A QFD-Based Quality and Capability Design Method for Transboundary Services

,e “transboundary”, an emerging phenomenon in the Internet service ecosystem, is leading to the flourishing of innovative services. A transboundary service incorporates services, resources, and technologies from multiple domains into its business to create a particular competitive advantage and unique user experiences. It is difficult to comprehensively consider all the constraints frommultiple domains to precisely design the nonfunctional characteristics of transboundary services, such as quality attributes and capability attributes. We propose a two-phase quality design method for transboundary services called value quality deployment-quality capability deployment (VQD-QCD) based on quality function deployment (QFD). Given the restrictions of transboundary services, VQD-QCD translates the value expectations of multiple stakeholders into an optimal configuration for global quality parameters (GQPs), local quality parameters, and capability parameters. Details of VQD are illustrated. Considering the inherent vagueness and uncertainty of relationships between value expectations and GQPs, and among GQPs, fuzzy least absolute regression and fuzzy nonlinear programming methods are incorporated into QFD to identify the quantitative relations between value indicators and GQPs, and among GQPs, and obtain an optimal configuration scheme for GQPs. Usability of the proposed method is validated through a case study on the “DiDi mobile transportation service”, which is a representative transboundary service in China. Compared with the current method, which is inaccurate and inefficient because its translation between value expectations and relevant quality and capability parameters is artificial and subjective, the proposed method integrates fuzzy least absolute regression and fuzzy nonlinear programming methods into QFD, which facilitate transboundary service designers to precisely and efficiently design the quality and capability characteristics of innovative services in the manner of semiautomatisation, which promotes the innovative design of transboundary services.


Introduction
Recently, numerous innovative services have appeared with an emerging phenomenon: the "transboundary" (also called "crossover"), for example, the Didi (https://www.didiglobal. com) service that belongs to the online taxi-hailing service field, Fliggy (https://www.fliggy.com) service that belongs to the online travel service field, and Nongcuntaobao (https:// cun.taobao.com) service that belongs to the online retail service field. is type of transboundary service invents a brand new business model by incorporating services, resources, or technologies from multiple domains into its business to create a particular competitive advantage for itself and unique user experiences for its customers. e essence of a transboundary service is the deep convergence of multiple independent services from different industries, different organisations, and different value chains [1]. e Internet of Services (IoS) [2] and Big Service [3] are two similar terms that have attracted wide attention in recent years. e design of transboundary services requires two phases: functional design and quality/capability design. In terms of functional design, designers incorporate specific design tools and their domain knowledge and personal experiences. For example, using the business process model and notation as the modelling language, designers can accurately delineate the transboundary collaboration process among multiple participants (i.e., stakeholders and customers) of a transboundary service, as shown on the lefthand side of Figure 1. is collaboration process consists of a set of activities, a set of resources, and the bindings between resources and activities.
In terms of quality/capability design, however, the "transboundary" makes it difficult to comprehensively consider all the constraints from multiple domains to precisely design the nonfunctional characteristics of transboundary services, as shown on the right-hand side of Figure 1.
ese nonfunctional characteristics consist of global quality parameters (GQPs) attached to the transboundary service, local quality parameters (LQPs) attached to the activities, and capability parameters (CPs) attached to the resources. erefore, in this paper, we focus on the phase of quality and capability design.
Compared with traditional service design in which design objectives are solely determined by one service provider, the design objectives of a transboundary service originate from the convergence of multiple stakeholders of the service. ese stakeholders are attached to different business domains, have different value expectations, and own different service capabilities. ere might be implicit conflicts or correlations among these nonfunctional perspectives, and the design of a transboundary service has to carefully consider all these perspectives and seek a global trade-off between them so that the stakeholders can collaborate effectively to reach the shared goal of the transboundary service.
In our opinion, the design process of a transboundary service is two-fold: "top-down," that is, transforming value expectations of all stakeholders of the service into a quality/ capability configuration scheme for the service functionalities, activities, and resources of the transboundary service (i.e., only if the service functionalities, activities, and resources reach such levels of quality and capability can the value expectations of all stakeholders be fully achieved); and "bottom-up," that is, if the capabilities that could be actually offered by these stakeholders are too limited to support the achievement of value expectations, the optimal quality/capability configuration scheme cannot be obtained, so an adjustment of the original value expectations has to be made. However, before engaging in an adjustment in a bottom-up manner, there are many complex top-down details that need to be understood, which this paper tries to do. e "top-down" design challenge is how to transform the value expectations of various stakeholders into a configuration scheme of multiple relevant quality/capability parameters accurately and efficiently. However, because there is no appropriate method, current transboundary service designers conduct this transformation artificially, which makes it difficult for designers to obtain an accurate quality/ capability configuration scheme efficiently. erefore, to meet the "top-down" design challenge of a transboundary service, in this paper, we propose a quality and capability design method for transboundary services to help designers to identify the optimal configuration scheme by incorporating quality function deployment (QFD) [4] and elaborate on considerations regarding the complex correlations between value expectations and the available capabilities of multiple stakeholders of a transboundary service.
QFD is a customer-driven product design method. Based on the philosophy of the system engineering theory, it translates customer needs for a product layer by layer into the production requirements and fulfils customer needs in the product design stage. Many early studies [5][6][7][8][9] are incomplete in the sense that they either do not contain all the important elements of QFD or do not handle well most information generated from human beings' perceptions and linguistic assessments that are quite subjective and vague. Chan et al. proposed a systematic approach to quality function deployment with a nine-step model for building the house of quality (HoQ) [10], which is a systematic and operational approach to the QFD process. However, its 1-to-9 scale that could help to unify the various measurements in QFD is not suitable for the optimal quality and capability design of transboundary services, and its nine-step model also cannot fully satisfy the optimal quality and capability design needs of transboundary services.
By incorporating QFD in the requirement development process (RDP) of software systems, QFD can facilitate the design of software systems by transforming user requirements into critical-to-system functions and then into functional requirements [11]. QFD-based RDP proposed for the design of software systems is not suitable for the design of transboundary services, and it also does not handle well most subjective and vague information generated from human beings' perceptions and linguistic assessments. In our previous work, a QFD-based service quality design method (SQFD) was presented, which consecutively transforms user expectations into the quality parameters of the service requirement model (SRM), service behaviour and capability model (SBCM), and service execution model to eliminate the gap between user expectations and service quality that customers perceive [12]. However, SQFD is applied only for the quality design of a service that is offered by a single provider and cannot manage the challenge of the transboundary convergence of multiple existing services offered by different service providers.
In this paper, we propose a two-phase model for the optimal quality and capability design of transboundary services called value quality deployment-quality capability deployment (VQD-QCD). As shown on the right-hand side of Figure 1, in the first phase, VQD transforms the value expectations of multiple stakeholders from different domains into a configuration scheme for GQPs of transboundary services. In the second phase, QCD transforms the configuration scheme for GQPs into a configuration scheme for LQPs and a configuration scheme for CPs. Methods that include fuzzy least absolute regression (FLAR) [13] and fuzzy nonlinear programming [14] are incorporated in the HoQ of classical QFD so that the optimal configuration schemes for GQPs, LQPs, and CPs are generated in the topdown manner. VQD-QCD can facilitate transboundary service designers to precisely design quality/capability characteristics of innovative services. It will become a popular design method for innovative services because it provides effective means for service innovation.
e main contributions of this paper are summarised as follows: (1) We present VQD-QCD for the nonfunctional design of transboundary services by elaborating on the considerations of value expectation conflicts, quality attribute correlations, and constraints of the actual service capabilities of different service providers from different business domains. (2) We apply a two-phase design process in VQD-QCD to seek the trade-off between high-level value expectations and real-world service capabilities. e optimal configuration scheme for GQPs, LQPs, and CPs is obtained in the top-down manner.
(3) Considering the inherent vagueness and uncertainty of relationships among value indicators (VIs) and GQPs of transboundary services, we incorporate FLAR and fuzzy nonlinear programming methods into VQD to identify quantitative relations between VIs and GQPs and the correlations among GQPs. e remainder of this paper is organised as follows: In Section 2, we present the two-phase model VQD-QCD. In Section 3, we explain the detailed design process of VQD. In Section 4, we demonstrate the use of the FLAR method to identify the quantitative relations between VIs and GQPs and the correlations among GQPs. In Section 5, we explain the use of fuzzy nonlinear programming model for the optimised design of the configuration scheme for GQPs. In Section 6, we present a case study on the "DiDi transportation service (which is referred to as DiDi hereafter) to validate the usability of the proposed method. In the final section, we present the conclusion and future work.

Overview of VQD-QCD
In Table 1, we compare our proposed VQD-QCD and QFD [10], QFD-based RDP [11], and SQFD [12]. In terms of the design targets, QFD is proposed for the design of products and QFD-based RDP is proposed for the design of manufacturing information systems, whereas SQFD and VQD-QCD are for the design of services. In terms of the core method, all the methods are based on the HoQ. In terms of handling subjective and vague information generated from human beings' perceptions and linguistic assessments, symmetric triangular fuzzy numbers (STFNs) are used to capture the vagueness in QFD and FLAR is used to capture the vagueness in VQD-QCD, but the related methods are not explained in detail for QFD-based RDP and SQFD. Additionally, SQFD is applied only for the quality design of a service that is offered by a single provider and cannot handle well the value expectation conflicts, quality attribute correlations, and constraints of the actual service capabilities of different service providers from different business domains. In conclusion, our VQD-QCD is focused on transboundary services that have multiple stakeholders from multiple domains, and the other three methods cannot manage the challenges posed by the "transboundary". e two-phase framework of VQD-QCD is shown in Figure 2. e VQD phase supports the design between value expectations of multiple stakeholders and the GQPs of service functions, and the QCD phase supports the design between the GQPs and LQPs of fine-grained service activities and CPs of service resources. VQD-QCD is the topdown generative design of a quality/capability configuration scheme. e input of VQD-QCD includes the following: (1) the functional design of a transboundary service, including a business process that consists of a set of activities, a set of resources with specific capabilities, and the bindings between resources and activities; (2) value expectations of multiple stakeholders who participate in the transboundary service by offering specific resources and are responsible for executing specific activities, including a set of VIs and constraints on them; and (3) the available quality levels of activities and capability of available resources that each stakeholder can offer to the transboundary service. e output of VQD-QCD includes the following: (1) configuration scheme for GQPs and (2) configuration scheme for LQPs and CPs.
In the VQD phase, the value expectations on VIs are the input on the left-hand side of the HoQ, and the importance rating of each VI is calculated. At the centre of the HoQ, quantitative relations between the VIs and GQPs of service functions are identified, and how and to what degree the realisation of each VI is affected by GQPs. e importance Mathematical Problems in Engineering ratings of the GQPs are calculated and listed in the penultimate row of the HoQ, and the value range of each GQP is calculated using an optimisation algorithm and listed at the bottom of the HoQ as the output of VQD, that is, the configuration scheme for GQPs. is is the top-down generative design of the GQP configuration scheme.
QCD is similar to VQD, but the objective is to design the configuration scheme for LQPs and CPs. First, the configuration scheme and importance ratings of GQPs, which are exactly the output of VQD, are used as the input on the left-hand side of the HoQ. Second, the quantitative relations between the "GQPs of service functions" and "LQPs of activities and CPs of resources" are identified and filled in at the centre of the HoQ. Next, the importance ratings of LQPs/ CPs are calculated, and then the configuration scheme for LQPs/CPs is obtained as the output of QCD using an optimisation algorithm. e top-down design stages are conducted until reasonable configuration schemes (for all GQPs, LQPs, and CPs) that are restricted by both value expectations and  available real-world quality/capabilities are obtained. We use DiDi as a transboundary service example to illustrate the design process mentioned above. In DiDi, there are many participants, such as the DiDi app provider, map service provider, taxi drivers, and individual travellers. Each participant has its own value expectations on VIs such as "Market Share," "Daily Order Volume," "Average Daily Income", and "Favourable Rate." For example, the app provider proposes the value expectation "Market Share is larger than or equal to 70%," the community of taxi drivers has the value expectation "Average Daily Income of Drivers is larger than 300 RMB Yuan," and the community of travellers has the value expectation "Favourable Rate is larger than or equal to 50%." By applying VQD-QCD to DiDi, such value expectations are transformed into the configuration scheme for quality/capabilities of fine-grained processes, activities, and resources in DiDi. Examples of GQPs include "Maximum Waiting Time during the Peak Period," "Drivers' Service Attitude," and "Security Guarantee Level," and examples of LQPs/CPs include "Number of Called Taxis," "Radius of Coverage," and "Longest Grab Time for Taxi Drivers." As mentioned in the previous section, the greatest challenge in the quality/capability design of transboundary services is the complex conflicts/correlations among value expectations, GQPs, LQPs, and CPs. In DiDi, such scenarios exist extensively. For example, the GQP "Maximum Waiting Time during Peak Period" has a quantitative relation with multiple LQPs, "Number of Called Taxis," "Radius of Coverage," and "Longest Grab Time for Taxi Drivers" and the realisation of the GQP depends on a reasonable configuration of these LQPs. In our VQD-QCD, a set of mathematical methods are used for this purpose.
Because of the limited space in this paper, we cannot introduce all the details of VQD-QCD. In the following sections, we use VQD as an example to demonstrate our idea about the quality design of transboundary services. e philosophy of QCD is quite similar to that of VQD, and readers who are interested in it may refer to our other papers. Note that most existing papers on QFD research also focus mainly on the first phase [5,8].

VQD: Design Method for the Optimal GQPs of Transboundary Services
3.1. Extension of QFD: VQD. As mentioned above, QFD is used to decompose the user demands to match the production requirements layer by layer. We propose an evolved method based on QFD called VQD to translate value expectations of multiple stakeholders into an optimal configuration scheme for GQPs for transboundary services. Before presenting the details of the VQD process, in this section, we explain the approach used to extend QFD to VQD: (1) Because of the differences between product design and the design of transboundary services, it is necessary to enhance the semantic expressive ability of QFD, for example, how to describe the value expectations and how to describe the constraints on GQPs. By contrast, the analysis methods of QFD must be extended according to the scenario of transboundary service design. For example, it must be able to calculate the competitive priority ratings of VIs based on competitive analysis rather than only the computation of competitive priority ratings of customer demand based on customer competitiveness analysis. (2) QFD uses 1-to-9 scale to characterise the satisfaction degree of customer demands supported by different product design attributes [6,9]. However, when designing a transboundary service, because of the restrictions of transboundary service capabilities, sometimes it is difficult to obtain a reasonable configuration scheme once; multiple stakeholders need to remake value propositions. us, it is necessary to establish quantitative relations between VIs and GQPs, which can greatly ease the transformation from a value expectation of each VI into the optimal configuration scheme for GQPs. In the intervening time, a set of functions, which can characterise the quantitative relations in VQD, is also required. Figure 3 shows the VQD-based design process of GQPs, which is used to generate the configuration scheme for GQPs. Considering the difference and relation between product design and the design of transboundary services, the current nine-step HoQ model [10] in the product design domain is extended to a 10-step HoQ model. Its steps are described in detail as follows:

VQD-Based Design Process of GQPs.
Step 1. Identify stakeholders and their value expectations First, the designers must determine the stakeholders that correspond to the VIs of the transboundary service concerned and then gather their value expectations through focus group and individual interviews [6]. e VIs identified are denoted as VI � {vi 1 , vi 2 , . . . , vi M }. e stakeholders make value propositions according to these M VIs, which propose a set of value . e former is used to describe continuous VIs, whereas the latter is used for discrete VIs. OperatorS could be, for example, ">," "<," or "≤." For example, when designing DiDi, if value expectation vp 1 of VI vi 1 "Market Share" is "larger than 70%", then the vp 1 collected can be denoted as vp 1 � (vi 1 , 70%, >).
, the multiple operands in the set vi i _EV 1 , vi i _EV 2 , . . . , vi i _EV k } are in ascending order, and operatorD may be, for example, "∈ up " or "∈ down ". For vp i � (vi i , vi i _EV h , . . . , vi i _EV k , ∈ up ), where 1 < h ≤ k, "∈ up " means that the vi i 's value belongs to the set vi i _EV h , . . . , vi i _EV k and it should be larger than

Mathematical Problems in Engineering
means that the vi i 's value belongs to the set vi i _EV 1 , . . . , vi i _EV j and it should be smaller than or equal to vi i _EV j . For example, if value expectation vp 2 of VI vi 2 "Customer Satisfaction" is "larger than or equal to 4 stars," then the vp 2 collected can be denoted as vp 2 � (vi 2 , 4 stars, Step 2. Determine the relative importance ratings of VIs e relative importance of the VIs is typically expressed as a set of ratings that can be determined by the stakeholders using their perceptions of the relative importance of these indicators, whereas the stakeholders' perceptions can be obtained by applying a fuzzy analytic hierarchy process (FAHP) [15], which starts from an individual interview or mail survey. en, the relevant fuzzy complementary judgment matrix and fuzzy consistent judgment matrix are established in turn. Finally, the relative importance ratings of the VIs are computed by normalising the rank aggregation method [16] and are described as Mdimensional vector VIW � (vi_w 1 , vi_w 2 , . . . , vi_w M ).
Step 3. Determine the final importance ratings based on competitive analysis To improve the competitiveness of the transboundary service operator (TSO 1 ) after investigating the relevant markets, it is necessary to consider the competitors' impact on vector VIW. Hence, first, it is essential for TSO 1 to identify the competitors who provide a similar service. Assume that L − 1 competitors are identified in the relevant markets, denoted as TSO 2 , . . ., TSO L . en, it is necessary to collect the stakeholders' perceptions of the relative performance of these L operators' services of a similar type in terms of the M VIs.
us, the operators' performance ratings on the M VIs can be obtained and denoted as a comparison matrix X � (x ml ) M×L , where x ml is the performance rating of operator TSO l on VI VI m .
Based on matrix X, the competitive priority ratings on the M VIs for operator TSO 1 can be obtained using the entropy method [17] and denoted as e � (e 1 , e 2 , . . ., e M ), where e m represents operator TSO 1 's priority rating on VI VI m . According to e, the performance goals of the M VIs could be set competitively and realistically by operator TSO 1 and denoted as a � (a 1 , a 2 , . . ., a M ). us, operator TSO 1 's improvement ratio for VI m is u m � a m /x m1 . It is obvious that the more ratio u m improves, the more operator TSO 1 should work on VI VI m and the more important VI m for operator TSO 1 .
us, the final importance ratings of the M VIs for operator TSO 1 are determined jointly by the relative importance, competitive priority, and improvement ratio. Additionally, they can be denoted Step 4. Generate GQPs e generation of GQPs actually involves solving the problem of which GQPs of transboundary services need to be sufficiently implemented to meet the stakeholders' value expectations. us, it should first analyse the existing data of the traditional services in the same domain as the transboundary service and determine which quality parameters in the traditional services may affect the realisation of VIs. en, through market investigation, it should identify more quality Step 3 Determine final importance ratings (VIW′) based on competitive analysis: Step 6 Determine correlation matrix (CM)N×N Step 5 Identify constraints on GQPs (CTQ): Step 4 Generate global quality parameters (GQPs): Step 8 Determine initial ratings of GQPs (QW): q_w1 q_w2 q_wN Step 9 Determine final ratings of GQPs (QW′) based on competitive analysis : Step 10 Generate configuration scheme of GQPs (CS): where: = the transboundary service operator = the competitor related to TSO 1 (l = 2, …, L) = competitive priority rating = performance goal = improvement ratio = a m/xm1 parameters that can be used to solve a series of pain points of traditional services in an innovative manner, which aims at achieving the "attack from higher dimensions" and ultimately generating the entire set of GQPs. During GQP generation, the brainstorming method is first used to realise the primary selection of GQPs based on the above analysis. Second, it needs to identify three relations that may exist between GQPs, that is, inclusion relationship, cross relationship, and independent relationship, and remove redundant GQPs. Furthermore, from the perspective of correlation, it is necessary to qualitatively identify another four relations that may exist, that is, positive correlation, negative correlation, mutual exclusion, and uncorrelation, and eliminate mutual exclusion. us far, a set of GQPs that affects the implementation of the VI has been generated and denoted as GQP � (q 1 , q 2 , . . ., q N ).
Step 5. Identify constraints on GQPs When identifying the constraints on GQPs, the designers have to consider the value constraints of GQPs themselves, which can be identified by analysing the existing data (i.e., the available quality of activities and capability of resources that the stakeholders can offer in the real world). For the continuous quality parameter, there are q j ∈ GQP and cq j � [q j _LP, q j _UP], where q j _LP represents the lower bound of the constraint on the q j and q j _UP represents the upper bound of the q j 's constraint; for discrete quality parameters, there are q j ∈ GQP and cq j � {q j _LP, . . ., q j _V j , . . ., q j _UP}.
By contrast, the designers also have to consider the constraints of the relationships between GQPs. In Step 5, the designers only need to consider the qualitative relational constraints caused by domain knowledge, policies, and business regulations, whereas the quantitative constraints of the relationships between GQPs are identified in Step 6. For qualitative constraints, the designers need to identify the necessary relationships between GQPs. For example, when improving DiDi, the quality parameter "Security Guarantee Level" is a necessary condition that relates to the other quality parameters.
Step 6. Determine the correlation matrix among GQPs e optimal configuration scheme for GQPs is affected not only by the constraints obtained in Step 5 but also by the value of the relevant GQPs. ere is a correlation among GQPs, which can be expressed as the correlation matrix.
rough the FLAR method, we use the collected data combined with expert knowledge to obtain the correlation matrix among GQPs. More details are provided in Section 4.
Step 7. Determine the quantitative relations between VIs and GQPs For each VI VI m , the designers need to determine the value range of the quality parameters related to VI m and the VI m 's own value range according to the actual scenario. ey also need to determine the degree of VI VI m that would be implemented according to different values of quality parameters. erefore, through the FLAR method, we determine the quantitative relations between VIs and GQPs by collecting data and expert knowledge. e same method is used in Steps 6 and 7, and more details are provided in Section 4.
Step 8. Determine the initial ratings of GQPs e initial ratings of GQPs are determined by two factors, the final importance ratings of VIs and the quantitative relations between VIs and GQPs, so the input of Step 8 is the output of Steps 3 and 7. In Step 7, we obtain the quantitative relations between VIs and GQPs. In the expressions of the quantitative relations, there exist the influence coefficient vectors of quality parameters on VIs, and the influence coefficient vectors reflect the strength of correlations between quality parameters and VIs. e greater the influence coefficient, the greater the influence of the corresponding quality parameter change on the VI. e initial ratings of GQPs indicate the basic importance of the GQPs designed in relation to the VIs. After the normalisation of the influence coefficient vector, the initial ratings of GQPs can be obtained by combining the output of Step 3 and the normalised results. ey can be computed as the simple weighted average over their relationships with the VIs: Step 9. Determine the final ratings of GQPs based on competitive analysis Step 9 can also be performed by investigating the relevant markets. Although some quality parameters of the competitors' service cannot be easily obtained, careful quality assessments should still be conducted to provide reliable ratings that represent the quality performance of the competitors' service in terms of the N GQPs. us, the operators' performance ratings for the N GQPs can be obtained and denoted as a comparison matrix Y � (y ml ) N×L , where y nl is the quality performance rating of operator TSO l on GQP q n .
Based on matrix Y, the competitive priority ratings on the N GQPs for operator TSO 1 can be obtained using the entropy method [17] and denoted by z � (z 1 , z 2 , . . ., z N ), where z n represents operator TSO 1 's quality competitive priority with respect to the competitors' quality performance ratings. According to z, the performance goals of the N GQPs could also be set by operator TSO 1

and denoted by
us, operator TSO 1 's improvement ratios for q n is v n � b n /y n1 (b n is a positive quality parameter) and y n1 / b n (b n is a negative quality parameter). us, the final ratings of the N GQPs for operator TSO 1 are determined jointly by the initial ratings, competitive priority, and improvement ratio. Additionally, they can be denoted by QW′ � (q_w 1 ′ , q_w 2 ′ , . . . , q_w N ′ ), where q_w n ′ � v n × q_w n × z n .
Step 10. Generate the configuration scheme for GQPs e input of step 10 is the output of Steps 1, 3, 5, 6, and 7. Based on these inputs, a method for generating a Mathematical Problems in Engineering 7 configuration scheme for GQPs is proposed. In this method, the constrained target optimisation model (i.e., fuzzy nonlinear programming model) is established to solve the problem of generating the configuration scheme. en, the concept of confidence is used to transform the fuzzy linear programming model into two linear programming models. Next, the two linear programming models are solved easily. Finally, the optimal configuration scheme for GQPs is obtained. e details of Step 10 are provided in Section 5.

Method for Determining the Correlation Matrix and the Quantitative Relations between VIs and GQPs
When determining function f i specifically, it is necessary to analyse which characteristics of GQPs are related to the realisation of VIs: (1)  rough the above analysis, we find that if we want to determine function f i , we should first describe the influence of the value of a single quality parameter on the realisation of a single VI when other relevant quality parameters remain unchanged. Specifically, this involves determining the quantitative relations between a single VI vi i and each quality parameter q j , which can be expressed as a set of one-to-one influence degree relation functions G � {g i1 , g i2 , . . . , g in }, where vi i _d � g ij (q j ) and variable vi i _d is the influence degree of the quality parameter q j 's change on VI vi i . e purpose of function g ij is to convert the values of quality parameters of different dimensions into the unified values of influence degree vi i _d, which facilitates the determination of weight relation function f i in the next step. A set of typical influence degree relation functions are given as follows: Table 2 presents the basic types of one-to-one quantitative relation between quality parameter q j and influence degree vi i _d from multiple angles (e.g., linear and nonlinear angles and positive and negative angles). Additionally, the more complex quantitative relation between both q j and vi i _d can be obtained by combining the basic types of relationships. For example, when quality parameter q j "Quantity of Available Taxis" of DiDi is significantly lower than the average level of competitors in the relevant market, the relationship between q j and influence degree vi i _d related to the VI "Market Share" is consistent with Type 1. When the value of q j is close to or even far exceeds the average level of competitors, the relationship between q j and vi i _d is consistent with Type 2. erefore, the relationship between both of them is an S-type quantitative relation as a whole.
Type 1: It is an increasing function whose derivative increases gradually. e degree of influence on the VI increases with the improvement of the quality parameter, and the rate of increase accelerates. Type 2: It is an increasing function whose derivative decreases gradually. e degree of influence on the VI increases with the improvement of the quality parameter, and the rate of increase decelerates.
Type 3: It is a decreasing function whose derivative increases gradually. e degree of influence on the VI decreases with the improvement of the quality parameter, and the rate of decrease decelerates.
Type 4: It is a decreasing function whose derivative decreases gradually. e degree of influence on the VI decreases with the improvement of the quality parameter, and the rate of decrease accelerates.
For the above four types, b > 0, and the greater the value of b, the greater the curvature of the function.
Type 5: It is an increasing function whose derivative is constant. e degree of influence on the VI increases with the improvement of the quality parameter, and the rate of increase is constant, where k > 0. Type 6: It is a decreasing function whose derivative is constant. e degree of influence on the VI decreases with the improvement of the quality parameter, and the rate of reduction is constant, where k > 0.
Next, because different correlations among GQPs have different influence degrees on the realisation of VIs, to generate an appropriate configuration scheme for GQPs, a set of correlation functions needs to be described as H � {h 1 , h 2 , . . ., h n }, where q j � h j (q 1 , q 2 , . . ., q j− 1 , q j+1 , . . ., q n ). is is similar to the idea of determining weight relationship function f i when determining the correlation function h j . It is also necessary to first determine the one-to-one influence degree relation function of a pair of GQPs using correlation. It should be noted that the type of influence degree relation function related to function h j is the same as the type of function in Table 2, but the meanings of the independent variable and dependent variables of the function are different.
Specifically, the influence degree relation function related to function h j can be expressed as G � {g j1 , g j2 , . . . , g j− 1 , g j+1 , . . . , g jn }, where q j _d � g jk (q k ), which means that q j has a correlation with q k , q k is the independent variable of function g jk , and q j _d is the dependent variable, and the influence degree of q k 's change on quality parameter q j . e purpose of function g jk is the same as that of the above function g ij .
Given the above, the realisation of the VIs is the result of the comprehensive influence of all the changes of the relevant quality parameters. Now, function g ij and function g jk have been determined, that is, the influence degree of quality 8 Mathematical Problems in Engineering parameter q j 's change on VI vi i can be identified and the influence degree of q k 's change on quality parameter q j can also be identified. en, the weight relation function and correlation function can be constructed.

Method for Constructing the Weight Relation Function and Correlation Function.
Machine learning paradigms (e.g., decision tree, hidden Markov model, and regression analysis) perform extremely well in identifying the relationships between multiple variables [18]. Considering the inherent vagueness and uncertainty of relationships between VIs related to value expectations and GQPs, in addition to those among GQPs [10,19], we adopt the fuzzy regression method to determine weight relation function f i and correlation function h j . Choi and Buckley [20] indicated that, in general regression models, the least absolute deviation estimation is more effective than the least squares method. In regression analysis, least squares estimation is mostly used. Least squares estimation performs poorly when the data contain  1 qmin qmax Value of quality parameter Influence degree on VI some outliers, whereas least absolute deviation estimation is more effective than least squares estimation in linear and nonlinear regression. erefore, for the estimation of the fuzzy regression coefficient, we believe that the minimum absolute deviation estimation using one norm is better than least squares estimation using two norms; Zeng's experiment [13] on FLAR also proved this conclusion. erefore, we use FLAR to determine weight relation function f i and correlation function h j .

FLAR and Sample Set Collection.
e FLAR model can define the absolute distance between fuzzy numbers so that the fuzzy regression problem can be transformed into the problem of minimising the fuzzy distance. Using FLAR, the problem in this section can be transformed into the problem of minimising the error between the observed value of the corresponding variable and its estimated value, thereby making the quantitative relation obtained as close as possible to the actual scenario. e input of FLAR is l sets of reliable and practical data: (X 1 , y * 1 ), (X 1 , y * 2 ), . . . , (X r , y * r ), . . . , (X l , y * l ), where X r � (x 1r , x 2r , x 3r , . . . , x nr ) and y * r � (y c r , y s r ), r � 1, 2, 3, . . ., l. Additionally, its output is the fuzzy regression coefficient μ * � (μ * 0 , μ * 1 , μ * 2 , . . . , μ * n ) of the regression equation of y with respect to X. In FLAR, the distance between symmetrical triangular fuzzy members A � (c 1 , s 1 ) and B � (c 2 , s 2 ) can be expressed as d � |c 1 − c 2 | + |s 1 − s 2 |. e problem is converted to minimising the sum of errors between y * r and the estimated value of the corresponding variable and can be denoted as For equation (1), we can make the following transformation: where α c r , β c r , α S r , and B s r are nonnegative real numbers. us, the original problem is transformed into solving the linear programming model: When collecting the sample set, it is first necessary to derive L sets of values of N GQPs in line with actual conditions through communication with transboundary service designers and domain experts. e designers and domain experts should have a very good understanding of transboundary services and can provide L sample sets according to their accumulated rich personal experience and domain knowledge. e values of N GQPs are denoted as Q r � (q 1r , q 2r , q 3r , . . . , q ir , . . . , q nr ), where r � 1, 2, . . ., L and q ir represents the observed value of the ith GQP in the rth sample set and is accurate data. en, it is necessary to derive the observed values of M VIs for each Q r , which is denoted as pvi * ir � (pvi c ir , pvi s ir ),

FLAR-Based Method for Constructing Functions f i and h j .
e FLAR model is applied to construct weight relation function f i , and the formulas of function f i are given as follows: In equation (4), q 1 , q 2 , . . ., q n represent the input vector, where q j represents the crisp input value of the jth GQPs; q 1 , q 2 , q 3 , . . ., q j 0 represent continuous GQPs and q j 0 +1 , q j 0 +2 , . . . , q n represent the discrete GQPs; vi * i represents the fuzzy output value of the ith VI; and μ * i � (μ * i0 , μ * i1 , μ * i2 , . . . , μ * in ) is the fuzzy coefficient vector that needs to be determined when constructing function f i . In this paper, the construction problem of function fi is transformed into the following: input l sets of data (Q 1 , pvi * i1 ), (Q 2 , pvi * i2 ), . . . . , (Q l , pvi * il )} and then determine the fuzzy coefficient vector (μ * i0 , μ * i1 , μ * i2 , . . . , μ * in ) so that output value vi * i of VI calculated by equation (4) has the best fitting influence on declared value pvi * i of the VI. Let Q r � (q 1r , q 2r , . . ., q nr ) denote the accurate input vector of the rth group and vi * ir represent the fuzzy output of VI calculated by equation (4)  e objective function and constraints for solving the problem of constructing weight relationship function f i are given as follows: To facilitate the calculation, the mathematical model is transformed into the following linear programming model: e above linear programming model can be solved using a MATLAB program, and then the fuzzy coefficient set can be obtained, that is, the construction of the weight relation function f i is complete. e construction method of correlation function h j is similar to that explained above, and its expression is as follows: where (q 1 , q 2 , . . . , q j− 1 , q j+1 , . . . , q n ) represents the input vector, q * j represents the fuzzy output of the jth quality parameter, and α * j � (α * j0 , α * j1 , α * j2 , . . . , α * j,j− 1 , α * j,j+1 , . . . , α * jn ) is the fuzzy coefficient vector that needs to be determined when constructing the function h j . Fuzzy coefficient α * jk is a symmetric triangular fuzzy number, which can be expressed as α * jk � (α c jk , α s jk ). en, the mathematical model for solving the construction of correlation function h j is as follows: α c jk g jk q kr + α c jo ⎛ ⎝ + n k�1&k≠j α s jk g jk q kr + α s jo ⎞ ⎠ , where q jr represents the actual crisp value of the jth quality parameter when inputting the rth vector and q * jr represents the fuzzy output value that corresponds to the input vector of the rth group. Similar to the process of solving function f i , the mathematical model is first converted into a linear programming model, and then a MATLAB program is used to solve it. us, fuzzy coefficient set α * j � (α * j0 , α * j1 , α * j2 , . . . , α * j,j− 1 , α * j,j+1 , . . . , α * jn ) can be obtained, that is, the construction of correlation function h j is complete.

Constraints for Generating the Configuration Scheme.
When generating the configuration scheme for GQPs according to the quantitative relations between the VIs and the GQPs obtained in Section 4, three aspects of constraints should be considered: (1) the value expectations should be met, (2) the correlation among GQPs should be considered, and (3) the value constraints of GQPs should be satisfied. erefore, the constraints of the mathematical model for generating the configuration scheme are given as follows: (1) Cons 1. Constraints related to the value expectations: where it is assumed that 0 ≤ i 0 ≤ m; when i ≤ i 0 , op-eratorS of vp i is ">" or "≥" and when i ≥ i 0 , operatorS of vp i is "<" or "≤." (2) Cons 2. Constraints related to the correlation among GQPs: α * jk g jk q j + α * j0 , j � 1, 2, . . . , n.
(3) Cons 3. Constraints related to the value ranges of GQPs: q j ∈ tq j _LP, tq j _UP , j � 1, 2, 3, . . . , j 0 , q j ∈ tq j LP, . . . , tq j _V j , . . . , tq j _UP , e above constraints determine the feasible region of GQPs. It can be seen that there are fuzzy numbers in equations (9) and (10). When solving the mathematical model to generate the configuration scheme for GQPs, to improve the solution efficiency, it is necessary to convert these fuzzy numbers into crisp numbers.
First, it is necessary to introduce confidence λ to convert fuzzy numbers into interval numbers in equation (9). For fuzzy number A � (a c , a s ), the confidence interval with confidence λ is expressed as the following formula:

Mathematical Problems in Engineering
where A is called the lower bound of the confidence interval and A is called the upper bound of the confidence interval. For Cons 1, when the operatorS is ">" or "≥," μ * ij � μ * ij ; and when operator S is "<" or "≤," μ * ij � μ * ij . us, equation (9) is converted into the following form: Provided the configuration scheme for GQPs can satisfy the constraints of equation (13), it can satisfy those of equation (9) because equation (13) is a special case of equation (9).
For Cons 2, because it represents the equality constraints with fuzzy numbers, taking the time complexity and solution accuracy of the method for generating the configuration scheme for GQPs into account comprehensively, it could just retain centre point value α c jk of fuzzy number α * jk . is is because when the fuzzy nonlinear programming problem contains n (more than one) equality constraints with fuzzy numbers, a large number of programming models need to be considered, but the final improvement in accuracy is limited. Considering the practical application scenarios in this paper, it is more important to improve the speed of solving the mathematical model on the premise that the solution can achieve a particular accuracy. us, equation (10) is converted into the following form: α c jk g jk q j + α c j0 , j � 1, 2, . . . , n.
Equation (14) is a special case of equation (10). Equations (11), (13), and (14) determine the final feasible region of GQPs, in which, regardless of what the fuzzy numbers are in the fuzzy intervals, the configuration scheme for GQPs can meet the value expectations.

Method for Generating the Configuration Scheme.
Quality and capability design for transboundary services is an optimisation problem. Similar to the traditional service composition optimisation problem [21], the design of the objective function [22] has a great influence on the result of the optimisation problem. Because the final feasible region is too large to provide guiding suggestions with reference value for designers, it is necessary to determine the detailed configuration scheme for GQPs. "Input Cost" is one key VI when designing transboundary services, and it is also the VI that most concerns all participants.
us, a method is provided to generate the optimisation configuration scheme for GQPs under the conditions of maximum cost and minimum cost in the feasible region. is can represent two extreme scenarios: one is inputting the highest cost to pursue the best fulfilment of the value expectations of the participants for transboundary services, and the other is pursuing the minimum input cost on the premise of the worst fulfilment of the value expectations. e above two scenarios are solved separately as follows.
"Input Cost" is denoted as vi k and its related value expectation is vi k ≤ vi k _EV. When building the mathematical model under the conditions of maximum cost, it is necessary to assign vi k _EV to vi k , that is, vi k � vi k _EV, where vi k _EV is the maximum value of vi k . en, it is necessary to generate the optimisation configuration scheme for the GQPs to meet the other value expectations. is is a multiobjective optimisation problem with constraints. e linear weighting method is applied to convert it into a singleobjective optimisation problem. e physical meaning of the overall optimisation objective is that the fulfilment of value expectations except "Input Cost" is maximised as a whole with the support of the optimisation configuration scheme for the GQPs. Its mathematical model is given as follows: where vi_w i ′ represents the importance ratings of the ith optimisation objective P vi i _EV + , where P vi i _EV + is the ith value expectation that should be met to the greatest extent and its calculation formula is where vi i _EV + represents the degree to which the realised value of the ith VI is superior to limit value vi i _EV of the ith value expectation, that is, the degree to which the value expectation is met. Because some VIs are of positive type, the greater their value, the better their corresponding expectations are met, whereas others are of negative type, and hence, the smaller their value, the better their corresponding expectations are met. us, the calculation of vi i _EV + is an absolute value: Furthermore, because different VIs have different dimensions, it is necessary to normalise the degree to which the value expectation is met. g ij (x j ) represents the degree to which the change of the value of the jth GQP affects the realisation of the ith VIs, and its maximum value is one. When g ij (x j ) � 1, parameter μ * i0 + n j�1 μ * ij in equation (18) represents the maximum value of the ith VI to be realised. e objective function of the mathematical model under the condition of maximum cost is expressed as When building the mathematical model under the condition of minimum cost, the purpose of the corresponding objective function is to pursue the minimum input cost on the premise of the worst fulfilment of the value expectations.
us, the objective function of the mathematical model under the condition of minimum cost is expressed as max n j�1 μ * kj g kj q j + μ * ko − vi k _EV . (19) In equations (18) and (19), because the optimisation configuration scheme for GQPs is constrained in the feasible region, when operator S is ">" or "≥," μ * ij � μ * ij , and when operator S is "<" or "≤," μ * ij � μ * ij . e two optimal configuration schemes for GQPs can be obtained by solving equations (18) and (19), as shown in Figure 4. Both can meet the value expectations of the stakeholders for transboundary services, but the former is superior to the latter because of the different input costs.
When the values of GQPs are between the optimal configuration schemes of the maximum cost and minimum cost, the value expectations can also be met, and the values of GQPs are an appropriate configuration scheme for GQPs.
us, the two optimal configuration schemes are considered as the upper and lower bounds of the set of optimal configuration schemes for GQPs.
To summarise, by solving equations (18) and (19), the value ranges of GQPs under a certain confidence level can be obtained, that is, the set of optimisation configuration schemes for GQPs. If no feasible solution is found when solving the above model, this means that under the given constraints of GQPs, the lowest fulfilment of value expectations cannot be achieved. e designers can determine the configuration scheme for GQPs in which the VIs are realised to the maximal degree under the current constraint condition and can take it as a reference standard for the negotiated adjustment of value expectations by designers of transboundary services. Based on this configuration scheme, the designers need to decide whether to reduce the corresponding value expectations by conducting a negotiation among multiple participants or to identify potential partners who can provide higher service capabilities.

Case Study
In this study, we applied the proposed VQD to the GQP design of DiDi. Unlike traditional taxi services, DiDi is a transboundary service because it can provide higher service values for multiple stakeholders (e.g., DiDi app provider, map service provider, taxi drivers, and individual travellers) through deeply converging many independent services in different domains (e.g., traditional taxi services, mobile payment services, and map services). VQD can help the designers to make an appropriate decision, which results in a better configuration scheme for GQPs.
When designing DiDi, the designers should first communicate with the stakeholders to collect their respective value expectations, as shown in Table 3.
Next are the generation of the GQPs of DiDi and the identification of value constraints on the GQPs. e results are shown in Table 4. en, the designers need to identify the one-to-one basic type of quantitative mapping between each quality parameter q j and impact degree vi i _d of each VI. Because of space limitations, only a partial set of influence degree relation functions is provided in Table 5.
Next, the designers need to provide the relevant data samples, as shown in Tables 6 and 7. Based on the given inputoutput sample sets, using the FLAR model, the objective function can be transformed into a linear programming model. e fuzzy coefficients that result from substituting the data into six linear programming models are shown in Table 8.
In Table 8, row "s" represents the spreads of the fuzzy numbers and row "c" represents the centre point values of the fuzzy members. Next, we need to identify the correlation among GQPs. Similar to the previous method, after a series of operations and ignoring the spread value, we can derive a correlation between Maximum Waiting Time during Peak Period q 2 and Quantity of Available Taxis q 3 . As q 3 changes, q 2 also changes.
Using VIW and μ * ij obtained above, we can calculate the importance rating of the GQPs. Here, only the centre point values of the fuzzy numbers are considered. To overcome the influence of different dimensions, the centre point values of the parameters in Table 8 P ij represents the coefficient between the ith VI and jth GQP. e importance rating of the GQPs can be obtained by calculation as follows: Next, we need to generate an optimal configuration scheme for GQPs. e λ-cut set of the fuzzy number is obtained by substituting the data obtained above into the nonlinear programming model and setting confidence λ to 0.2, as shown in Table 9.

Conclusion and Future Work
Based on QFD, we proposed a two-phase model called VQD-QCD to facilitate designers to precisely design quality/capability characteristics of transboundary services by elaborating on the considerations of value expectation conflicts, quality attribute correlations, and constraints of the actual service capabilities of different service providers from different business domains. VQD-QCD can be applied to seek a trade-off between high-level value expectations and realworld service capabilities, and then the optimal configuration scheme for GQPs, LQPs, and CPs can be obtained in a top-down manner. In particular, considering the inherent vagueness and uncertainty of relationships among the VIs and GQPs of transboundary services, FLAR and fuzzy nonlinear programming methods were incorporated into VQD to identify quantitative relations between VIs and GQPs, and correlations among GQPs.
ere are two issues that still need to be solved in our VQD-QCD. One is the lack of related data. e other is that because of the lack of related data, there has been no in-depth study on negotiation design for the bottom-up approach. For the former, more data related to models in VQD can be collected during the execution of the designed transboundary service. In this case, the parameters of these models would be continuously optimised and then the updated VQD could be used to obtain a more appropriate configuration scheme for GQPs. For the latter, this is future work because when the available capabilities of stakeholders in the real-world service cannot meet their value expectations, this bottom-up negotiation method can help multiple stakeholders to make reasonable and iterative adjustments to their respective value expectations. e adjustment scheme of the value expectations can help to reconduct the generative design and obtain a reasonable configuration scheme. erefore, future work will be to conduct an in-depth study on this negotiation design method based on game theory to further improve VQD and then help designers to achieve the GQP design of transboundary services.

Data Availability
No data were used to support this study.