A life cycle decision framework of China offshore wind turbines with ANP-Intuitionistic fuzzy TOPSIS method

10 In China, offshore wind energy is a popular source of green energy. The selection of offshore wind 11 turbine design scheme is a decision problem based on multiple criteria. However, the selection is hardly 12 made from the point view of life cycle due to the complex association of evaluation criteria, especially in 13 the conceptual design stage. To solve this problem, a new multi-criteria decision-making framework for 14 selecting the life cycle design scheme of offshore wind turbines is designed. The design information of 15 the life cycle process of offshore wind turbine is expressed using 16 Function-Structure-Material-Process-Transportation (FSMPT) model in this framework; The life cycle 17 evaluation index system of offshore wind turbine was established, and mapped with FSMPT model to 18 carry out rapid evaluation of various schemes; In light of this, an intuitive fuzzy Technique for Order of 19 Preference by Similarity to Ideal Solution (TOPSIS) method based on Analytic Network Process (ANP) 20 was proposed to process fuzzy decision information and establish criteria correlation. The case study 21 showed that the evaluation model, criteria, and methods presented in this work can give theoretical and 22 technical support for decision making and long-term development of offshore wind turbines, as well as 23 improve the sustainability benefits of wind power generation.


INTRODUCTION
Energy consumption is rising daily as a result of the world economy's quick development, and all nations are deeply concerned about the greenhouse gas emissions and environmental damage that the old energy production method causes.Nowadays, the new energy has entered a stage of rapid development, and many researchers are paying more and more attention to wind energy resources.The primary way that wind energy is used is through wind power, compared with other new energy, its cost is low, clean and significant benefits.The global wind power business has been flourishing in recent years, particularly with the quick advancement of offshore wind turbines.Offshore wind turbines have several advantages over onshore wind turbines, including not occupying land, high wind speed, long utilization time and stable wind energy resources.In addition, offshore wind turbines are usually located near the power load center, and wind power is more easily connected to the grid.In the context of low-carbon energy transition, factors such as the reduction of offshore wind power costs and large-scale wind turbines will drive the installed capacity to continue to increase, and offshore wind power will usher in a period of rapid growth.The cumulative installed capacity of offshore wind power reached 3051 million kilowatts by the end of 2022, and the cumulative installed capacity is expected to reach 3470 million kilowatts by 2023, as shown in Figure 1.Nowadays, offshore wind farms have become one of the key directions of the future wind energy industry.
However, due to the complexity of the offshore environment compared to the onshore environment, including high salt spray, lightning strikes, and offshore typhoons, offshore wind turbines are significantly more complex than onshore structures, the technical difficulty and cost of installation, operation and maintenance are high.As a result, there are higher requirements for the selection of offshore wind turbine [1,2].Although offshore wind power generation helps to reduce environmental pollution and greenhouse gas emissions, the manufacturing, transportation and decommissioning produce a lot of greenhouse gas emissions and consume energy [3].Therefore, during the life cycle of offshore wind turbines, the influence on the environment should be considered.In this context, the effective way to solve the above problems is Life Cycle Design (LCD) to integrate green characteristics into the whole process of product life cycle.

Figure 1. Installation of wind turbines in China
According to the existing research on design scheme representation model, evaluation criteria and decision method, three key problems of offshore wind turbines must be solved, namely: Life cycle design representation model considering life cycle information; The evaluation index system of the life cycle stage; The life cycle design decision-making method taking the correlation of evaluation index into consideration.ANP-Intuitionistic fuzzy TOPSIS is used to provide a multi-criteria decision-making framework for the life cycle design of offshore wind turbines to compensate for these shortcomings.
1)The FSMPT model of the life cycle design for offshore wind turbines is proposed.In the conceptual design stage, the product function, structure, material, process, transportation and other information are considered to support the generation and decision of the life cycle design.
2) The multi-attribute green evaluation criteria system of offshore wind turbines is constructed, and the Annual increase of installed capacity Accumulated installed capacity life cycle evaluation criteria system is further established, and the design scheme is quickly evaluated by association with the FSMPT model.
3)A decision-making framework using the ANP-intuitionistic fuzzy TOPSIS for the life cycle design of offshore wind turbines is proposed to efficiently handle ambiguous information and solve the decision problem of the mutual influence of multiple criteria.
The remainder of this work is structured as follows.Section 2 reviews the literature on offshore wind turbines decision-making.Section 3 focuses on the FSMPT conceptual model and the evaluation index system for the offshore wind turbine life cycle design.Section 4 introduces the decision-making framework for the offshore wind turbine life cycle design based on ANP-Intuitionistic fuzzy TOPSIS.
Section 5 provides examples of offshore wind turbines to demonstrate the implementation process and efficacy of this framework.The conclusions are presented in the final section of the paper.

LITERATURE REVIEW
Because of the importance of wind energy, there has been a great deal of research done on it.In the past few years, an increasing number of academics researched the evaluation and decision-making of offshore wind turbines.The conceptual design of products has been supported by a significant number of design schema representation models.Meanwhile, to address the selection and design optimization issues of offshore wind turbines, a variety of evaluation criteria systems and evaluation decision-making methods for offshore wind turbines are proposed.This section includes a survey of the literature on the problems discussed in this work.Studies related to this study can be categorized into three categories: design scheme expression model, evaluation criteria system, and design scheme decision-making method for offshore wind turbines.Comparisons of relevant studies for each group are provided below.
The life cycle design is widely regarded as the most critical stage to achieve product greenness [4].
Conceptual design is a key factor affecting product performance, cost and environment, and the program decisions made at this stage also have an important effect on the environment.Gero and Kannengiesser [5] took the lead in proposing the conceptual design model of Function-Behavior-Structure (FBS), and generated design schemes through the establishment of functional decomposition and association mapping [6].In order to adapt to complex and variable product design requirements, many improvements have been made to FBS model, such as functional decomposition and modeling [7], requirement-function-behavior-structure model [8], function-behavior-state model [9], demand-function-Principle-system model [10], etc.However, most of these models only meet the functional and design requirements of products, and lack the consideration of product environment information.In order to support life cycle design modeling effectively, many scholars have introduced environmental information into FBS models.Deng [11] proposed a function-environment-behavior-structure conceptual design approach for environmental protection.Li et al. [12] used FBS model to establish an energy consumption model, and linked design aspects with energy use in order to take the environmental impact into account.In order to solve environmental problems, especially to reduce resource consumption and waste, Umeda et al. [13] proposed an upgradable product design method based on FBS mode.The above research based on the improved FBS model can support the green design of products, but the life cycle design takes into account the green characteristic of the products' life cycle, and there are problems such as too much design information, wide range and difficult access.The above studies rarely consider material, process, transportation and other information, and cannot effectively generate and express product lifecycle design solutions, which is hard to sustain the life cycle design of offshore wind turbines.
Selection of suitable design scheme for the life cycle of offshore wind turbines can not only boost power generation profits and lower operation and maintenance costs [14], but also help offshore wind turbines perform more sustainably by addressing potential environmental issues at the outset of the design process.
Most studies only take into account the influencing factors when determining the best offshore wind turbine, including technical performance [15], economic performance [16], environmental problems [17], wind resources [18], etc.What's more, the impact on society for those who gain from it must be considered.As a result of this, Abdel-Basset et al. [19] established a site selection evaluation system for offshore wind turbines by comprehensively considering six indicators.Wind resources, construction, economy, environment, society, and risk, as well as related secondary indicators, are all considered.Yu et al. [20] put forward a standard system for evaluating offshore wind turbines, including technical reliability, resources, economy, environmental impact and supplier performance.Offshore wind turbines have a very complex operating environment, which makes maintenance time-consuming and expensive.
Based on the initial criteria, Ma et al. [21] incorporated technology for intelligent monitoring, anti-corrosion, lightning protection, and anti-typhoon.Rotor diameter was one of the selection factors for offshore wind turbines that Wang et al. [22] took into consideration with the ongoing improvement of decision index.However, in the existing evaluation index system of offshore wind turbines, the evaluation index is isolated with each other, which result in the final evaluation results are not comprehensive from a life cycle perspective.
Generally, the choice of offshore wind turbines is thought of a multi-criteria decision methods (MCDM) problem [23], and one of the most commonly used models is Analytic Hierarchy Process (AHP).Huang et al. [24] come up with a decision-making method based on AHP to study the selection of wind turbines by evaluating the effective performance of three representative bidding wind turbines for an offshore Fujian wind farm.Wind turbines incorporate the AHP and other MCDM approaches while making decisions.Through the TOPSIS technique, Lozano-Minguez et al. [25] suggest a method for assessing the selection of support structures for offshore wind turbines in various designs.Bagočius et al. [26] used the AHP method to ascertain criteria weights and used Weighted Aggregates Sum Product Assessment (WASPAS) method to evaluate offshore wind turbines.However, considering the fuzziness and subjectivity of expert judgment, the MCDM method in conjunction with fuzzy set theory are applied.
Using fuzzy Bayesian networks and expert domain knowledge, Xue et al. [27] offer a new offshore wind turbine selection method.Deveci et al. [28] used Interval Rough Numbers (IRN) in conjunction with the Best-Worst Method (BWM) to select the greatest offshore wind farm sites in the Turkish coastal region.
Through the analysis of different MCDM methods, conclusions can be drawn in Table 1.Even though the above decision-making methods is widely used in offshore wind turbines selection, the evaluation criteria are independent of each other and do not consider the correlation between criteria, which reduces the precision of the decision-making results.In particular, the evaluation criteria of offshore wind turbines are numerous and interrelated.

EXPRESSION AND CRITERIA SYSTEM OF THE LIFE CYCLE DESIGN OF OFFSHORE WIND TURBINES FSMPT model for the life cycle design of offshore wind turbines
The conceptual design model of most products only considers the function and product design requirements, and lacks the product life cycle information, which cannot effectively generate and express the product life cycle design scheme.Therefore, based on FBS model [6] and product structure tree, a life cycle design scheme expression model of offshore wind turbines, namely Function-Structure-Material-Process-Transportation (FSMPT) model, was built, as shown in Figure 2.
Through the direct mapping of function to structure, the model is integrated in the interdomain (vertical) and intra-domain (horizontal) to realize the interaction of the five aspects of offshore wind turbine information, so as to provide support for the life cycle design of offshore wind turbines.
In the FSMPT model, F represents function domain, which is generally determined according to user requirements and design requirements; S stands for structure domain: structure is the carrier to realize the function, that is, the design unit, refers to the relationship between various parts of the offshore wind turbine, so as to achieve certain functions; M stands for material domain: the main raw materials used to produce various offshore wind turbine structures, including auxiliary materials, etc.; P stands for process domain: during the production process of offshore wind turbine, depending on the structural characteristics of raw materials and offshore wind turbine, appropriate processing methods have been chosen to process raw materials to obtain the structure required by the offshore wind turbine; T stands for transportation domain: transportation of components and raw materials for offshore wind turbine.

The life cycle process of offshore wind turbines
The life cycle process of offshore wind turbines is divided into five stages: raw material acquisition, production and manufacturing, transportation and installation, operation and maintenance, and disassembly and disposal [35], as shown in Figure 3.Each phase involves a number of processes.Raw material acquisition phase is mainly raw material steel smelting.During the production and manufacturing phase, components of the foundation, tower, engine room, rotor and transmission grid are manufactured in the offshore wind turbine factory [36].The parts will then be transported from the plant to the offshore wind farm and assembled and installed through crane work and other on-site construction work during the transportation and installation phase, including the hoisting method, the type of installation ship, and the transportation organization of materials in the yard.The operation and maintenance phase includes oil and lubricant changes, gear and generator refurbishment, and transportation to and from the wind turbine for regular inspections [36], taking into account the wind farm's capacity, location away from the shore or port, marine climate and hydrological conditions.Finally, in the disassembly and disposal phase, the main processes include the dismantling of the offshore equipment, the transportation from the installation location to the disposal location, and the disposal of materials [37].These five stages describe the entire life cycle of an offshore wind generator from birth to death, with various properties at different stages influencing each other.Trans. Trans.Trans. Trans.

Evaluation criteria system for the life cycle design
A literature survey was conducted to preliminarily determine the criteria to be used in decision studies for offshore wind turbines.Then, by referring to the evaluation criteria system of green mechanical and electrical products of some scholars and following the principle of establishing the evaluation criteria system of green products [38,39], the multi-attribute green evaluation index system of offshore wind turbines is established in accordance with the current research progress on selection of offshore wind turbines and product attributes.There are six main criteria (environment, technology, resources, energy, economic and social attributes) with 25 sub-criteria.
The above attributes cover all stages of the life cycle for offshore wind turbines.Due to the different emphases of each stage, some attributes or sub-criteria of the multi-attribute green evaluation criteria system should be selectively ignored at different stages in practical application.In addition, so as to facilitate the subsequent calculation during the calculation process, the attribute layer will be crossed, the criteria layer will be directly modeled, and the specific sub-criteria value of the criteria layer will be calculated separately [40].Therefore, based on the multi-attribute green evaluation index system of the design decision and life cycle process of offshore wind turbines, the evaluation criteria system of the life cycle phase is constructed.As shown in Figure 4, there are five main criteria, including 33 sub-criteria.Table 2 lists these criteria and their explanations.Some of these wind turbines base indicators combine the product attributes of offshore wind turbines, such as: 1) The transportation and installation phase of offshore wind turbines is considered more over onshore, including transport distance, mode of transport, cable laying, foundation installation and wind turbine installation, 81% of the total cost is due to the installation of towers, nacelles, blades and foundations.
Offshore wind turbines can often be installed entirely at once or in sections.Although there are few hoisting times over the entire hoisting procedure and little time is spent building at sea, the assembly yard must be set up on land.Meanwhile, there are transportation concerns and very high requirements for the dock's loading capacity, the barge's loading capacity, and the lifting and hoisting capability.The hoisting period is lengthy and there are numerous hoisting times during the segmented hoisting procedure.To sum up, the technical complexity and cost of transportation installation need to be considered in the index system.
2) All stages of the life cycle of offshore wind turbines will affect Marine life and birds, resulting in greenhouse gas emissions and resource energy consumption.Indicators such as ecological impact, greenhouse gas emissions and resource energy consumption are thus taken into account in these stages.
3) In addition to rain, snow, fog, wind and other bad weather, onshore wind farms can generally be quickly and timely on-site maintenance.However, due to the changing climate of the offshore environment, the complex situation of the sea wave ditch, the operation environment of offshore wind turbines is harsh, and maintenance personnel can only reach the designated place through the work boat or helicopter to repair or replace the equipment.This adds to the difficulty and high cost of repair and maintenance, which influences the cost of wind power.Therefore, high requirements are put forward for the operation safety and maintenance simplicity in the operation and maintenance phase.4) As offshore wind turbines must withstand strong wind loads at sea, seawater corrosion and wave impact, etc., offshore wind turbines are far more complicated than those on land, with high technical difficulty and high construction costs.For example, how to optimize the design of wind turbine structure so that it can effectively withstand strong wind load fatigue load and unbalanced wind turbine load during the life cycle of the unit?How to optimize the tower structure and mechanical support structure design to meet the requirements of offshore wind turbine load as much as possible to reduce the weight of the whole machine, how to design the wind turbine transmission chain and the layout of the system to improve the reliability and maintainability of the wind turbine, so the manufacturing process and cost in the production and manufacturing phase is very important.Ease of maintenanceS22

System conversion rateS23
Operational safetyS24

Operating costS25
Sales profitS26 (Operation and maintenance phase) Ecological impactS27 Noise and visual impactS28

Recovery of energyS29
Resource recovery rateS30

Recovery technology levelS31
Recovery costS32 Recovery of greenhouse gas emissionsS33 Evaluation criteria system for the life cycle of offshore wind turbines Decision on the life cycle design of offshore wind turbines Energy is consumed in manufacturing, logistics and decommissioning of offshore wind turbines [3].Roughly more than 84 percent of the energy is used to produce wind turbines, with the rest used for transportation, foundation, maintenance and demolition.

Association between FSMPT model and evaluation criteria system
Aiming at the problems such as low integration degree and lack of effective correlation between FSMPT model and life cycle stage, the correlation mapping between FSMPT model and the evaluation criteria system of the offshore wind turbines life cycle is constructed, and the mapping correlation between the criteria of the life cycle phase and the model domain is used to accurately and rapidly evaluate the design scheme of the offshore wind turbines life cycle.
In the FSMPT model, the material domain represents the raw materials needed to produce offshore wind turbines and is associated with the raw material acquisition phase; The function domain represents the wind turbine's functions and is associated with the operation and maintenance phase; The process domain represents the production and processing mode of wind turbine, and is associated with production and (S2 Raw material acquisition, S7 Production and manufacturing, S13 Transportation and installation, S20 Operation and maintenance, S30 Disassembly and disposal phase) Resource consumption Resources mainly refer to machinery and equipment resources, material resources, water resources and human resources [41].

S3Material acquisition technology level
The raw material of offshore wind turbine is mainly steel, and the smelting process of steel is very important.Therefore, the technical level of raw material acquisition should be considered.

S4 Raw material cost
The cost of purchasing and acquiring raw materials for offshore wind turbine components.(S5 Raw material acquisition, S11 Production and manufacturing, S18 Transportation and installation, S33 Disassembly and disposal phase) Greenhouse gas emissions The manufacturing, logistics and decommissioning of offshore wind turbines will generate greenhouse gas emissions [3].The steel in the tower, the engine room and the concrete in the foundation are the main causes of environmental impact.

S8
Manufacturing process complexity Offshore wind turbine to adapt to a variety of materials, a variety of processes, a variety of processes, parameters matching to ensure the production of high-quality wind turbines.

S9 Manufacturing technology level
Including structural reliability, assembly technology level, etc. Specifically refers to the physical strength, safety and dependability of offshore wind turbine systems.

S10 Manufacturing process cost
The process cost of producing and manufacturing the offshore wind turbine parts.S14 The technical complexity of transportation and installation Some measures taken during transportation and installation of offshore wind turbines include cable laying, foundation and installation of wind turbines, etc. [42].

S15 Transportation and installation cost
The cost of installing and purchasing offshore wind turbines [22].

S16 Degree of social need
It is composed of residents' opinions and has an important impact on future development [16]; On the other hand is the dual carbon policy, green environmental protection needs.(S17 Transportation and installation, S27 Operation and maintenance phase) Ecological impact Offshore wind turbines will produce noise pollution during construction and operation, which will have a negative impact on Marine animals.
Influence the flight of birds [17].

S21 Turbine output power
The efficiency of wind turbine capturing wind energy is related to wind speed and rotational speed.S22 Ease of maintenance Maximum generating power, low start-up wind speed, and the rate of conversion of wind energy to electricity are desirable.

S23 System conversion rate
Due to the complexity of the offshore wind farm environment, maintenance time and expense are high in case of failure, so the maintenance simplicity is very important [22].S24 Operational safety Offshore wind farms by the hostile environment have high requirements for wind turbines, and their operation safety deserves high attention [22].S25 Operating cost Labor, maintenance, and energy consumption costs are all included in the total cost of an offshore wind turbine in operation [15].

S26 Sales profit
Annual funds generated by offshore wind turbine [43].

S28 Noise and visual impact
Noise from offshore wind turbine operations causes sleep disorders and hearing loss among residents; The blades interrupt sunlight and produce shadow flickering [17].

S31 Recovery technology level
Offshore wind turbine recovery measures taken when the reinforced concrete foundation is abandoned; Waste iron and steel are raw materials for metal smelting and processing.
manufacturing phase; The structure domain associated disassembly and disposal phase; The transportation domain associates the transportation and installation phase.
The correlation between the FSMPT model and the life cycle evaluation criteria system is shown in Figure 5.The FSMPT model is on the left, while the 5 main criteria of the criteria system are on the right.
The two sides are collectively called the correlation mapping between the FSMPT model and the life cycle evaluation criteria system of the offshore wind turbine.

DECISION-MAKING FRAMEWORK FOR THE LIFE CYCLE DESIGN OF OFFSHORE WIND TURBINES
The Intuitionistic Fuzzy Set (IFS) is Bulgarian scholar Atanassov's extension of Zadeh's classic Fuzzy Set Theory (FST).It also considers three characteristics of membership, non-membership and hesitation [44], and has strong flexibility and applicability in solving fuzzy problems.TOPSIS is a commonly used multiple index decision analysis method.The relative distance between each scheme and the ideal scheme is computed by creating "positive ideal solution" and "negative ideal solution" of assessment issue to rank the pros and cons.Boran et al. introduced intuitive fuzzy TOPSIS.After determining the weights of evaluation criteria, they constructed an intuitive fuzzy evaluation matrix for design schemes, and then used TOPSIS method to evaluate and rank design schemes [45].
Weight determination is the basis of design scheme evaluation.In the evaluation criteria system, there is often a mutual relationship between the criteria, but AHP fails to reflect this internal relationship.To solve the structure of decision problems with dependency and feedback, Professor T. L. Saaty of University of Pittsburgh devised the weight determination method (ANP) [46] based on AHP [47].
The criteria correlation is not considered in the selection process of the life cycle design schemes of offshore wind turbines and the uncertainty information will be generated when the expert decision is made.As a result, this study provides the intuitionistic fuzzy TOPSIS framework based on ANP theory to analyze offshore wind turbine design schemes and assist firms in finding the optimal design scheme.As shown in Figure 6, the proposed framework can be separated into four components: scheme expression, criteria calculation, expert evaluation and result ranking.First, experts select and express alternative life cycle design schemes of offshore wind turbines based on experience and FSMPT model.Secondly, ANP is used to establish criteria relation and calculate its weight.Thirdly, the expert weights are determined and the schemes are scored with intuitionistic fuzzy number according to the correlation between criteria and model.Finally, to rate the design schemes and find the ideal option, TOPSIS is employed.
Investigate the whole life cycle design scheme of offshore wind turbines Step 1: Identify alternative life cycle design schemes of offshore wind turbines.The FSMPT model including material, transportation, process, use and recycling is adopted to express the design schemes.
Step 2: Use ANP to establish the criteria network and determine the criteria weight.There are many factors influencing the selection of design scheme of offshore wind turbines.Different criteria and correlations have different influences on the selection of design scheme.These are the precise steps: 1. Build the network structure.
Assemble the thoughts of various experts, determine the evaluation criteria, ignore the factors that have less impact on the overall, group the factors, form the factor group, and determine the interaction between levels, between and within the factor group.The ANP structure is then built based on the hierarchy in the control layer and the influence relationship between criteria in the network layer, as shown in Figure 7.  Experts are consulted to determine the relative weights of the two evaluation criteria, and values are then assigned using the "1-9 scale method" in Table 3 in order to create the decision matrix.First, the criteria Ps (s = 1, 2, . .., m) selected during network construction, namely other factor group Ci, is considered the primary norm, and the factor ejl (l = 1, 2, …., nj) of a certain factor group Cj in the network is considered the sub-criteria, the judgment matrix is built based on how much each factor in factor group Ci influences factor ejl, or how much factor ejl influences each factor in factor group Ci, and the normalized feature vector is obtained.The consistency test is passed:

Control
Then, factor group Ci is compared with factor group Cj in pairs in order to generate their own judgment matrices, taking each factor in Cj as the sub-norm in turn.To depict the influence relationship between factors in factor groups Ci and Cj, the normalized feature vectors of each judgment matrix are assembled into a matrix called Wij.

Scale Description 1
The i factor is as significant as the j factor.3 The i factor is slightly more significant over the j factor.5 The i factor is obviously significant over the j factor.7 The i factor is strongly significant over j factor.9 The i factor is critically significant over the j factor.2、4、6 、8 Somewhere in between.
Taking N factor groups as the main norm, the internal and external relations among factors of each factor group were compared in turn, and the weighting matrix Ws was obtained.This matrix does not display the priority, and pairs of factor groups need to be compared to make the non-weighted matrix become the weighted matrix.12 4. Create the weight super matrix.
Taking the factor group Cj as the norm, the pair comparison of the factor group is carried out, and the matrix aj is constructed.The normalization is carried out to obtain the normalized eigenvector (a1j, a2j, …, aNj) T .
Then, taking N factor groups as the norm, the normalized feature vectors of each matrix aj are summarized into a weight matrix As to reflect the relationship between factor groups.Finally, the ultimate super matrix W l s is employed to display the correlation between factors.When the limit converges and is unique, the weight of each factor in the matrix is obtained.
When ANP method involves a high number of criteria, calculating the matrix becomes difficult and complicated, which is easy to produce errors.Without the aid of software, it is challenging to apply ANP to resolve real-world decision issues.So, to calculate complex matrices in this study, Super Decision (SD) software is utilized [48].This software, created by Rozann W. Satty and William Adams in accordance with the principles of AHP and ANP, makes it easier to apply the ANP approach practically, which is particularly helpful for solving the MCDM problem.The steps of the software to implement the ANP method are shown in Figure 8.

Establish criteria system
Establish correlation

Form judgment matrix
Form unweighted super matrix Form weighted super matrix Form limit super matrix

Determine criteria weight
According to Figure 3 According to Table 8 Input relative importance of criteria As shown in Figure 9 Figure 8.The calculation steps of ANP method Step 3: Experts and design the importance of the linguistic terminology and assignment.
Ambiguity and uncertainty arise when experts evaluate design proposals based on their own experience and subjective consciousness, and each expert has a different weight.As a result, fuzzy language can be utilized to solve the uncertainty of expert and design scheme evaluation attribute value.The fuzzy language is divided into several levels and the evaluation semantics are obtained by experts on the basis of a comprehensive understanding of the actual situation of offshore wind turbines by referring to the relevant standards.In order to process the data more conveniently and intuitively, we can employ mathematical method to convert the fuzzy language of qualitative index into numbers.This work introduces IFS that quantifies the fuzziness of expert evaluations.
In a finite set X, let M be the IFS [49].The following is the definition of IFS M: Where αM(x): X → [0,1] represents the membership function, βM(x): X → [0,1] represents the non-membership function, 0 ( ) In comparison to traditional FST, IFS adds a third component called as hesitancy.If ηM(x) indicates the degree of uncertainty about whether x belongs to M, ηM(x) can be represented as follows: ( ) 1 ( ) ( ) When ηM(x) is low, x is more certain that it belongs to M. When ηM(x) is large, it is even more uncertain that x belongs to M. When αM(x) = 1 -βM(x), IFS changes to FST.M and N are two IFS in set X, λ is a positive integer, then the formula is [44]: Therefore, the linguistic terms in Table 4 are employed and quantified by intuitive fuzzy numbers (IFNs) to calculate the weight of Decision Makers (DMs).To evaluate alternative design options, the linguistic terms in Table 5 are employed and quantified with intuitive fuzzy numbers.

Table 4. The significance of linguistic terms for DMs Table 5. The significance of linguistic terms of alternative design options
Step 4: Determine expert weights.Step 5: Gather expert opinions to evaluate alternative design proposals.
According to the mapping association between the life cycle criteria and the FSMPT model and Table 5, experts estimate alternative offshore wind turbine life cycle design schemes under different life cycle criteria, and convert these evaluation results into corresponding intuitive fuzzy numbers.
By calculating the weight W of the index and constructing the matrix T, the aggregate weighted intuitionistic fuzzy decision matrix can be generated by using Equation ( 17) and ( 18) for intuitionistic fuzzy multiplication.The weighted matrix is shown below: ' ' 1 Step 7: Get intuitionistic fuzzy ideal solutions.
Suppose that Q1 and Q2 are respectively benefit and cost indicators, U + and U -respectively represent positive and negative intuitionistic fuzzy ideal solutions.Equation (19) determines U + and U -: Step 8: Determine the distance measures.
According to Equation ( 24) and ( 25), the normalized Euclidean distance Ei+ and Eirelated to intuitionistic fuzzy positive and negative ideal solutions for each alternative design scheme are calculated [51]. ( Step 9: Determine the relative proximity.Equation ( 26) is used to define the relative proximity for alternative design scheme Ai in relation to the intuitionistic fuzzy ideal solution: * where0 1 Step 10: Determine the ranking of alternative design options.
According to the calculation results of relative proximity, the alternative design schemes are arranged in descending order, and the life cycle design scheme of green offshore wind turbines is selected.

Case description
The life cycle design schemes of the offshore wind turbine manufactured by China's CRRC Shandong Wind Power Co., Ltd. are evaluated and decided in this study.Table 6 displays the primary technical characteristics of the offshore wind turbine.Among them, FSMPT model of A1 is shown in Figure 9.

Determination of the correlation and weights of criteria
The evaluation index of the life cycle for offshore wind turbines has a complex mutual influence relation.
Four researchers that specialize in offshore wind turbines construct the criteria correlation questionnaire according to the actual situation.
After establishing the correlation of criteria, the particular steps to compute the weight of criteria are below: SD software is used to build the network structure of the life cycle evaluation criteria system for offshore wind turbines.Design schemes evaluation is set as the target layer, criteria as the norm layer, and sub-criteria as factors are added to the network layer, as shown in Figure 10. 4 experts and technicians in the field of offshore wind turbines were invited to discuss the questionnaire to fill in the judgment matrix; After the judgment matrix is substituted into ANP network, the weights of criteria and sub-criteria are obtained.The relevant data and calculation results are presented in Supplementary Table   Determination for the life cycle design scheme of green offshore wind turbine Step 1: Importance and weight of DMs.
The importance of the three experts (DM1, DM2, DM3) were determined by the offshore wind turbine Company, and the linguistic terms and weights of the importance of DMs were obtained according to Table 4 and Equation (14).
Step 2: Establish the aggregate intuitionistic fuzzy decision matrix.
On the basis of Table 5, the scores of DMs on the design schemes are obtained, and these scores are converted into intuitive fuzzy numbers.The relevant data and calculation results are presented in Supplementary Table 5-7.
In order to aggregate the opinions of DMs, the aggregate matrix T is obtained according to Equation ( 16), as shown below:  ( ) Step 3: Establish the aggregate weighted intuitionistic fuzzy decision matrix.
According to Section 5.2.2, the weights of aggregate criteria and sub-criteria (ACS) are below: .
Step 4: Get the intuitionistic fuzzy ideal solution.

  
Step 5: Determine the distance measures.
According to Equation (24) and Equation ( 25), euclidean distance for each alternative design schemes is obtained, as shown in Table 7.
The alternative design schemes were ranked in Table 7 in descending order of relative proximity: A1 >A6> A2>A3>A5>A4, A1 was chosen as the finest life cycle design scheme for offshore wind turbine.

Discussion
The weight results indicate that summing the weights of the sub-criteria will obtain the weight of the index.C1 and C2 have the highest weight, which are 0.2914 and 0.4147 separately.C3 and C4 have the least weight of 0.1099 and 0.0468, separately.The results indicate that when it comes to choosing the life cycle design schemes of offshore wind turbines, the experts pay much attention to the C2 production and manufacturing phase.The environmental impact of this phase accounts for a bigger share of the total life cycle, with over 84% of the energy used for production.This is mainly because the equipment and foundation consume a lot of steel materials, but also need to deal with the complex climate and dangerous operating environment, complex structure and technology, difficult maintenance, higher requirements for this stage; Offshore wind farms are relatively expensive, with material costs typically accounting for about 40 to 50 per cent of total investment.Therefore, it is clearly reasonable to use the C1 raw material acquisition phase to evaluate the competitiveness of wind turbines; When dealing with the discarded wind turbine, the metal in the foundation, blades, engine room and tower barrel can be recycled, and the remaining chemical materials can be landfill.Therefore, the importance of C5 disassembly and disposal phase is obvious; Although the weight of the C3 transportation and installation phase does not dominate this decision, it is still important.Marine fuel is needed for the transportation of wind turbine equipment and building materials, installation and construction of equipment, and transportation of operations and maintenance personnel and consumables; There is a small amount of self-consumption power in the commissioning phase of operation and maintenance of wind turbines, which consumes almost no power in operation and has fewer maintenance times, so C4 operation and maintenance phase has the least impact.TOPSIS means that the best design scheme is closest to the ideal solution, and A1 was chosen as the greenest life cycle design for offshore wind turbines.

Comparison of different methods
We compared the ANP-Intuitionistic fuzzy TOPSIS method with classical intuitionistic fuzzy TOPSIS and AHP-Intuitionistic fuzzy TOPSIS methods and conducted comparative analysis on the outcomes of the same case to confirm the effectiveness and viability of the method proposed in this paper, as shown in Table 8.To visually compare the results of different approaches, Figure 11 shows the ranking of alternative design options for different approaches.It can be seen that Figure 11 shows that the curve trends of the three methods are very similar, A1 is obviously the best choice of the three methods, and the optimal results are the same, which indicates that the proposed method is credible and acceptable.Additionally, the difference between the predictive ranking of the proposed method and AHP-Intuitionistic fuzzy TOPSIS lies in the position of A5, and the difference between the proposed method and Intuitionistic fuzzy TOPSIS lies in the ranking position of A3 and A5.The relationship between criteria will obviously lead to the difference in ranking results.In conclusion, through comparative analysis, we can conclude that the ANP-Intuitionistic fuzzy TOPSIS method does have its advantages in terms of stability and feasibility.Therefore, the evaluation method suggested in this paper can be applied as the core method in the life cycle design scheme selection for offshore wind turbines.

Sensitivity analysis of index association
Sensitivity analysis was carried out to confirm the stability of the ANP-Intuitionistic fuzzy TOPSIS framework.The outcomes of the three scenarios were analyzed in accordance with changes in the associations between criteria, as shown in Table 9 and Figure 12.
Table 9. Ranking of alternative design schemes for 3 scenarios

Figure 12. The results of sensitivity analysis
The purpose of the sensitivity analysis is to determine the stability of the proposed ANP-Intuitionistic fuzzy TOPSIS framework in the decision-making process.A small change in the relationship between criteria has little impact on the ranking of alternative offshore wind turbine life cycle designs.Table 9 and Figure 12 show that A1 has the highest score of the three experiments; Ranking sequence (A1> A6> A2) makes up a large proportion of the 3 scenarios, with only scenario 3 being different from the others.
However, scene 3 and the original scene keep the same bottom state of A4.Therefore, based on the evaluation obtained, the decision process of this paper was correspondingly robust in relation to the index, and in most cases alternative design A1 emerged as the winner.In conclusion, the results suggest that the proposed framework is practicable, effective, and robust.This work proposes a new multi-criteria hybrid decision-making framework for offshore wind turbines.

CONCLUSIONS
Firstly, on the basis of the FBS model and product structure tree theory, the system integrates the product design information such as function, structure, material, process and transportation, and establishes the FSMPT model to realize the life cycle information representation of the design scheme for offshore wind turbines.Then, combined with the peculiarities of the actual offshore wind turbines and the literature research, and referring to the opinions of related industries and experts, the life cycle evaluation criteria system is established.The index system consists of 5 criteria and 33 sub-criteria, which can cover all phases of the wind turbine life cycle.Meanwhile, it can be mapped and correlated with the FSMPT model to quickly evaluate the design scheme.Finally, the ANP-Intuitionistic fuzzy TOPSIS evaluation method is constructed and used in the case study of evaluating and selecting the offshore wind turbines design scheme.The results show that the decision method put forth in this study effectively addresses the issue of reciprocal feedback of the life cycle criteria for offshore wind turbines, fully accounts for evaluation uncertainty, enhances the objectivity and precision of the evaluation outcomes, and can provide a reference for enterprises to design green offshore wind turbines.
There are still many limitations in the follow-up research on the decision of the life cycle design for offshore wind turbines.First, the life cycle evaluation criteria system needs to be further optimized; Second, the weight assigned by experts is static.Further consideration should be given to the volatile environment of offshore wind farms so that the decision criteria are weighted to account for the possibility of future variations.According to the particular circumstance, the weights of the various decision index should be updated and modified.

Figure 4 .
Figure 4. Evaluation criteria system for the life cycle of offshore wind turbinesTable 2. Explanations of the life cycle evaluation criteria system of offshore wind turbines Sub-criteria Explanation (S1 Raw material acquisition, S6 Production and manufacturing, S12 Transportation and installation, S19 Operation and maintenance, S29 Disassembly and disposal phase) energy consumption

Figure 5 .
Figure 5. Association between FSMPT model and evaluation criteria system

Figure 6 .
Figure 6.Flowchart of a multi-criteria decision framework for life cycle design Suppose X = {X1, X2, …, Xq} is a set of indices, Y = {Y1, Y2, …, Yz} is a set of subindices, and A = {A1, A2, …, Ap} is a set of alternative design options.The implementation of ANP-intuitionistic fuzzy TOPSIS method requires the following steps.

Figure 7 .
Figure 7. Network structure of ANP

5 .
matrix As, the non-weighted super matrix Ws can be transformed into the weighted super matrix WObtain the ultimate super matrix.
The experts have different academic backgrounds and individual abilities, which means that each expert's decision can have a different effect on the final result.To this end, offshore wind turbine design companies determine the importance of an expert by considering three factors: (1) relevant experience in wind turbine design schemes; (2) relevant educational background in wind turbine design schemes; (3) the position of the expert.Assuming there are l DMs, Dk = [αk, βk, ηk] can be used to indicate the intuitionistic fuzzy number of kth DM, and the weight of kth DM can be calculated as:

Figure 9 .
Figure 9. Life cycle design of offshore wind turbine A1

Figure 10 .
Figure 10.Build an ANP network Investigate the whole life cycle design scheme of offshore wind turbines Use the FSMPT model to express the design solution Use ANP to construct the relationship between criteria Use ANP to weight the criteria Score the scheme according to the correlation between criteria and model Assign importance to experts and design scheme Weight the experts Create the aggregated intuitionistic fuzzy decision matrix making framework for the life cycle design of offshore wind turbines Result analysis abstract graph

Table 1 . Advantages and disadvantages of MCDM methods References Methods Advantages Disadvantages
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Table 6 . Main technical parameters of offshore wind turbine Decision on the life cycle design of offshore wind turbines
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gmojournal.com selected
six design schemes for offshore wind farms (labeled as A1, A2, A3, A4, A5 and A6).The life cycle design model of FSMPT was established to express six design schemes.The life cycle design scheme of offshore wind turbines is mainly divided into five functions: energy conversion, variable pitch, transmission, yaw and support.Each function contains several sub-functions, structure, materials, process and transportation information.The relevant information is presented in Supplementary Table1-2.

Table 8 . Comparison of the proposed method with other methods Figure
11. Ranking of alternative design options for different approaches