2014, 0.2507}.

$$A=\left[\begin{array}{ccccc}1& 2& 4& 7& 9\\ 1/2& 1& 2& 3& 5\\ 1/4& 1/2& 1& 2& 4\\ 1/7& 1/3& 1/2& 1& 2\\ 1/9& 1/5& 1/4& 1/2& 1\end{array}\right]$$

(16)

6.4. Aggregate Project Risk Information

Based on the scoring of the criteria system by the expert group and the weights of the expert group, the risk values of each criterion are calculated by the AHFOWA operator and AHFOWG operator, as shown in Figure 2.

Take the weights of the criteria ω = {ω_i = 1/17}, i = 1, 2, …, 17. The project risk value is calculated to be 0.4764. It can be known from

Table 5. The correspondence between the risk score value and the risk level.

Score Value	Risk Level
0~0.15	VL (Very low)
0.15~0.3	L (Low)
0.3~0.45	RL (Relatively low)
0.45~0.55	M (Medium)
0.55~0.7	RH (Relatively high)
0.7~0.85	H (High)

that the overall risk level of the OCWPHP project located in the East China Sea is “Medium”.

6.5. Analysis and Discussion

6.5.1. Sensitivity Analysis

To test the stability of the proposed risk assessment framework, this paper conducts a sensitivity analysis by changing the weights of the criteria. To calculate the risk changes of the project, the weights of the criteria in the economy, technology, society, politics and environment aspects are increased or decreased by 20% and 50%, respectively. The results of the sensitivity test are shown in

Table 6. Results of sensitivity analysis.

	Economy	Technology	Society	Politics	Environment
+20%	0.4762	0.4766	0.4783	0.4766	0.4751
−20%	0.4698	0.4840	0.4666	0.4835	0.4789
+50%	0.4805	0.4717	0.4865	0.4720	0.4723
−50%	0.4646	0.4902	0.4574	0.4894	0.4820

.

As shown in Table 6, although variations in criteria weights affect the project’s risk value, the overall risk level remains stable at “Medium”. Figure 3 further reveals that social and technical criteria exhibit the highest sensitivity: adjusting their weights leads to notable (yet <3%) fluctuations in risk value. Consequently, investors should prioritize monitoring these factors, while environmental criteria demonstrate minimal impact, with risk levels remaining virtually unchanged despite weight adjustments.

6.5.2. Comparative Analysis

The classical Cumulative Prospect Theory (CPT), introduced by Kahneman and Tversky, is widely recognized for modeling decision-making under uncertainty. It incorporates key behavioral factors, such as reference dependence, loss aversion, and probability weighting, making it highly suitable for capturing how individuals evaluate gains and losses relative to a reference point. In CPT, the overall utility of a decision alternative is calculated by integrating two core components: the value function and the probability weighting function. These two components combine to compute the overall prospect value of each alternative as the sum of the weighted subjective values of outcomes, allowing CPT to more accurately represent real-world decision-making under risk, as opposed to traditional expected utility theory. In the context of project risk assessment, CPT has been widely applied to analyze stakeholder preferences, particularly in situations where psychological factors significantly influence decision outcomes [61,62].

Building on its proven capability to capture psychological factors influencing decision-making, CPT is employed in this study to analyze project risks under uncertainty The CPT-calculated project risk value is 0.4745, with comparative results shown in

Table 7. Comparative analysis results.

	Risk Value	Risk Level
Method of this paper	0.4764	Medium
CPT	0.4745	Medium

.

Both methods yield a “Medium” risk level for the project, with minimal differences in calculated risk values, thereby validating the reliability of the proposed methodology. The conventional cumulative prospect value approach necessitates preliminary identification of positive and negative ideal solutions, where selection accuracy critically influences the final valuation. In contrast, the aggregation operator systematically organizes the target project’s risk information without relying on subjective decision-maker inputs, demonstrating clear methodological advantages.

Moreover, the results of this study are consistent with findings reported in the literature. For example, research on hydrogen energy storage systems coupled with renewable energy indicates an overall risk value of 0.4868 [43]. This comparison demonstrates that the risk assessment framework proposed in this study is feasible, effectively identifying the major risk factors in offshore multi-energy hydrogen projects, and providing a reliable basis for management decisions and preventive measures.

7. Conclusions

This study establishes a systematic and multi-level risk assessment framework for the OCWPHP system, addressing the methodological gap in evaluating complex offshore multi-energy coupling projects. The main conclusions are summarized as follows:

(1) A comprehensive and hierarchical risk criteria system was developed to characterize the multi-dimensional risks of OCWPHP projects. Drawing on a literature review and expert consultation, five key dimensions—economic, technical, social, political, and environmental—were identified, providing a structured foundation for subsequent quantitative assessment.

(2) A dual weighting mechanism integrating the Analytic Hierarchy Process (AHP) and the entropy weight method was constructed to balance subjective expert judgment and objective data information. Furthermore, Kendall’s coefficient of concordance (Kendall’s W) was introduced to adjust inter-expert consistency, forming a hybrid weighting approach that enhances both the accuracy and robustness of the final weights. This improvement effectively mitigates bias associated with either purely subjective or objective methods.

(3) Hesitant fuzzy set (HFS) theory and aggregation operators (AHFOWA and AHFOWG) were applied to manage uncertainty and hesitation in expert evaluations, ensuring that the complex and ambiguous nature of offshore hybrid energy risks is adequately captured. Comparative analysis with the cumulative prospect theory (CPT) method confirmed that the proposed model achieves higher reliability and computational efficiency, while maintaining interpretability.

(4) A case study of an OCWPHP project in the East China Sea demonstrated the applicability of the proposed framework. The overall risk level was assessed as “Medium”, aligning with results from conventional methods, thus validating the framework’s reliability. Moreover, the model enabled the identification of critical risk sources within each dimension, supporting the formulation of targeted risk mitigation strategies.

The proposed risk assessment framework demonstrates distinct utility for both practitioners and theorists, offering wide applicability beyond the specific case study in the East China Sea. For practitioners such as policymakers and project investors, the framework provides a systematic tool for preliminary risk screening, supporting early-stage project planning, resource allocation, and policy design. Sensitivity analysis further highlights the social and technical dimensions as priority areas for risk control. Although the model was calibrated using regional data, its methodological foundation—integrating multi-dimensional risk criteria and a hybrid weighting mechanism—can be readily transferred to other maritime regions with similar renewable energy profiles, such as the North Sea or the Caribbean. Key adaptation considerations include local policy frameworks, marine ecological sensitivities, and the maturity of offshore infrastructure supply chains. For mathematicians and model developers, the integrated methodology combining HFS theory, hybrid weighting, and aggregation operators offers an extensible modeling structure and computational foundation for addressing other complex multi-criteria decision-making problems under uncertainty. This dual utility reinforces the framework’s significance as both a practical decision-support tool and a foundation for further methodological innovation in risk assessment.

However, this study still exhibits certain limitations. Specifically, the criteria are assigned equal weights, future research should consider applying weighting methods to allocate appropriate weights to each criterion.