A comprehensive resilience assessment framework for hydrogen energy infrastructure development

(cid:1) A Holistic taxonomy of resilience is proposed for hydrogen infrastructure. (cid:1) A Novel IFWINGS is proposed for advanced qualitative resilience assessment. (cid:1) Importance of regulation, government preparation


a b s t r a c t
In recent years, sustainable development has become a challenge for many societies due to natural or other disruptive events, which have disrupted economic, environmental, and energy infrastructure growth.Developing hydrogen energy infrastructure is crucial for sustainable development because of its numerous benefits over conventional energy sources.However, the complexity of hydrogen energy infrastructure, including production, utilization, and storage stages, requires accounting for potential vulnerabilities.Therefore, resilience needs to be considered along with sustainable development.This paper proposes a decision-making framework to evaluate the resilience of hydrogen energy infrastructure by integrating resilience indicators and sustainability contributing factors.A holistic taxonomy of resilience performance is first developed, followed by a qualitative resilience assessment framework using a novel Intuitionistic fuzzy Weighted Influence Nonlinear Gauge System (IFWINGS).The results highlighted that Regulation and legislation, Government preparation, and Crisis response budget are the most critical resilience indicators in the understudy hydrogen energy infrastructure.A comparative case study demonstrates

Toward renewable energy
Moving toward renewable energy and minimizing the utilization of conventional ones is a crucial issue nowadays for sustainability and high quality of life.Sustainability refers to the ability of a system or community to meet its present needs without compromising the ability of future generations to meet their own needs.It involves responsible resource management, equitable distribution of benefits and burdens, and a long-term perspective that considers the social, economic, and environmental impacts of current actions on future generations [1].At this point, hydrogen energy has been acquiring much more popularity and attracting attention from different government and private sectors to invest in developing hydrogen technology [2].For example, in European countries, hydrogen has become the primary vehicle fuel type promising to be an uncontaminated and clean type of energy source [3].However, developing and advancing the hydrogen infrastructure for having everyday handy and mobility is still in its early stage concerning different aspects.The hydrogen production, utilization, and storage stages are associated with several safety issues that should be examined and managed adequately to ensure safe and resilient operations and performance functionalities.In this respect, studying the potential characteristics of hydrogen energy infrastructure prone to resilience change is of interest and an essential academic concern [4,5].Resilience refers to the ability of a system to withstand and recover from disruptions, shocks, or stressors while maintaining its basic functions and structures.It involves the capacity to absorb and adapt to changing conditions, learn from past experiences, and prepare for future challenges [6,7].Thus, the resilience of hydrogen infrastructure is the capacity of the hydrogen system to deliver and sustain an acceptable level of functionalities after a suddenly undesired disruption (i.e., resilience indicator changes).Performance functionality loss in the hydrogen infrastructure can lead to catastrophic accidents and interrupt the energy network's services.

Literature review
As illustrated in Fig. 1, resilience and its various improvements have been broadly used in different application domains, notably in Engineering (43%, 6718 documents), Computer Science (12%, 1808 documents), Social Sciences (9%, 1437 documents), Environmental sciences (6%, 1018 documents), Energy (6%, 994 documents), and so on.A brief bibliometric and meta-data analysis using Bibliometrix software (https://www.bibliometrix.org/home/), a user interface for the R package Bibliometrix [8] as a flexible and robust bibliometric analysis tool, is adopted to reveal, analyze, and visualize the trend and patterns of published scientific literature in the hydrogen infrastructure improvement area.The outcomes of bibliometric analysis would provide valuable understanding for researchers and practitioners working in this area.It also sheds light on the academic gaps and needs in the existing literature and illustrates an overall trend of hotspots in this field.Analyzing published articles with the keywords "Hydrogen Infrastructure" AND "Safety", OR "Risk" OR "Reliability", OR "Resilience" in the Scopus database by the end of September 2022 indicated that there are only 253 studies focused on "Hydrogen Infrastructure" underlying different safety concept.Fig. 2 depicts both the most frequent keywords and Thematic Evolution investigating "Hydrogen Infrastructure" based on the "Keywords Plus" analysis, including authors and index keywords, considering that the minimum number of occurrences equals 15.The "Keywords Plus" analysis is derived according to the references' titles of a published article using a unique algorithm [9].This analysis is more predominantly descriptive than keyword analysis.In addition, Thematic Evolution is a term used to describe the changes and developments in a particular theme or topic over time [10,11].It involves the analysis of how a specific subject has been discussed, interpreted, and understood across different periods or contexts.This analysis would help to identify patterns and trends, and would provide insights into the ways in which a field of study has developed and changed over time.
Based on the thematic evolution analysis, it is apparent that the primary focus of initial research related to hydrogen fuel cells was the development of standards for safe design and operation of fuel cells, as well as exploring the use of hydrogen as a fuel.Safety concerns were also a major consideration during this period, particularly with regards to the flammability and explosiveness of hydrogen, which resulted in the development of various safety codes and standards.The subsequent phase of research focused on the practical application of hydrogen as a fuel, particularly in the automotive industry, with efforts to develop hydrogenpowered vehicles.During this period, significant progress was made in developing safety standards and regulations, with a focus on risk assessment methods to ensure safe usage.The subsequent two periods focused on large-scale projects for utilizing hydrogen fuel, with a particular emphasis on developing risk assessment and management methods for controlling risks.Currently, the research focus has shifted towards integrating hydrogen technologies with existing energy systems, exploring new sources for hydrogen production, and implementing advanced safety systems to create more resilient infrastructure.As can be seen from our data analysis and having support from the literature [12], the "Hydrogen Infrastructure" is located in the center surrounded by "Hydrogen production", "Hydrogen storage", "Hydrogen economy" and "Fuel cells", demonstrating its significance and how much it is common in the field of hydrogen studies.It is then closely margined by a requirement of risk assessment methods and safety measurement approaches, including quantitative and qualitative methodologies.For example, in some of the published research works, Zarei et al. [13] used a probabilistic method (Bayesian Network) to dynamically assess the safety risks in the hydrogen generation plant.Mohammadfam and Zarei [14] carried out the Hazard and Operability (HAZOP) and Quantitative Risk Assessment methods (e.g., "event tree analysis (ETA)", and "fault tree analysis (FTA)") to analyze the hydrogen gas release in the hydrogen production unit of an oil refinery.Viana et al. [15] proposed a multi-dimensional risk-based approach by categorizing hydrogen pipeline transportation.Shi et al. [16] proposed a method to manage uncertainty and reduce computational intensity in explosion risk analysis (ERA) for hydrogen production facilities.The method integrates a Bayesian Regularization Artificial Neural Network (BRANN) methodology with ERA, which generates non-simulation data to develop scenario-based probability models for estimating the exceedance frequency of maximum overpressure.Shi et al. [17] also proposed a new method for analyzing the fire risk associated with urban Hydrogen Refueling Stations in China, which will support Fuel Cell Vehicles.Due to a lack of data, there is high parametric uncertainty, and the proposed method uses BRANN and statistical approaches to reduce uncertainty and computational intensity.The method is demonstrated through a case study and achieves significant reductions in uncertainty and computation cost.In a separate investigation [18], the authors introduce an advanced decision-making framework designed to effectively manage the risk associated with hydrogen refueling station leakage.This framework incorporates the Bow-tie analysis methodology and leverages Interval-Value Spherical Fuzzy Sets to appropriately address the subjective elements inherent in the risk assessment process.Al-shanini et al. [19] presented a method for assessing the safety of a hydrogen station in a ground transportation network.The approach incorporates prevention barriers related to human factors, management, and organizational failures using FTA and ETA.The results can help predict outcomes, update failure probabilities, and plan maintenance and management.In a study conducted by Dadashzadeh et al. [20], the Computational Fluid Dynamics (CFDs) is a safer and cost-effective method to predict its behavior after an accidental release.This study proposes a CFD-based approach to evaluate the dispersion behavior of hydrogen gas in an enclosed area after a release from a hydrogen fuel cell car.In another study, Xing et al. [21] proposed a "Process Hydrogen Accident Risk Assessment" model to help decision-makers control the associated risks of hydrogen refueling stations.However, there is no compressive study to assess the resilience of hydrogen infrastructure concerning resilience indicators and sustainable contributing factors.Therefore, there is still room and calls a requirement to seek further investigation into the topic.

Decision making in resilience assessment of hydrogen infrastructure
The decision-making tools can adequately perform a promising investigation in various complex circumstances, when there is uncertain information.Uncertainty is a critical issue in real-world decision-making problems and needs extra attention to deal with it in computation, optimization, and other similar processes.It is of paramount importance to utilize accurate values as much as possible to examine the interrelationships and casualties of factors in the decisionmaking process.Due to the dynamic features of hydrogen energy infrastructure and the limitation of decision-makers' experience, they could share their opinions using linguistic terms when decision-makers are unfamiliar with the resilience indicators.This simply means that the confidence level of decision-makers and the reliability of their opinions might be variable.Under such conditions, it is worth further investigating how to acquire more precise, efficient, and practical knowledge during the decision-making process.Table 1 compares the different decision-making methods in terms of hierarchical decision-making issues with causality contributing factors.As it can be seen, uncertainty handling is an inevitable part of the decision-making process.At this juncture, the fuzzy set theory and its broad developments can be integrated appropriately with the Multi-Criteria Decision-Making (MCDM) tools without precise and known information.In fact, it is vital to formalize the decision-makers rational opinions when there is a lack of or partial information, and it is required to make rational decisions [22].This can be achieved by converting the linguistic terms into the proper numerical values reflecting the decision-makers' opinions [23].
In this sense, Atanassov (1986) [40] introduced Intuitionistic fuzzy set (IFS) as an advanced extension to the conventional fuzzy set [41], which included three membership functions (i) membership, (ii) non-membership, (iii) hesitation degree.In the state of the arts, there are extensive research works indicating that integrating data using IFS is much more comprehensive than the fuzzy conventional set (only considering the membership function), dealing with the ambiguities and uncertainties of subjective decision-makers' opinions.In addition, it has less complexity in computations, application, and practicality compared with new extensions such as Pythagorean fuzzy set, Rough fuzzy set, Interval Type-2 Fuzzy Sets, and Neutrosophic Fuzzy set.Some examples of research work to support above mentioned statement are but not limited to Refs.[42e46].Considering the reliability, simplicity, and practicality of IFS and having significant demonstrated applications in the existing literature, in the present study, the concept of IFS is used and integrated into the decision-making process to assess the resilience of hydrogen energy infrastructure.
The resilience assessment of hydrogen energy infrastructure can fall under a typical MCDM problem, which aims to derive the resilience index, the most significant contributing factors, and their causality evaluation utilizing a soft computing approach.The study by Guo et al. [47] presents a comprehensive review of resilience assessment methodologies for different critical infrastructures.Besides, the authors determined the most common resilience indicators and dimensions in critical infrastructures.In another review study [48], the authors overviewed an in-depth analysis of resilience quantification frameworks for energy systems.Among all the decision-making tools, the WINGS (Weighted Influence Nonlinear Gauge System) technique seems to have superiority compared to the other MCDM methods in causality identification with several factors.Reviewing the existing state of the arts and to the best of the authors' knowledge, the issues mentioned earlier can be addressed with the integration of the WINGS method and fuzzy logic.Unlike other MCDM approaches [49], the present study extends the WINGS method underlying the Intuitionistic fuzzy set environment to extract the contributing factors' dependencies in a complex system.Moreover, the WINGS method using an influential diagram has enough capacity to account for the hierarchical causality and interrelationships between the factors, which other MCDM tools like ISM cannot determine, and DEMATEL.Besides, it can adequately compute the influence intensity and indicators' power, which cannot be reliably derived from other common MCDM tools [50].
It should be added that evaluating causality and interrelationships between the resilience indicator is a complex and challenging task for assessors, which are the decision-makers, especially when the resilience assessment of hydrogen energy does not follow the hierarchical structure.In this regard, it is necessary to establish an accurate hierarchical structure demonstrating the resilience indicators' causality and interrelationships with WINGS.Using its capacity to map influence diagrams would help to visualize the connection between the factors.Nevertheless, while WINGS perform a cause-and-effect analysis with the set of identified resilience indicators, integration of IFN can reduce subjective uncertainty and enhance the accuracy of the analysis.
The main contributions of the present research work are triple and highlighted as the following points.
The study presents a new taxonomy for assessing the resilience of hydrogen infrastructure, which identifies key dimensions, indicators, and contributing factors.This taxonomy provides a comprehensive framework for evaluating the resilience of hydrogen infrastructure in various scenarios and situations.An advanced decision-making framework is developed to establish the causality between indicators and contributing factors.This framework enables a more accurate assessment of the factors that impact the resilience of hydrogen infrastructure and provides insights for developing effective mitigation strategies.An intuitionistic fuzzy set is integrated with the WINGS method as a robust and reliable approach to dealing with subjective uncertainty during the knowledge elicitation process.Examine and validation of the proposed framework's capability and effectiveness in assessing the resilience of hydrogen energy infrastructure.
The organization of the present work is constructed as the following.In Section 2, the new methodology is proposed to assess the resilience of energy infrastructure by extending the Weighted Influence Nonlinear Gauge System method under the environment of the Intuitionistic fuzzy set.Section 3 investigates an application of study to assess the resilience of hydrogen energy infrastructure.Finally, the conclusion highlights the existing challenges, remarks, and direction for future research, in Section 4. i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( x x x x ) x x x The proposed methodology

1) a novel resilience assessment taxonomy
The resilience assessment of hydrogen energy infrastructure is a complex process [51,52].Therefore, the assessment cannot be carried out based on a single aspect and needs evaluation of various dimensions.Considering the concept of the case study, its inherent features, having support from existing pieces of literature [47,51,53,54], and to the best of the authors' knowledge, the four dimensions of key resilience indicators underlying the sustainable contributing factors are developed in Fig. 3.The detail of each indicator is provided as the following.

Recoverability (R-TR)
This indicator shows the infrastructure's capacity to restore its loss of performance functionality after sudden disruption [55,56].This recovery helps system performance reach close to the original functionality (i.e., greater, equal, or less).The recovery processes and material, financial, and human resources are the main attributes in determining recoverability.The hydrogen energy infrastructure will be highly recoverable and strengthen the system resilience if all attributes meet the demand.
Redundancy (Re-TR) This indicator shows the degree to which interchangeable critical systems are present and satisfy the functional requirement in the occurrence of disruption (e.g., degradation, functionality performance loss, interruption, and so on) [57].In other words, Redundancy means the availability of replicate/backup alternative recourses.The hydrogen energy infrastructure will be resilient if more backup alternative resources become available.

(i) Indicators of TR Dimension
Robustness (Ro-TR) This indicator refers to the system's capacity to withstand undesired disruption without performance functionality loss [58].Technically, if the infrastructure robustness level was equal to the highest point (100%); then it can totally resist the impact of undesired shock and pressure.In the study has been conducted by Rehak [59], robustness can be evaluated considering the five different variables redundancy, detection, responsiveness, physical-based resistance, and crisis preparedness.
Maintenance (M-TR) This indicator refers to the acceptable operational procedure to sustain the infrastructure asset operating safely and reliably, including post-accidents procedure [60].Performing effective asset maintenance with high quality will minimize the recovery time and assist in resisting sudden shock [61].Technically, maintenance indicators can be divided into two categories preventive and corrective maintenance.Preventative maintenance means applying a set of practices to avoid failures before disruption (i.e., reducing the value probability of failure).The infrastructure with properly established Fig. 3 e The four key dimensions for resilience indicators.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( x x x x ) x x x preventive maintenance helps early warning signs, which can be handled before disruption occurrences.Corrective maintenance means applying a set of practices to repair malfunctioning after disruption occurrences.This requires that after disruption occurrence, the root cause analysis should be conducted, and corrective actions should be carried out to avoid recurrence.
Emergency equipment (E-TR) This indicator refers to the crisis response, which absorbs the impact of undesired events and ensures employees' safety [61,62].This is an essential resilience indicator since it can properly measure the hydrogen energy infrastructure's internal and external resilience, including emergency personnel and reliable technical equipment.It should be added that emergency equipment must always be available during the occurrence of a sudden disruptive event.The internal emergency equipment has a much more impact on the resilience stages than external ones.
Safety design (S-TR) The safety design indicator refers to the hydrogen infrastructure security levels and its ability to adequately absorb the impacts of shocks and pressure [58].The safety design indicator refers to the hydrogen infrastructure security levels and its ability to adequately absorb the impacts of shocks and pressure.According to the existing literature, this indicator has considerably contributed to resilience infrastructure [63].The safety design can be divided into four sub-indicators as (i) system safety, (ii) redundancy, (iii) simplicity, and (iv) internal and external auditing [64].
Data collection and system monitoring (D-TR) This indicator refers to the infrastructure resilience data acquisition, which must be established appropriately throughout the process.It has two sub-indicators named (i) collecting data equipment (e.g., sensors): and (ii) monitoring information equipment (e.g., infrastructure processing, transmission, and storage) [64].(ii) Dimension of Social Resilience (SR) indicator.
Social condition preparations and awareness (S-SR) The Social condition preparations and awareness indicator refer to the risk awareness level of the public as well as the vulnerabilities they withstand in unfavourable circumstances.Social training, social situations, and awareness/ commitment are two sub-indicators of social condition preparations and awareness indicators [62].In addition, society can provide extensive resources and collaboration to improve the energy infrastructure resilience and strengthen undesired event management.The risk of implementing energy infrastructure, all potential undesired events, and the system commitment to managing the possible disaster must be informed to society.

Public crisis response budget (P-ER)
This indicator highlighted that energy infrastructure requires saving investment to absorb the shocks and pressures and repair/replace the facilities to recover the functionality performance loss during disruption [65].In order to improve the economic resilience and further the resilience of hydrogen energy infrastructure, there should be enough allocated budget to repair, purchase the backup components, and temporarily engage the new workers and equipment.In case of a lack of a public crisis response budget, the infrastructure resilience will be reduced over time.
Crisis response budget (C-ER) This indicator is similar to the P-ER; however, the subjects' recourses response is different.This is an additional funding and enables the energy infrastructure (i.e., system, organization), first responders, and society to obtain the recourses in an acceptable period.There are some examples: performing repair, replacement, and reconstruction.The government level of awareness and commitment impact the structure of these resources, which will affect this indicator.

Adaptability (A-OR)
Adaptability is a critical resilience indicator, which means the system can adapt dynamically to adverse conditions with some changes [66].This indicator is the energy infrastructure capacity for planning and adapting the emergency for survival and evolution in an uncertain environment.It is worth mentioning that the adaptive capacity of a system is different from what is called absorptive system capabilities.The latter refers to the system ability for potential interference absorption; that is, while the system adaptability indicates that once absorptivity fails, the system can adapt to the undesired events the system undergoes with some changes.This resilience indicator can be improved by utilizing risk management, development, education, and innovation throughout the infrastructure lifecycle.
First responder preparation (F-OR) This indicator refers to how firefighters and other kinds of first responder teams are well-trained and prepared to withstand disruption prior to the occurrence [62].This includes two sub-indicators: (i) first responders' preparation and training and (ii) first responders' commitment and awareness.First responders should be trained and how to act prior to, during, and after the disruption.In addition, they always have to be knowledgeable about all potential dilemmas and commit to being on the frontline of empowering resilience infrastructure [67].
Change readiness (C-OR) This indicator refers to the organization's infrastructure capacity by predicting and preserving the possible hazards, breaking them down using root cause analysis tools, and providing an early warning of disruptions.This indicator can be improved by adequately understanding the energy infrastructure vulnerability.According to the existing state of arts [68,69], it also consists of flexibility and changing capacity, developing or adopting strategic alternatives to the dynamic environment, and lessening learned from them.The Change readiness indicator has many sub-indictors, including but not limited to employee communication systems, backup essential information, scenario planning, training/drills, general public awareness, and more [70].
Leadership and culture (L-OR) This indicator refers to the system capacity to cultivate a culture and an organizational mentality devoted to challenges, skill, flexibility, adaptability, and innovation.In addition, it i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( x x x x ) x x x takes opportunities and advantages over time [47].The organizational resilience must cultivate the capacity by implementing trust, empowering the staff, clarifying the objectives, and inspiring staff to improve their interpersonal skills and resilience.This indicator includes the following sub-indicators: leadership, situational understanding, creation and originality, political intention, and employee involvement [71].
Government preparation (G-OR) This indicator refers to the governmental preparation, in which they must predict the probable occurrences that might impact the energy infrastructure to some extent [63].Like the first responders' preparation indicator, the government must also determine the emergency response procedures before undesired events and learn how to act quickly.In contrast, they have enough authority to improve organizational commitment and awareness and make the energy infrastructure much more resilient.This Government preparation indicator includes five sub-indicators: commitment and condition awareness, training, communication, leadership capability, and response agents' coordination.
Regulation and legislation (ReOR) This indicator indicates how regulations and laws look at compliance and maturity levels.Legislation is a law supported by the whole government, while the regulations developed by agencies' authorities describe how to execute the legislation in practice.The resilience of energy infrastructure can be improved by dynamically updating the legislation/regulations.This indicator makes the energy infrastructure much more secure, taking more acceptable guard against undesired events and having better remedy when it happens.This indicator can be divided into two sub-indicators: (i) updates/ revisions and (ii) compliance level of laws/regulations.
The quantification approach: intuitionistic fuzzy Weighted Influence Nonlinear Gauge System (IFWINGS)

The concept of intuitionistic fuzzy set
The concept of the classical fuzzy sets has been generalized by Atanassov (1986) [72]  An IFS Ã in the universe of discourse X is given by Where m Ã : X/½0; 1 and v Ã : X/½0; 1 are membership and non-membership functions, respectively, where For every value x2X, the values m Ã ðxÞ and v Ã ðxÞ represent the degree of membership and degree of non-membership to Ã4X, respectively.Moreover, the uncertainty level or hesitation degree of the membership of x in Ã is denoted as: If p ÃðxÞ ¼ 0; cx2X; then the IFS becomes a classical fuzzy set.
If the membership and non-membership functions of an IFS Ã (i.e., m ÃðxÞ and v ÃðxÞ) satisfies the following conditions given by Equations (4) and (5), then Ã in X is considered as IFconvex Suppose there exist at least two points x 1 ; x 2 2X such that m ÃðxÞ is an upper and v ÃðxÞ is a lower semi-continuous.Supp Ã ¼ fx 2X : v ÃðxÞ < 1g is bounded (refer to Fig. 4).
A Triangular-IFN is an IFN given by.

Intuitionistic fuzzy Weighted Influence Nonlinear Gauge System (IFWINGS)
As it can be seen from Fig. 5, the proposed methodology as an extension of WINGS using IFS is constructed with three main steps: (i) Determining the decision-makers-based evaluation using IFS, (ii) Aggregating the group-based evaluation using IFWINGS, and (iii) Investigating the contributions of As a pre-step, the process of the under-study application should be properly understood, and the set of evaluation resilience indicators and sustainable contributing factors required to be identified.In addition, the causality and their interdependencies need to be examined.
Step 1. Determining the decision-makers-based evaluation using IFS Step 1.1.Creating a heterogeneous group of decision-makers This step gathers a heterogeneous group of decisionmakers (e.g., four to six individuals as subject matter experts (SMEs)).It is essential to emphasize that the decision-makers involved in the study must possess relevant backgrounds, expertise, or education that are applicable to the research area.They should also have a comprehensive understanding of the proposed methodology, the rationale behind the work, and how their contributions can add significant value to the scientific community.Additionally, it is crucial that the decision-makers declare any potential conflicts of interest or relationships that could potentially impact the elicitation process and the outcomes of the investigation.This will help ensure the integrity and objectivity of the decision-making process and maintain the trust of the scientific community.
Moreover, decision-makers can provide valuable input for evaluating criteria and identifying interdependencies.In some situations, the evaluation criteria can interactively be determined by the group of decision-makers.
Step 1.2.Defining a proper linguistic term for evaluation The best fitting, fitting linguistic term and their corresponding IFNs are defined in this step and listed in Table 2.
Step 1.3.Generating the initial group-based strength influence matrix  Let us assume that there is l number of decision-makers, DM ¼ fDM 1 ; DM 2 ; DM 3 ; …; DM l g to generate the initial groupbased strength influence matrix and evaluate the importance of contributing factors as well as their interdependency.The u j ¼ fu 1 ; u 2 ; u 3 ; …; u l g is the decision-makers importance weight considering their level of quality profile.Then, the initial group-based strength influence matrix based on IFS from DM l can be constructed as the: P k ¼ ½p k ij mÂn ðk ¼ 1;2;…;lÞ, and p k ij ¼ ða 1k ; a 2k ; a 3k ; a 0 1k ; a 2k ; a 0 3k Þ.
In order to integrate all of the decision-makers opinions into a single one, considering their importance weights, the similarity aggregation method has been used [74].The similarity S uv ðp ij u ; pij v Þ between the opinions pij u and pij v of decisionmakers E u and E v can be derived as the following equation: where S uv ðp ij u ; pij v Þ2½0; 1 is the function to measure similarity, where pij u and pij v are two regular IFNs, EV u and EV v are the expectancy evaluation for pij u and pij v , respectively.The EV of pij ¼ ðã 1k ; ã2k ; ã3k ; ã0 1k ; ã2k ; ã0 3k Þ, can be computed as follows: A similarity matrix ðSMÞ for l number of decision-makers is defined as: where Once the similarity matrix is determined, the "average agreement degree" AAðDM l Þ for each decision-maker is derived as the following equation: S uv (11) where k ¼ 1; 2; …; l.Following that, the "relative agreement computation" is obtained: where k ¼ 1; 2; …; l: Considering the importance weights of decision-makers u j ; and the computed RAD ðDM k Þ, the "Consensus Coefficient" (CC) degree is computed as the following: where að0 a 1Þ is the relaxation factor (RF), also known as a relaxation factor which is assigned to u j ðDM k Þ and RADðDM k Þ by defining their relative importance.The aggregated result for each contributing factor can be computed from Equation ( 14) as: Where CC k is the computed "Consensus Coefficient" degree for all decision-makers, and Pj is the aggregated decision-makers opinions for the contributing factor j in the format of IFNs as ðã 1 ; ã2 ; ã3 ; ã0 1 ; ã2 ; ã0 3 Þ.
Step 2. Aggregating the group-based evaluation using

IFWINGS
Step 2.1.Constructing normalized IFS strength influence matrix In this step, the matrix P ¼ ½p ij mÂn is normalized using the following equation: and 3 , where ÑP represents the normalized IFS strength influence matrix, and the value of s is computed using Equation ( 16) as: Step 2.2.Obtaining IFS total strength influence matrix In this step, the total strength influence matrix based on IFS is computed in the following equation: Tã 1 ; Tã 2 ; Tã 3 ; Tã 0 1 ; Tã 2 ; Tã 0 and where I indicated the n Â n identical matrix.
Step 2.3.Obtaining the total impact, total receptivity, and engagement scores First of all, the total impact cores are in this step ri and the total receptivity cj are computed using the following equations: Step 3. Investigating the contributions of influential factors Step 3.1.Deriving the cause and effect relationship diagram In the present step, the Euclid method, and the concept of ideal (best) refers to the best or most favorable situation, and nadir (worst) refers to the lowest point or the worst possible solutions have been used to derive the preference point and plot the cause and effect relationship diagram in 2dimensional space, in which the scores of ted in the horizontal axis.The scores of ðr i def À cj def Þ are put in the vertical axis.
Step 3.2.Examining the impact of contributing factors and making decisions This step involves examining the impact of all contributing factors and making a final decision by ranking them based on their Euclidean distances from the ideal solutions.To evaluate the set of contributing factors, the Resilience Index (RI) is defined for hydrogen energy infrastructure.In this study, the RI is utilized for backward propagation analysis to identify the most critical factors and provide intervention actions.Furthermore, the RI can facilitate comparative analysis between different hydrogen energy infrastructures.The equation used to define the RI is Equation ( 22 where a and b are the numbers of factors in the first and second levels of hierarchy, respectively.The H 1 ij and H 2 ij are the factors in the first and second levels of the hierarchy in the same accordance.

The proposed model application
Case study: hybrid wind-hydrogen power plant This section assesses the resilience of a hydrogen energy infrastructure using the proposed IFWINGS methodology.In the current study, we assumed that the resilience lifecycle contains three and only three stages: (i) prevention, (ii) absorption, and (iii) recovery.Considering the significance, advantages, and criticality infrastructure of hybrid windhydrogen power plants to produce hydrogen from wind turbines that are drastically different from hydrocarbon fuels [75,76]; thus, this calls a necessity and immediate attention to assessing the resilience of this critical energy infrastructure.Some of the advantages of a hybrid wind-hydrogen power plant are.
The intermittent availability of wind turbines necessitates the storage of generated electricity.Hydrogen is used for long-term storage.It also reuses the electricity in the infrastructure since it is a suitable alternative that helps overcome some of the challenges associated with battery technology.These challenges include the limitations of certain metals for manufacturing, the costs of maintenance, and the environmental impact associated with their disposal [77,78], Since a hybrid wind-hydrogen power system utilizes local energy sources, it is an appropriate infrastructure for areas that are far from power grids and for those areas where the connection to the power grid requires substantial financial resources [79], and Implementing wind-hydrogen power systems contributes to sustainable development and minimizes carbon i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( x x x x ) x x x footprint by reducing fossil fuel consumption and carbon emissions [80].
As shown in Fig. 6, the system consists of six main parts, including: (i) A wind turbine produces electricity from winds, (ii) An electrolyzer unit in the plant converts the electricity into hydrogen, (iii) The produced hydrogen gas is compressed in a two-stage compressor, (iv) In the first stage, it is compressed to 7 bar in a single-stage reciprocating compressor, and (v) then to 200 bar in a high-pressure compressor, and finally (vi) The compressed gas is stored in a storage tank.A combustion generator is adopted in the plant to provide electricity by using hydrogen as a gas fuel.Since the system is joined to a weak grid, grid stabilizing equipment is required, which includes a flywheel, a synchronous machine, and a battery.Due to the unique properties of hydrogen, establishing the infrastructure of a hybrid wind-hydrogen power plant is associated with safety issues.It is prone to several hazards (e.g., high pressure of hydrogen gas) that must be identified and managed to ensure safe operational conditions [79].Regarding the critical roles that hybrid wind-hydrogen power plants play in energy production, particularly in small communities [77,81], assessing the resilience index during the system design phase is vital.
The detail of performing each single step of the proposed methodology is delivered in the following steps: Pre-Step: Selecting the evaluation resilience indicators, and sustainable contributing factors, and identifying the interdependencies among them.
As outlined in the methodology section, the assessment of the resilience index of the hydrogen energy infrastructure requires the selection of appropriate resilience indicators and sustainable contributing factors.Identifying the interdependencies among these indicators is a crucial step in the assessment process.To achieve this, there are several options available, such as allowing the research team to identify the interdependencies, seeking input from the decision-makers, or engaging in an interactive process to identify them collaboratively.For this particular study, the engaged decision-makers group will be asked to identify the interdependencies among the resilience indicators and sustainable contributing factors.This approach will provide valuable insights and perspectives that are essential for a comprehensive and accurate assessment of the hydrogen energy infrastructure's resilience index.
In this step, for the sake of simplicity, we assumed that there would be a heterogeneous group of decision-makers comprising five individuals with significant relevant background, expertise, and education would participate in the study.The profile of quality of the five decision-makers, as well as their corresponding importance weights, are presented in Table 3.In real study analysis, to ensure the validity of the study's results, assessors must confirm that the participating  i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( x x x x ) x x x decision-makers have disclosed any potential conflicts of interest or relationships that could affect the investigation's outcome.In this study, both spatial and temporal data, which may include various formats such as point data, raster data, or vector data for spatial data, and time-series or longitudinal data for temporal data are considered.The dimensionality of the data will vary depending on the specific application, and we have taken this into consideration when analyzing the results as part of a partial study.
Step 1.2: Defining a proper linguistic term for evaluation It is asked from the employed decision-makers group to express their opinions in linguistic terms as provided in Table 2, presented in the methodology section.
Step 1.3: Generating the initial group-based strength influence matrix Assumed that SMEs collaborated with the authors to create an initial group-based strength influence matrix that assesses the significance of contributing factors and their interrelationships.The matrix was developed based on the opinions of the first decision-makers, and a relaxation factor of 0.5 was used.Table 4 shows the resulting initial matrix.The online Appendix A contains the opinions of the remaining decision-makers regarding the matrix.
Step 1.4: Obtaining the IFS strength influence matrix In this step, the group-based IFS strength influence matrix is obtained, and the results are provided in Table 5.In addition, Table 6 presents the process of five decision-makers' opinion aggregation process for the influence OR on RI.
Step 2: Aggregating the group-based evaluation using IFWINGS Step 2.1: Constructing normalized IFS strength influence matrix In this step, using Equations ( 15) and ( 16), the normalized IFS strength influence matrix P ¼ ½p ij mÂn is constructed.
Step 2.2: Obtaining IFS total strength influence matrix In this step, the total strength influence matrix TP ¼ ½ tp ij mÂn based on IFS is computed utilizing Equation ( 17).
Step 2.3: Obtaining the total impact, total receptivity, and engagement scores Utilizing Equations ( 18)e( 21), the total impact, total receptivity, and total engagement scores are computed, and the relevant results are represented in Table 7.
Step 3: Investigating the contributions of influential factors Step 3.1: Deriving the cause-and-effect relationship diagram Using the Euclid method, the ideal (best), and nadir (worst) solutions have been used to derive the preference point and plot the cause and effect relationship diagram in 2-dimensional space, as depicted in Fig. 7.This dimension of prominence and relation is separated using the notation of Pan and Chen [82].Similar to the DEMATEL technique, the first Zone has a high prominence and relationship in the proposed approach.This means that there are cause contributing factors and basic factors that influence the other factors.The second Zone has a high prominence and low relationship (also called the longterm zone).The third zone has low prominence and high relationship, meaning that this group of contributing factors has a moderate influence and impact on the other factors.Finally, Zone four is called the non-priority Zone and has low prominence and relationship, meaning that it has the challenging task of having direct contributing factors for improvement in the short term.As can be seen from Fig. 7, the indicator OR played a driving factor, following the indicator SR.That is, the hands, ER, and TR belong to the linkage and dependence factors, respectively.In addition, in linkage factors, we have three sub-indicators as, E-OR, G-OR, and D-TR, which are required to be considered differently for developing and implementing any strategic plan over the rest of the sub-indicators.There are also Table 4 e The initial group-based strength influence matrix is based on the first decision-makers opinions.In this step, the Resilience Index (RI) is determined for hydrogen energy infrastructure to evaluate the set of contributing factors.The impact of total contributing factors is examined, and the final decision is made by ranking the contributing factors based on the Euclidean distances from the ideal solutions.Using Equation ( 22), the RI is obtained as 0.1518.In addition, a backward propagation analysis determines the impact of contributing factors, and the results are presented in Table 8.According to backward propagation analysis, ReOR (Regulation and legislation), G-OR (Government preparation), and C-ER (Crisis response budget) are the most critical resilience indicators in the understudy hydrogen energy infrastructure.Thus, it is required to take adequate attention to improve the resilience of hydrogen energy infrastructure over time.

DM.1 RI TR SR ER OR R-TR Re-TR Ro-TR M-TR E-TR S-TR D-TR S-SR P-ER C-ER A-OR F-OR C-OR L-OR G-OR ReOR
In the following sub-section, the Sensitivity Analysis (SA) is carried out to show the effectiveness and robustness s of the methodology.
RF, varying from zero to 1, shows that the value of worst and ideal priority ranking is the same.Therefore, it is concluded that the differences between the ranking concerning them in the present study is negligible.
To the best of the authors' understanding and having support from the state of the arts, it is crystal clear that selecting the proper value of RF is critical to reaching a reliable aggregation of decision-makers thoughts.For an instant, in the study of Yazdi et al. [83], it is discussed that the value of RF can significantly impact the ranking for further intervention actions.Hence, it is essential to take into account the value of RF considering the following aspects: (i) decision-makers can consider the historical data from similar resilience hydrogen infrastructure assessment and reflect them into the assessment process, (ii) obtaining the value of RF can be utilized from spreading a questionnaire as well as some available robust methods.The higher value of RF can be considered if the decision-makers express their opinion with a high level of confidence, and finally (iii) the value of RF can be selected with consideration of real case scenarios, meaning that the RF needs to be allocated a higher value when it is easy to obtain the subjective weight.
The determined SA in this sub-section indicated that the proposed approach does not vary by changing the value of RF.Therefore, it can provide valuable information for decision-

Conclusion
Hydrogen energy infrastructure is essential for a sustainable energy future.However, its deployment is accompanied by potential hazards and safety issues due to its complexity and sensitivity to disruption and changes in functionality parameters.Therefore, it is crucial to assess the resilience of hydrogen infrastructure to ensure safe and reliable operations in the face of sudden changes.This necessitates the identification, assessment, and evaluation of a set of resilience indicators and sustainable contributing factors as a preliminary step in managing malfunctioning hydrogen energy infrastructure.In this study, a reliable and robust decision-making framework based on the WINGS method was proposed to assess the resilience of complex energy infrastructure.The concept of Intuitionistic fuzzy sets was utilized to address subjective uncertainty during the elicitation process.The proposed framework's efficiency, robustness, and effectiveness were confirmed through different comparative analyses.Moreover, the study highlighted that ReOR (Regulation and legislation), G-OR (Government preparation), and C-ER (Crisis response budget) are the most critical resilience indicators in the understudy hydrogen energy infrastructure.This emphasizes the need for adequate attention to improve the resilience of hydrogen energy infrastructure over time.
However, during the study, several challenges were encountered that require further work as a direction for future studies.Firstly, it is worth investigating how the resilience of hydrogen infrastructure varies over time, although resilience is the inherent property of the system.Integrating system dynamic or dynamic Bayesian models can help decision-makers have a practical understanding of resilience behaviour in a dynamic manner.Secondly, decision-makers' confidence level in their opinions needs to be measured and considered in the study.For future research, the framework can be extended to incorporate probability theory, evidence theory, or Z-number to consider decision-makers' confidence levels during the elicitation process.Finally, the proposed approach's applicability can be demonstrated in different domains, considering even further sub-indicators, such as healthcare, transport, project, and asset integrity management.
In conclusion, the proposed decision-making framework provides a robust and reliable method for assessing the resilience of complex energy infrastructure, particularly in the case of hydrogen energy infrastructure.The study's findings emphasize the criticality of ReOR, G-OR, and C-ER as the most crucial resilience indicators in hydrogen infrastructure, and further work is required to investigate the variation of resilience over time and incorporate decision-makers' confidence levels into the framework.The applicability of the proposed approach can also be extended to different domains, including even further sub-indicators.Additionally, it is worth noting that the proposed framework can help decision-makers evaluate the effectiveness of existing resilience strategies and identify potential areas for improvement.This can lead to the development of more targeted and effective resilience policies and investments in infrastructure systems.Moreover, the framework's incorporation of subjective uncertainty through the use of Intuitionistic fuzzy sets makes it a suitable tool for addressing the complexity and ambiguity inherent in decision-making processes related to resilience.The proposed approach can be used by policymakers, regulators, and stakeholders to evaluate the resilience of hydrogen energy infrastructure projects and investments.This can help ensure that the infrastructure is designed, developed, and operated with the necessary resilience capabilities to withstand potential hazards and disruptions.The proposed future directions for research will help refine and improve the

Fig. 1 e
Fig. 1 e Distribution of published papers according to the different domains in the Scopus database by the end of September 2022.

Fig. 2 e
Fig. 2 e The most frequent keywords-plus (UP side) and Thematic Evolution (DOWN side) analysis in the Scopus database by the end of September 2022.
into an Intuitionistic fuzzy set (IFS) through the introduction of a non-membership function v ÃðxÞ indicating the evidence against x2X along with the membership value m ÃðxÞ indicating evidence for x2X and this admits an aspect of indeterminacy.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( x x x x ) x x x

Fig. 6 e
Fig. 6 e The schematic diagram of a hybrid wind-hydrogen power plant.

Fig. 7 e
Fig. 7 e The cause and effect relationship among the contributing factors (the driving and dependence power diagram).

Fig. 8 e
Fig. 8 e The results of SA by varying the RF.

Table 1 e
A causality comparison among different decision-making methods.

Table 2 e
Linguistic (qualitative) terms with their equivalent IFNs.

Table 3 e
The profile quality of a heterogeneous decision-makers group and their importance weights.

Table 6 e
The aggregation process for the influence OR on RI (A simple example).

Table 7 e
The total impact, total receptivity, and total engagement scores.

Table 8 e
The backward propagation analysis and criticality ranking.

Table 9 e
The value ri def þ cj def with consideration of different relaxation factors (varies from zero to1).makers during the resilience assessment of hydrogen energy infrastructure or other critical infrastructures.