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

Authors: Chao Ma; Wei Dong Liu; Zhi Ying Tu; Zhong Jie Wang; Xiao Fei Xu
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

The “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 from multiple 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.


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## Body

## 1. 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. This 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. The essence of a transboundary service is the deep convergence of multiple independent services from different industries, different organisations, and different value chains [1]. The Internet of Services (IoS) [2] and Big Service [3] are two similar terms that have attracted wide attention in recent years.The 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 left-hand side of Figure1. This collaboration process consists of a set of activities, a set of resources, and the bindings between resources and activities.Figure 1
Design of transboundary services.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 Figure1. These 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. Therefore, 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. These stakeholders are attached to different business domains, have different value expectations, and own different service capabilities. There 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.The “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. Therefore, 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 [5–9] 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 Figure1, 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 top-down 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.The 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. The 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.The remainder of this paper is organised as follows: In Section2, 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.


## 2. Overview of VQD-QCD

In Table1, 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”.Table 1
Comparison of the QCD-VQD with QFD, QFD-based RDP, and SQFD.
Related methods
Targets to be designed
Deployment process
Phase 1
Phase 2
QFD
Products
VOCB
Product CTQ
Part CTQ
QFD-based RDP
Manufacturing information systems
URs
Critical-to-system functions
Functional requirements
SQFD
Services with one single provider
UEs
QPs of SRM
QPs of SBCM
VQD-QCD
Transboundary services with multiple stakeholders from multiple domains
VEs
GQPs
LQPs/CPs
VOCB: voice of customers and business; CTQ: critical to quality; URs: user requirements; UEs: user expectations; QPs: quality parameters; VEs: value expectations.The two-phase framework of VQD-QCD is shown in Figure2. The 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 top-down generative design of a quality/capability configuration scheme.Figure 2
Two-phase framework of VQD-QCD.The 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. The 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. The importance 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. This 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.The 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. The 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].


## 3. 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. Thus, 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.


### 3.2. VQD-Based Design Process of GQPs

Figure3 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:Step 1. Identify stakeholders and their value expectationsFirst, 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]. The VIs identified are denoted as VI = {vi1,vi2,…,viM}. The stakeholders make value propositions according to these M VIs, which propose a set of value expectations VP = {vp1,vp2,…,vpM} on these value M indicators, where each vpi ∈ VP is either vpi=vii,vii_EV,operatorS or vpi=vii,vii_EV1,vii_EV2,…,vii_EVk,operatorD. The 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 vp1 of VI vi1 “Market Share” is “larger than 70%”, then the vp1 collected can be denoted as vp1=vi1,70%,>.Forvpi=vii,vii_EV1,vii_EV2,…,vii_EVk,operatorD, the multiple operands in the set vii_EV1,vii_EV2,…,vii_EVk are in ascending order, and operatorD may be, for example, “∈up” or “∈down”. For vpi=vii,vii_EVh,…,vii_EVk,∈up, where 1 < h ≤ k, “∈up” means that the vii’s value belongs to the set vii_EVh,…,vii_EVk and it should be larger than or equal to vii_EVh; while for vpi=vii,vii_EV1,…,vii_EVj,∈down, where 1 ≤ j < k, “∈down” means that the vii’s value belongs to the set vii_EV1,…,vii_EVj and it should be smaller than or equal to vii_EVj. For example, if value expectation vp2 of VI vi2 “Customer Satisfaction” is “larger than or equal to 4 stars,” then the vp2 collected can be denoted as vp2=vi2,4stars,5stars,∈up.Step 2. Determine the relative importance ratings of VIsThe 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. Then, 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 M-dimensional vector VIW=vi_w1,vi_w2,…,vi_wM.Step 3. Determine the final importance ratings based on competitive analysisTo improve the competitiveness of the transboundary service operator (TSO1) after investigating the relevant markets, it is necessary to consider the competitors’ impact on vector VIW. Hence, first, it is essential for TSO1 to identify the competitors who provide a similar service. Assume that L − 1 competitors are identified in the relevant markets, denoted as TSO2, …, TSOL. Then, 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. Thus, the operators’ performance ratings on the M VIs can be obtained and denoted as a comparison matrix X = (xml)M×L, where xml is the performance rating of operator TSOl on VI VIm.Based on matrixX, the competitive priority ratings on the M VIs for operator TSO1 can be obtained using the entropy method [17] and denoted as e = (e1, e2, …, eM), where em represents operator TSO1’s priority rating on VI VIm. According to e, the performance goals of the M VIs could be set competitively and realistically by operator TSO1 and denoted as a = (a1, a2, …, aM). Thus, operator TSO1’s improvement ratio for VIm is um = am/xm1. It is obvious that the more ratio um improves, the more operator TSO1 should work on VI VIm and the more important VIm for operator TSO1. Thus, the final importance ratings of the M VIs for operator TSO1 are determined jointly by the relative importance, competitive priority, and improvement ratio. Additionally, they can be denoted as VIW′ = vi_w1′,vi_w2′,…,vi_wM′, where vi_wm′=um×vi_wm×em.Step 4. Generate GQPsThe 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. Thus, 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. Then, through market investigation, it should identify more quality 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. Thus far, a set of GQPs that affects the implementation of the VI has been generated and denoted as GQP = (q1, q2, …, qN).Step 5. Identify constraints on GQPsWhen 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 areqj ∈ GQP and cqj = [qj_LP, qj_UP], where qj_LP represents the lower bound of the constraint on the qj and qj_UP represents the upper bound of the qj’s constraint; for discrete quality parameters, there are qj ∈ GQP and cqj = {qj_LP, …, qj_Vj, …, qj_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 GQPsThe 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. There is a correlation among GQPs, which can be expressed as the correlation matrix. Through the FLAR method, we use the collected data combined with expert knowledge to obtain the correlation matrix among GQPs. More details are provided in Section4.Step 7. Determine the quantitative relations between VIs and GQPsFor each VI VIm, the designers need to determine the value range of the quality parameters related to VIm and the VIm’s own value range according to the actual scenario. They also need to determine the degree of VI VIm that would be implemented according to different values of quality parameters. Therefore, through the FLAR method, we determine the quantitative relations between VIs and GQPs by collecting data and expert knowledge. The same method is used in Steps 6 and 7, and more details are provided in Section 4.Step 8. Determine the initial ratings of GQPsThe 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. The greater the influence coefficient, the greater the influence of the corresponding quality parameter change on the VI.The 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. They can be computed as the simple weighted average over their relationships with the VIs:q_wn=vi_w1′×vi1n∗ + vi_w2′×vi2n∗+⋯+vi_wM′×viMn∗, n = 1, 2, …, N.Step 9. Determine the final ratings of GQPs based on competitive analysisStep 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 theN GQPs. Thus, the operators’ performance ratings for the N GQPs can be obtained and denoted as a comparison matrix Y = (yml)N×L, where ynl is the quality performance rating of operator TSOl on GQP qn.Based on matrixY, the competitive priority ratings on the N GQPs for operator TSO1 can be obtained using the entropy method [17] and denoted by z = (z1, z2, …, zN), where zn represents operator TSO1’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 TSO1 and denoted by b = (b1, b2, …, bN). Thus, operator TSO1’s improvement ratios for qn is vn = bn/yn1 (bn is a positive quality parameter) and yn1/bn (bn is a negative quality parameter). Thus, the final ratings of the N GQPs for operator TSO1 are determined jointly by the initial ratings, competitive priority, and improvement ratio. Additionally, they can be denoted by QW′ = (q_w1′,q_w2′,…,q_wN′), where q_wn′=vn×q_wn×zn.Step 10. Generate the configuration scheme for GQPsThe input of step 10 is the output of Steps 1, 3, 5, 6, and 7. Based on these inputs, a method for generating a 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. Then, 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. The details of Step 10 are provided in Section5.Figure 3
VQD-based design process of GQPs for 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. Thus, 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.


## 3.2. VQD-Based Design Process of GQPs

Figure3 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:Step 1. Identify stakeholders and their value expectationsFirst, 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]. The VIs identified are denoted as VI = {vi1,vi2,…,viM}. The stakeholders make value propositions according to these M VIs, which propose a set of value expectations VP = {vp1,vp2,…,vpM} on these value M indicators, where each vpi ∈ VP is either vpi=vii,vii_EV,operatorS or vpi=vii,vii_EV1,vii_EV2,…,vii_EVk,operatorD. The 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 vp1 of VI vi1 “Market Share” is “larger than 70%”, then the vp1 collected can be denoted as vp1=vi1,70%,>.Forvpi=vii,vii_EV1,vii_EV2,…,vii_EVk,operatorD, the multiple operands in the set vii_EV1,vii_EV2,…,vii_EVk are in ascending order, and operatorD may be, for example, “∈up” or “∈down”. For vpi=vii,vii_EVh,…,vii_EVk,∈up, where 1 < h ≤ k, “∈up” means that the vii’s value belongs to the set vii_EVh,…,vii_EVk and it should be larger than or equal to vii_EVh; while for vpi=vii,vii_EV1,…,vii_EVj,∈down, where 1 ≤ j < k, “∈down” means that the vii’s value belongs to the set vii_EV1,…,vii_EVj and it should be smaller than or equal to vii_EVj. For example, if value expectation vp2 of VI vi2 “Customer Satisfaction” is “larger than or equal to 4 stars,” then the vp2 collected can be denoted as vp2=vi2,4stars,5stars,∈up.Step 2. Determine the relative importance ratings of VIsThe 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. Then, 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 M-dimensional vector VIW=vi_w1,vi_w2,…,vi_wM.Step 3. Determine the final importance ratings based on competitive analysisTo improve the competitiveness of the transboundary service operator (TSO1) after investigating the relevant markets, it is necessary to consider the competitors’ impact on vector VIW. Hence, first, it is essential for TSO1 to identify the competitors who provide a similar service. Assume that L − 1 competitors are identified in the relevant markets, denoted as TSO2, …, TSOL. Then, 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. Thus, the operators’ performance ratings on the M VIs can be obtained and denoted as a comparison matrix X = (xml)M×L, where xml is the performance rating of operator TSOl on VI VIm.Based on matrixX, the competitive priority ratings on the M VIs for operator TSO1 can be obtained using the entropy method [17] and denoted as e = (e1, e2, …, eM), where em represents operator TSO1’s priority rating on VI VIm. According to e, the performance goals of the M VIs could be set competitively and realistically by operator TSO1 and denoted as a = (a1, a2, …, aM). Thus, operator TSO1’s improvement ratio for VIm is um = am/xm1. It is obvious that the more ratio um improves, the more operator TSO1 should work on VI VIm and the more important VIm for operator TSO1. Thus, the final importance ratings of the M VIs for operator TSO1 are determined jointly by the relative importance, competitive priority, and improvement ratio. Additionally, they can be denoted as VIW′ = vi_w1′,vi_w2′,…,vi_wM′, where vi_wm′=um×vi_wm×em.Step 4. Generate GQPsThe 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. Thus, 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. Then, through market investigation, it should identify more quality 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. Thus far, a set of GQPs that affects the implementation of the VI has been generated and denoted as GQP = (q1, q2, …, qN).Step 5. Identify constraints on GQPsWhen 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 areqj ∈ GQP and cqj = [qj_LP, qj_UP], where qj_LP represents the lower bound of the constraint on the qj and qj_UP represents the upper bound of the qj’s constraint; for discrete quality parameters, there are qj ∈ GQP and cqj = {qj_LP, …, qj_Vj, …, qj_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 GQPsThe 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. There is a correlation among GQPs, which can be expressed as the correlation matrix. Through the FLAR method, we use the collected data combined with expert knowledge to obtain the correlation matrix among GQPs. More details are provided in Section4.Step 7. Determine the quantitative relations between VIs and GQPsFor each VI VIm, the designers need to determine the value range of the quality parameters related to VIm and the VIm’s own value range according to the actual scenario. They also need to determine the degree of VI VIm that would be implemented according to different values of quality parameters. Therefore, through the FLAR method, we determine the quantitative relations between VIs and GQPs by collecting data and expert knowledge. The same method is used in Steps 6 and 7, and more details are provided in Section 4.Step 8. Determine the initial ratings of GQPsThe 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. The greater the influence coefficient, the greater the influence of the corresponding quality parameter change on the VI.The 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. They can be computed as the simple weighted average over their relationships with the VIs:q_wn=vi_w1′×vi1n∗ + vi_w2′×vi2n∗+⋯+vi_wM′×viMn∗, n = 1, 2, …, N.Step 9. Determine the final ratings of GQPs based on competitive analysisStep 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 theN GQPs. Thus, the operators’ performance ratings for the N GQPs can be obtained and denoted as a comparison matrix Y = (yml)N×L, where ynl is the quality performance rating of operator TSOl on GQP qn.Based on matrixY, the competitive priority ratings on the N GQPs for operator TSO1 can be obtained using the entropy method [17] and denoted by z = (z1, z2, …, zN), where zn represents operator TSO1’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 TSO1 and denoted by b = (b1, b2, …, bN). Thus, operator TSO1’s improvement ratios for qn is vn = bn/yn1 (bn is a positive quality parameter) and yn1/bn (bn is a negative quality parameter). Thus, the final ratings of the N GQPs for operator TSO1 are determined jointly by the initial ratings, competitive priority, and improvement ratio. Additionally, they can be denoted by QW′ = (q_w1′,q_w2′,…,q_wN′), where q_wn′=vn×q_wn×zn.Step 10. Generate the configuration scheme for GQPsThe input of step 10 is the output of Steps 1, 3, 5, 6, and 7. Based on these inputs, a method for generating a 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. Then, 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. The details of Step 10 are provided in Section5.Figure 3
VQD-based design process of GQPs for transboundary services.


## 4. Method for Determining the Correlation Matrix and the Quantitative Relations between VIs and GQPs

### 4.1. Influence Factor Analysis and Determining the Influence Degree Relation Function

To meet value expectations VP = {vp1,vp2,…,vpm} stated by the stakeholders of transboundary services for VIs VI = {vi1,vi2,…,vim}, it is necessary to generate an appropriate configuration scheme for GQPs for transboundary services. Therefore, it is necessary to first identify the relationships between VIs and GQPs. Specifically, this involves determining the quantitative relations between both VIs and GQPs, which can be expressed as a set of weight relation functions F = {f1, f2, …, fm}, where vii = fi (q1, q2, …, qn).When determining functionfi specifically, it is necessary to analyse which characteristics of GQPs are related to the realisation of VIs: (1) types of GQPs: different types of GQPs have different ranges and units of measurement, and their influence on the realisation of VIs varies greatly; (2) values of GQPs: the change of the same GQP in different value ranges has a different influence on the realisation of VIs; and (3) correlation among GQPs: different correlations among GQPs have different influences on the realisation of VIs.Through the above analysis, we find that if we want to determine functionfi, 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 vii and each quality parameter qj, which can be expressed as a set of one-to-one influence degree relation functions G = {gi1,gi2,…,gin}, where vii_d=gijqj and variable vii_d is the influence degree of the quality parameter qj’s change on VI vii. The purpose of function gij is to convert the values of quality parameters of different dimensions into the unified values of influence degree vii_d, which facilitates the determination of weight relation function fi in the next step. A set of typical influence degree relation functions are given as follows:Table2 presents the basic types of one-to-one quantitative relation between quality parameter qj and influence degree vii_d from multiple angles (e.g., linear and nonlinear angles and positive and negative angles). Additionally, the more complex quantitative relation between both qj and vii_d can be obtained by combining the basic types of relationships. For example, when quality parameter qj “Quantity of Available Taxis” of DiDi is significantly lower than the average level of competitors in the relevant market, the relationship between qj and influence degree vii_d related to the VI “Market Share” is consistent with Type 1. When the value of qj is close to or even far exceeds the average level of competitors, the relationship between qj and vii_d is consistent with Type 2. Therefore, the relationship between both of them is an S-type quantitative relation as a whole.Table 2
Typical influence degree relation functions.
Type of function
Formula of function
Image of function
Type 1
v
i
i
_
d
=
1
/
e
b
−
1
⋅
e
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
−
1
/
e
b
−
1
Type 2
v
i
i
_
d
=
−
e
b
/
e
b
−
1
⋅
e
−
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
+
e
b
/
e
b
−
1
Type 3
v
i
i
_
d
=
e
b
/
e
b
−
1
⋅
e
−
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
−
1
/
e
b
−
1
Type 4
v
i
i
_
d
=
−
1
/
e
b
−
1
⋅
e
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
+
e
b
/
e
b
−
1
Type 5
v
i
i
_
d
=
k
q
j
+
b
Type 6
v
i
i
_
d
=
−
k
q
j
+
bType 1: It is an increasing function whose derivative increases gradually. The 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. The 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. The 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. The 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. The degree of influence on the VI increases with the improvement of the quality parameter, and the rate of increase is constant, wherek > 0.
Type 6: It is a decreasing function whose derivative is constant. The degree of influence on the VI decreases with the improvement of the quality parameter, and the rate of reduction is constant, wherek > 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 asH = {h1, h2, …, hn}, where qj = hj(q1, q2, …, qj−1, qj+1, …, qn). This is similar to the idea of determining weight relationship function fi when determining the correlation function hj. 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 hj 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 functionhj can be expressed as G = {gj1,gj2,…,gj−1,gj+1,…,gjn}, where qj_d = gjkqk, which means that qj has a correlation with qk, qk is the independent variable of function gjk, and qj_d is the dependent variable, and the influence degree of qk’s change on quality parameter qj. The purpose of function gjk is the same as that of the above function gij.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, functiongij and function gjk have been determined, that is, the influence degree of quality parameter qj’s change on VI vii can be identified and the influence degree of qk’s change on quality parameter qj can also be identified. Then, the weight relation function and correlation function can be constructed.


### 4.2. 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 fi and correlation function hj.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 some outliers, whereas least absolute deviation estimation is more effective than least squares estimation in linear and nonlinear regression. Therefore, 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. Therefore, we use FLAR to determine weight relation function fi and correlation function hj.


#### 4.2.1. FLAR and Sample Set Collection

The 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.The input of FLAR isl sets of reliable and practical data: X1,y1∗,X1,y2∗,…,Xr,yr∗,…,Xl,yl∗, where Xr=x1r,x2r,x3r,…,xnr and yr∗=yrc,yrs, r = 1, 2, 3, …, l. Additionally, its output is the fuzzy regression coefficient μ∗=μ0∗,μ1∗,μ2∗,…,μn∗ of the regression equation of y with respect to X. In FLAR, the distance between symmetrical triangular fuzzy members A = (c1, s1) and B = (c2, s2) can be expressed as d = |c1 − c2| + |s1 − s2|. The problem is converted to minimising the sum of errors between yr∗ and the estimated value of the corresponding variable and can be denoted as(1)dmin=∑r=1lyrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c+yrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s.For equation (1), we can make the following transformation:(2)yrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc+βrcyrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc−βrcyrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs+βrsyrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs−βrsαrc≥0,βrc≥0,αrs≥0,βrs≥0,r=1,2,3,…,l,where αrc,βrc,αrS,andBrs are nonnegative real numbers.Thus, the original problem is transformed into solving the linear programming model:(3)dmin=∑r=1lαrc+βrc+αrs+βrs,yrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc+βrc,yrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs+βrs,αrc≥0,βrc≥0,αrs≥0,βrs≥0,r=1,2,3,…,l,μic≥0,μis≥0,i=1,2,3,…,n.When collecting the sample set, it is first necessary to deriveL sets of values of N GQPs in line with actual conditions through communication with transboundary service designers and domain experts. The 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. The values of N GQPs are denoted as Qr=q1r,q2r,q3r,…,qir,…,qnr, where r = 1, 2, …, L and qir represents the observed value of the ith GQP in the rth sample set and is accurate data.Then, it is necessary to derive the observed values ofM VIs for each Qr, which is denoted as pviir∗=pviirc,pviirs, where r = 1, 2, …, L and i = 1, 2, …, M. Because the observed values of M VIs are determined by designers based on the observed values of the relevant GQPs, they are subjective and imprecise. Thus, fuzzy numbers should be assigned to the M VIs’ observed values so that their vagueness can be captured, where pviir∗ represents the observed value of the ith VI with respect to Qr and is a fuzzy number. Centre point value pviirc describes the most likely value of pviir∗, whereas the spread pviirs describes the precision of pviir∗. Thus, we collect the l sets of sample data that contain the quantitative relations between GQPs and VIs and conform to the correlations among GQPs.


#### 4.2.2. FLAR-Based Method for Constructing Functionsfi and hj

The FLAR model is applied to construct weight relation functionfi, and the formulas of function fi are given as follows:(4)vii∗=fiq1,q2,…,qn=∑j=1nμij∗gijqj+μio∗.In equation (4), q1, q2, …, qn represent the input vector, where qj represents the crisp input value of the jth GQPs; q1, q2, q3, …, qj0 represent continuous GQPs and qj0+1,qj0+2,…,qn represent the discrete GQPs; vii∗ represents the fuzzy output value of the ith VI; and μi∗=μi0∗,μi1∗,μi2∗,…,μin∗ is the fuzzy coefficient vector that needs to be determined when constructing function fi. In this paper, the construction problem of function fi is transformed into the following: input l sets of data Q1,pvii1∗,Q2,pvii2∗,.…,Ql,pviil∗ and then determine the fuzzy coefficient vector μi0∗,μi1∗,μi2∗,…,μin∗ so that output value vii∗ of VI calculated by equation (4) has the best fitting influence on declared value pvii∗ of the VI.LetQr = (q1r, q2r, …, qnr) denote the accurate input vector of the rth group and viir∗ represent the fuzzy output of VI calculated by equation (4) after Qr is input. viir∗ is a symmetric triangular fuzzy number, which can be expressed as viir∗=viirc,viirs, where viirc represents the centre point value of fuzzy number viir∗, which means the most likely value, and viirs represents the spread of fuzzy number viir∗, which means the precision of viir∗. Let viirmax=viirc+viirs and viirmin=viirc−viirs represent the upper and lower limits of the fuzzy number, respectively, and pviir∗ represent the declared value of VIs that correspond to the input vector of the rth group. pviir∗ and fuzzy coefficient μij∗ are also symmetric triangular fuzzy numbers, which have the same meaning as viir∗ and can be expressed as pviir∗=pviirc,pviirs and μij∗=μijc,μijs, respectively.The objective function and constraints for solving the problem of constructing weight relationship functionfi are given as follows:(5)mind=∑r=1lpviir∗−viir∗=∑r=1lpviirc−∑j=1nμijcgijqjr+μioc+pviirs−∑j=1nμijsgijqjr+μios,s.t.μijs≥0,μijc≥0,j=1,2,…,n.To facilitate the calculation, the mathematical model is transformed into the following linear programming model:(6)mind=∑r=1lμr+νr+ωr+δr,s.t.viirc−∑j=1nμijcgijqjr+μioc=μr−νr,viirs−∑j=1nμijsgijqjr+μios=ωr−δr,μr≥0,νr≥0,ωr≥0,δr≥0,r=1,2,3,…,l,μijs≥0,μijc≥0,j=1,2,3,…,n.The above linear programming model can be solved using a MATLAB program, and then the fuzzy coefficient setμi∗=μi0∗,μi1∗,μi2∗,…,μin∗ can be obtained, that is, the construction of the weight relation function fi is complete.The construction method of correlation functionhj is similar to that explained above, and its expression is as follows:(7)qj∗=hjq1,q2,…,qj−1,qj+1,…,qn=∑k=1&k≠jnαjk∗gjkqj+αjo∗,where q1,q2,…,qj−1,qj+1,…,qn represents the input vector, qj∗ represents the fuzzy output of the jth quality parameter, and αj∗=αj0∗,αj1∗,αj2∗,…,αj,j−1∗,αj,j+1∗,…,αjn∗ is the fuzzy coefficient vector that needs to be determined when constructing the function hj. Fuzzy coefficient αjk∗ is a symmetric triangular fuzzy number, which can be expressed as αjk∗=αjkc,αjks. Then, the mathematical model for solving the construction of correlation function hj is as follows:(8)mind=∑r=1lqjr−qjr∗=∑r=1lqjr−∑k=1&k≠jnαjkcgjkqkr+αjoc+∑k=1&k≠jnαjksgjkqkr+αjos,s.t.αjks≥0,αjkc≥0,where qjr represents the actual crisp value of the jth quality parameter when inputting the rth vector and qjr∗ represents the fuzzy output value that corresponds to the input vector of the rth group. Similar to the process of solving function fi, the mathematical model is first converted into a linear programming model, and then a MATLAB program is used to solve it. Thus, fuzzy coefficient set αj∗=αj0∗,αj1∗,αj2∗,…,αj,j−1∗,αj,j+1∗,…,αjn∗ can be obtained, that is, the construction of correlation function hj is complete.


## 4.1. Influence Factor Analysis and Determining the Influence Degree Relation Function

To meet value expectations VP = {vp1,vp2,…,vpm} stated by the stakeholders of transboundary services for VIs VI = {vi1,vi2,…,vim}, it is necessary to generate an appropriate configuration scheme for GQPs for transboundary services. Therefore, it is necessary to first identify the relationships between VIs and GQPs. Specifically, this involves determining the quantitative relations between both VIs and GQPs, which can be expressed as a set of weight relation functions F = {f1, f2, …, fm}, where vii = fi (q1, q2, …, qn).When determining functionfi specifically, it is necessary to analyse which characteristics of GQPs are related to the realisation of VIs: (1) types of GQPs: different types of GQPs have different ranges and units of measurement, and their influence on the realisation of VIs varies greatly; (2) values of GQPs: the change of the same GQP in different value ranges has a different influence on the realisation of VIs; and (3) correlation among GQPs: different correlations among GQPs have different influences on the realisation of VIs.Through the above analysis, we find that if we want to determine functionfi, 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 vii and each quality parameter qj, which can be expressed as a set of one-to-one influence degree relation functions G = {gi1,gi2,…,gin}, where vii_d=gijqj and variable vii_d is the influence degree of the quality parameter qj’s change on VI vii. The purpose of function gij is to convert the values of quality parameters of different dimensions into the unified values of influence degree vii_d, which facilitates the determination of weight relation function fi in the next step. A set of typical influence degree relation functions are given as follows:Table2 presents the basic types of one-to-one quantitative relation between quality parameter qj and influence degree vii_d from multiple angles (e.g., linear and nonlinear angles and positive and negative angles). Additionally, the more complex quantitative relation between both qj and vii_d can be obtained by combining the basic types of relationships. For example, when quality parameter qj “Quantity of Available Taxis” of DiDi is significantly lower than the average level of competitors in the relevant market, the relationship between qj and influence degree vii_d related to the VI “Market Share” is consistent with Type 1. When the value of qj is close to or even far exceeds the average level of competitors, the relationship between qj and vii_d is consistent with Type 2. Therefore, the relationship between both of them is an S-type quantitative relation as a whole.Table 2
Typical influence degree relation functions.
Type of function
Formula of function
Image of function
Type 1
v
i
i
_
d
=
1
/
e
b
−
1
⋅
e
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
−
1
/
e
b
−
1
Type 2
v
i
i
_
d
=
−
e
b
/
e
b
−
1
⋅
e
−
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
+
e
b
/
e
b
−
1
Type 3
v
i
i
_
d
=
e
b
/
e
b
−
1
⋅
e
−
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
−
1
/
e
b
−
1
Type 4
v
i
i
_
d
=
−
1
/
e
b
−
1
⋅
e
b
⋅
q
j
−
q
j
l
p
/
q
j
u
p
−
q
j
l
p
+
e
b
/
e
b
−
1
Type 5
v
i
i
_
d
=
k
q
j
+
b
Type 6
v
i
i
_
d
=
−
k
q
j
+
bType 1: It is an increasing function whose derivative increases gradually. The 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. The 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. The 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. The 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. The degree of influence on the VI increases with the improvement of the quality parameter, and the rate of increase is constant, wherek > 0.
Type 6: It is a decreasing function whose derivative is constant. The degree of influence on the VI decreases with the improvement of the quality parameter, and the rate of reduction is constant, wherek > 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 asH = {h1, h2, …, hn}, where qj = hj(q1, q2, …, qj−1, qj+1, …, qn). This is similar to the idea of determining weight relationship function fi when determining the correlation function hj. 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 hj 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 functionhj can be expressed as G = {gj1,gj2,…,gj−1,gj+1,…,gjn}, where qj_d = gjkqk, which means that qj has a correlation with qk, qk is the independent variable of function gjk, and qj_d is the dependent variable, and the influence degree of qk’s change on quality parameter qj. The purpose of function gjk is the same as that of the above function gij.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, functiongij and function gjk have been determined, that is, the influence degree of quality parameter qj’s change on VI vii can be identified and the influence degree of qk’s change on quality parameter qj can also be identified. Then, the weight relation function and correlation function can be constructed.


## 4.2. 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 fi and correlation function hj.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 some outliers, whereas least absolute deviation estimation is more effective than least squares estimation in linear and nonlinear regression. Therefore, 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. Therefore, we use FLAR to determine weight relation function fi and correlation function hj.


### 4.2.1. FLAR and Sample Set Collection

The 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.The input of FLAR isl sets of reliable and practical data: X1,y1∗,X1,y2∗,…,Xr,yr∗,…,Xl,yl∗, where Xr=x1r,x2r,x3r,…,xnr and yr∗=yrc,yrs, r = 1, 2, 3, …, l. Additionally, its output is the fuzzy regression coefficient μ∗=μ0∗,μ1∗,μ2∗,…,μn∗ of the regression equation of y with respect to X. In FLAR, the distance between symmetrical triangular fuzzy members A = (c1, s1) and B = (c2, s2) can be expressed as d = |c1 − c2| + |s1 − s2|. The problem is converted to minimising the sum of errors between yr∗ and the estimated value of the corresponding variable and can be denoted as(1)dmin=∑r=1lyrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c+yrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s.For equation (1), we can make the following transformation:(2)yrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc+βrcyrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc−βrcyrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs+βrsyrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs−βrsαrc≥0,βrc≥0,αrs≥0,βrs≥0,r=1,2,3,…,l,where αrc,βrc,αrS,andBrs are nonnegative real numbers.Thus, the original problem is transformed into solving the linear programming model:(3)dmin=∑r=1lαrc+βrc+αrs+βrs,yrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc+βrc,yrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs+βrs,αrc≥0,βrc≥0,αrs≥0,βrs≥0,r=1,2,3,…,l,μic≥0,μis≥0,i=1,2,3,…,n.When collecting the sample set, it is first necessary to deriveL sets of values of N GQPs in line with actual conditions through communication with transboundary service designers and domain experts. The 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. The values of N GQPs are denoted as Qr=q1r,q2r,q3r,…,qir,…,qnr, where r = 1, 2, …, L and qir represents the observed value of the ith GQP in the rth sample set and is accurate data.Then, it is necessary to derive the observed values ofM VIs for each Qr, which is denoted as pviir∗=pviirc,pviirs, where r = 1, 2, …, L and i = 1, 2, …, M. Because the observed values of M VIs are determined by designers based on the observed values of the relevant GQPs, they are subjective and imprecise. Thus, fuzzy numbers should be assigned to the M VIs’ observed values so that their vagueness can be captured, where pviir∗ represents the observed value of the ith VI with respect to Qr and is a fuzzy number. Centre point value pviirc describes the most likely value of pviir∗, whereas the spread pviirs describes the precision of pviir∗. Thus, we collect the l sets of sample data that contain the quantitative relations between GQPs and VIs and conform to the correlations among GQPs.


### 4.2.2. FLAR-Based Method for Constructing Functionsfi and hj

The FLAR model is applied to construct weight relation functionfi, and the formulas of function fi are given as follows:(4)vii∗=fiq1,q2,…,qn=∑j=1nμij∗gijqj+μio∗.In equation (4), q1, q2, …, qn represent the input vector, where qj represents the crisp input value of the jth GQPs; q1, q2, q3, …, qj0 represent continuous GQPs and qj0+1,qj0+2,…,qn represent the discrete GQPs; vii∗ represents the fuzzy output value of the ith VI; and μi∗=μi0∗,μi1∗,μi2∗,…,μin∗ is the fuzzy coefficient vector that needs to be determined when constructing function fi. In this paper, the construction problem of function fi is transformed into the following: input l sets of data Q1,pvii1∗,Q2,pvii2∗,.…,Ql,pviil∗ and then determine the fuzzy coefficient vector μi0∗,μi1∗,μi2∗,…,μin∗ so that output value vii∗ of VI calculated by equation (4) has the best fitting influence on declared value pvii∗ of the VI.LetQr = (q1r, q2r, …, qnr) denote the accurate input vector of the rth group and viir∗ represent the fuzzy output of VI calculated by equation (4) after Qr is input. viir∗ is a symmetric triangular fuzzy number, which can be expressed as viir∗=viirc,viirs, where viirc represents the centre point value of fuzzy number viir∗, which means the most likely value, and viirs represents the spread of fuzzy number viir∗, which means the precision of viir∗. Let viirmax=viirc+viirs and viirmin=viirc−viirs represent the upper and lower limits of the fuzzy number, respectively, and pviir∗ represent the declared value of VIs that correspond to the input vector of the rth group. pviir∗ and fuzzy coefficient μij∗ are also symmetric triangular fuzzy numbers, which have the same meaning as viir∗ and can be expressed as pviir∗=pviirc,pviirs and μij∗=μijc,μijs, respectively.The objective function and constraints for solving the problem of constructing weight relationship functionfi are given as follows:(5)mind=∑r=1lpviir∗−viir∗=∑r=1lpviirc−∑j=1nμijcgijqjr+μioc+pviirs−∑j=1nμijsgijqjr+μios,s.t.μijs≥0,μijc≥0,j=1,2,…,n.To facilitate the calculation, the mathematical model is transformed into the following linear programming model:(6)mind=∑r=1lμr+νr+ωr+δr,s.t.viirc−∑j=1nμijcgijqjr+μioc=μr−νr,viirs−∑j=1nμijsgijqjr+μios=ωr−δr,μr≥0,νr≥0,ωr≥0,δr≥0,r=1,2,3,…,l,μijs≥0,μijc≥0,j=1,2,3,…,n.The above linear programming model can be solved using a MATLAB program, and then the fuzzy coefficient setμi∗=μi0∗,μi1∗,μi2∗,…,μin∗ can be obtained, that is, the construction of the weight relation function fi is complete.The construction method of correlation functionhj is similar to that explained above, and its expression is as follows:(7)qj∗=hjq1,q2,…,qj−1,qj+1,…,qn=∑k=1&k≠jnαjk∗gjkqj+αjo∗,where q1,q2,…,qj−1,qj+1,…,qn represents the input vector, qj∗ represents the fuzzy output of the jth quality parameter, and αj∗=αj0∗,αj1∗,αj2∗,…,αj,j−1∗,αj,j+1∗,…,αjn∗ is the fuzzy coefficient vector that needs to be determined when constructing the function hj. Fuzzy coefficient αjk∗ is a symmetric triangular fuzzy number, which can be expressed as αjk∗=αjkc,αjks. Then, the mathematical model for solving the construction of correlation function hj is as follows:(8)mind=∑r=1lqjr−qjr∗=∑r=1lqjr−∑k=1&k≠jnαjkcgjkqkr+αjoc+∑k=1&k≠jnαjksgjkqkr+αjos,s.t.αjks≥0,αjkc≥0,where qjr represents the actual crisp value of the jth quality parameter when inputting the rth vector and qjr∗ represents the fuzzy output value that corresponds to the input vector of the rth group. Similar to the process of solving function fi, the mathematical model is first converted into a linear programming model, and then a MATLAB program is used to solve it. Thus, fuzzy coefficient set αj∗=αj0∗,αj1∗,αj2∗,…,αj,j−1∗,αj,j+1∗,…,αjn∗ can be obtained, that is, the construction of correlation function hj is complete.


## 4.2.1. FLAR and Sample Set Collection

The 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.The input of FLAR isl sets of reliable and practical data: X1,y1∗,X1,y2∗,…,Xr,yr∗,…,Xl,yl∗, where Xr=x1r,x2r,x3r,…,xnr and yr∗=yrc,yrs, r = 1, 2, 3, …, l. Additionally, its output is the fuzzy regression coefficient μ∗=μ0∗,μ1∗,μ2∗,…,μn∗ of the regression equation of y with respect to X. In FLAR, the distance between symmetrical triangular fuzzy members A = (c1, s1) and B = (c2, s2) can be expressed as d = |c1 − c2| + |s1 − s2|. The problem is converted to minimising the sum of errors between yr∗ and the estimated value of the corresponding variable and can be denoted as(1)dmin=∑r=1lyrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c+yrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s.For equation (1), we can make the following transformation:(2)yrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc+βrcyrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc−βrcyrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs+βrsyrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs−βrsαrc≥0,βrc≥0,αrs≥0,βrs≥0,r=1,2,3,…,l,where αrc,βrc,αrS,andBrs are nonnegative real numbers.Thus, the original problem is transformed into solving the linear programming model:(3)dmin=∑r=1lαrc+βrc+αrs+βrs,yrc−x1rμ1c−x2rμ2c−⋯−xnrμnc−μ0c=αrc+βrc,yrs−x1rμ1s−x2rμ2s−⋯−xnrμns−μ0s=αrs+βrs,αrc≥0,βrc≥0,αrs≥0,βrs≥0,r=1,2,3,…,l,μic≥0,μis≥0,i=1,2,3,…,n.When collecting the sample set, it is first necessary to deriveL sets of values of N GQPs in line with actual conditions through communication with transboundary service designers and domain experts. The 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. The values of N GQPs are denoted as Qr=q1r,q2r,q3r,…,qir,…,qnr, where r = 1, 2, …, L and qir represents the observed value of the ith GQP in the rth sample set and is accurate data.Then, it is necessary to derive the observed values ofM VIs for each Qr, which is denoted as pviir∗=pviirc,pviirs, where r = 1, 2, …, L and i = 1, 2, …, M. Because the observed values of M VIs are determined by designers based on the observed values of the relevant GQPs, they are subjective and imprecise. Thus, fuzzy numbers should be assigned to the M VIs’ observed values so that their vagueness can be captured, where pviir∗ represents the observed value of the ith VI with respect to Qr and is a fuzzy number. Centre point value pviirc describes the most likely value of pviir∗, whereas the spread pviirs describes the precision of pviir∗. Thus, we collect the l sets of sample data that contain the quantitative relations between GQPs and VIs and conform to the correlations among GQPs.


## 4.2.2. FLAR-Based Method for Constructing Functionsfi and hj

The FLAR model is applied to construct weight relation functionfi, and the formulas of function fi are given as follows:(4)vii∗=fiq1,q2,…,qn=∑j=1nμij∗gijqj+μio∗.In equation (4), q1, q2, …, qn represent the input vector, where qj represents the crisp input value of the jth GQPs; q1, q2, q3, …, qj0 represent continuous GQPs and qj0+1,qj0+2,…,qn represent the discrete GQPs; vii∗ represents the fuzzy output value of the ith VI; and μi∗=μi0∗,μi1∗,μi2∗,…,μin∗ is the fuzzy coefficient vector that needs to be determined when constructing function fi. In this paper, the construction problem of function fi is transformed into the following: input l sets of data Q1,pvii1∗,Q2,pvii2∗,.…,Ql,pviil∗ and then determine the fuzzy coefficient vector μi0∗,μi1∗,μi2∗,…,μin∗ so that output value vii∗ of VI calculated by equation (4) has the best fitting influence on declared value pvii∗ of the VI.LetQr = (q1r, q2r, …, qnr) denote the accurate input vector of the rth group and viir∗ represent the fuzzy output of VI calculated by equation (4) after Qr is input. viir∗ is a symmetric triangular fuzzy number, which can be expressed as viir∗=viirc,viirs, where viirc represents the centre point value of fuzzy number viir∗, which means the most likely value, and viirs represents the spread of fuzzy number viir∗, which means the precision of viir∗. Let viirmax=viirc+viirs and viirmin=viirc−viirs represent the upper and lower limits of the fuzzy number, respectively, and pviir∗ represent the declared value of VIs that correspond to the input vector of the rth group. pviir∗ and fuzzy coefficient μij∗ are also symmetric triangular fuzzy numbers, which have the same meaning as viir∗ and can be expressed as pviir∗=pviirc,pviirs and μij∗=μijc,μijs, respectively.The objective function and constraints for solving the problem of constructing weight relationship functionfi are given as follows:(5)mind=∑r=1lpviir∗−viir∗=∑r=1lpviirc−∑j=1nμijcgijqjr+μioc+pviirs−∑j=1nμijsgijqjr+μios,s.t.μijs≥0,μijc≥0,j=1,2,…,n.To facilitate the calculation, the mathematical model is transformed into the following linear programming model:(6)mind=∑r=1lμr+νr+ωr+δr,s.t.viirc−∑j=1nμijcgijqjr+μioc=μr−νr,viirs−∑j=1nμijsgijqjr+μios=ωr−δr,μr≥0,νr≥0,ωr≥0,δr≥0,r=1,2,3,…,l,μijs≥0,μijc≥0,j=1,2,3,…,n.The above linear programming model can be solved using a MATLAB program, and then the fuzzy coefficient setμi∗=μi0∗,μi1∗,μi2∗,…,μin∗ can be obtained, that is, the construction of the weight relation function fi is complete.The construction method of correlation functionhj is similar to that explained above, and its expression is as follows:(7)qj∗=hjq1,q2,…,qj−1,qj+1,…,qn=∑k=1&k≠jnαjk∗gjkqj+αjo∗,where q1,q2,…,qj−1,qj+1,…,qn represents the input vector, qj∗ represents the fuzzy output of the jth quality parameter, and αj∗=αj0∗,αj1∗,αj2∗,…,αj,j−1∗,αj,j+1∗,…,αjn∗ is the fuzzy coefficient vector that needs to be determined when constructing the function hj. Fuzzy coefficient αjk∗ is a symmetric triangular fuzzy number, which can be expressed as αjk∗=αjkc,αjks. Then, the mathematical model for solving the construction of correlation function hj is as follows:(8)mind=∑r=1lqjr−qjr∗=∑r=1lqjr−∑k=1&k≠jnαjkcgjkqkr+αjoc+∑k=1&k≠jnαjksgjkqkr+αjos,s.t.αjks≥0,αjkc≥0,where qjr represents the actual crisp value of the jth quality parameter when inputting the rth vector and qjr∗ represents the fuzzy output value that corresponds to the input vector of the rth group. Similar to the process of solving function fi, the mathematical model is first converted into a linear programming model, and then a MATLAB program is used to solve it. Thus, fuzzy coefficient set αj∗=αj0∗,αj1∗,αj2∗,…,αj,j−1∗,αj,j+1∗,…,αjn∗ can be obtained, that is, the construction of correlation function hj is complete.


## 5. Generation of the Configuration Scheme for GQPs

### 5.1. 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 inSection 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. Therefore, the constraints of the mathematical model for generating the configuration scheme are given as follows:(1)
Cons 1. Constraints related to the value expectations:(9)∑j=1nμij∗gijqj+μi0∗≥vii_EV,i=1,2,3,…,i0,∑j=1nμij∗gijqj+μi0∗≤vii_EV,i=i0+1,i0+2,i0+3,…,m,where it is assumed that 0 ≤i0 ≤ m; when i ≤ i0, operatorS of vpi is “>” or “≥” and when i ≥ i0, operatorS of vpi is “<” or “≤.”(2)
Cons 2. Constraints related to the correlation among GQPs:(10)qj=∑k=1&k≠jnαjk∗gjkqj+αj0∗,j=1,2,…,n.(3)
Cons 3. Constraints related to the value ranges of GQPs:(11)qj∈tqj_LP,tqj_UP,j=1,2,3,…,j0,qj∈tqj_LP,…,tqj_Vj,…,tqj_UP,j=j0+1,j0+2,…,n.The 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 confidenceλ to convert fuzzy numbers into interval numbers in equation (9). For fuzzy number A=ac,as, the confidence interval with confidence λ is expressed as the following formula:(12)A¯,A¯=ac−as+λas,ac+as−λas,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 “≥,” μij∗=μij∗¯; and when operator S is “<” or “≤,” μij∗=μij∗¯. Thus, equation (9) is converted into the following form:(13)∑j=1nμij∗¯gijqj+μi0∗¯≥vii_EV,i=1,2,3,…,i0,∑j=1nμij∗¯gijqj+μi0∗¯≤vii_EV,i=i0+1,i0+2,i0+3,…,m,μij∗¯=μijc−μijs+λμijs,j=0,1,2,3,…,n,μij∗¯=μijc+μijs−λμijs,j=0,1,2,3,…,n.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 valueαjkc of fuzzy number αjk∗. This 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. Thus, equation (10) is converted into the following form:(14)qj=∑k=1&k≠jnαjkcgjkqj+αj0c,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.


### 5.2. 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. Thus, 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. This 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. The above two scenarios are solved separately as follows.“Input Cost” is denoted asvik and its related value expectation is vik≤vik_EV. When building the mathematical model under the conditions of maximum cost, it is necessary to assign vik_EV to vik, that is, vik = vik_EV, where vik_EV is the maximum value of vik. Then, it is necessary to generate the optimisation configuration scheme for the GQPs to meet the other value expectations. This is a multiobjective optimisation problem with constraints. The linear weighting method is applied to convert it into a single-objective optimisation problem. The 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:(15)maxW=∑i=1&i≠kmvi_wi″×Pvii_EV+,where vi_wi′ represents the importance ratings of the ith optimisation objective Pvii_EV+, where Pvii_EV+ is the ith value expectation that should be met to the greatest extent and its calculation formula is(16)Pvii_EV+=vii_EV+∑j=1nμij∗+μi0∗,where vii_EV+ represents the degree to which the realised value of the ith VI is superior to limit value vii_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. Thus, the calculation of vii_EV+ is an absolute value:(17)vii_EV+=∑j=1nμij∗gijxj+μi0∗−vii_EV.Furthermore, because different VIs have different dimensions, it is necessary to normalise the degree to which the value expectation is met.gijxj 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 gijxj=1, parameter μi0∗+∑j=1nμij∗ in equation (18) represents the maximum value of the ith VI to be realised. The objective function of the mathematical model under the condition of maximum cost is expressed as(18)maxW=∑i=1&i≠kmvi_wi′⋅∑j=1nμij∗gijqj+μio∗−vii_EV∑j=1nμij∗+μio∗.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. Thus, the objective function of the mathematical model under the condition of minimum cost is expressed as(19)max∑j=1nμkj∗gkjqj+μko∗−vik_EV.In equations (18) and (19), because the optimisation configuration scheme for GQPs is constrained in the feasible region, when operator S is “>” or “≥,” μij∗=μij∗¯, and when operator S is “<” or “≤,” μij∗=μij∗¯.The 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. Thus, the two optimal configuration schemes are considered as the upper and lower bounds of the set of optimal configuration schemes for GQPs.Figure 4
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. The 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.


## 5.1. 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 inSection 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. Therefore, the constraints of the mathematical model for generating the configuration scheme are given as follows:(1)
Cons 1. Constraints related to the value expectations:(9)∑j=1nμij∗gijqj+μi0∗≥vii_EV,i=1,2,3,…,i0,∑j=1nμij∗gijqj+μi0∗≤vii_EV,i=i0+1,i0+2,i0+3,…,m,where it is assumed that 0 ≤i0 ≤ m; when i ≤ i0, operatorS of vpi is “>” or “≥” and when i ≥ i0, operatorS of vpi is “<” or “≤.”(2)
Cons 2. Constraints related to the correlation among GQPs:(10)qj=∑k=1&k≠jnαjk∗gjkqj+αj0∗,j=1,2,…,n.(3)
Cons 3. Constraints related to the value ranges of GQPs:(11)qj∈tqj_LP,tqj_UP,j=1,2,3,…,j0,qj∈tqj_LP,…,tqj_Vj,…,tqj_UP,j=j0+1,j0+2,…,n.The 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 confidenceλ to convert fuzzy numbers into interval numbers in equation (9). For fuzzy number A=ac,as, the confidence interval with confidence λ is expressed as the following formula:(12)A¯,A¯=ac−as+λas,ac+as−λas,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 “≥,” μij∗=μij∗¯; and when operator S is “<” or “≤,” μij∗=μij∗¯. Thus, equation (9) is converted into the following form:(13)∑j=1nμij∗¯gijqj+μi0∗¯≥vii_EV,i=1,2,3,…,i0,∑j=1nμij∗¯gijqj+μi0∗¯≤vii_EV,i=i0+1,i0+2,i0+3,…,m,μij∗¯=μijc−μijs+λμijs,j=0,1,2,3,…,n,μij∗¯=μijc+μijs−λμijs,j=0,1,2,3,…,n.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 valueαjkc of fuzzy number αjk∗. This 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. Thus, equation (10) is converted into the following form:(14)qj=∑k=1&k≠jnαjkcgjkqj+αj0c,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.


## 5.2. 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. Thus, 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. This 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. The above two scenarios are solved separately as follows.“Input Cost” is denoted asvik and its related value expectation is vik≤vik_EV. When building the mathematical model under the conditions of maximum cost, it is necessary to assign vik_EV to vik, that is, vik = vik_EV, where vik_EV is the maximum value of vik. Then, it is necessary to generate the optimisation configuration scheme for the GQPs to meet the other value expectations. This is a multiobjective optimisation problem with constraints. The linear weighting method is applied to convert it into a single-objective optimisation problem. The 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:(15)maxW=∑i=1&i≠kmvi_wi″×Pvii_EV+,where vi_wi′ represents the importance ratings of the ith optimisation objective Pvii_EV+, where Pvii_EV+ is the ith value expectation that should be met to the greatest extent and its calculation formula is(16)Pvii_EV+=vii_EV+∑j=1nμij∗+μi0∗,where vii_EV+ represents the degree to which the realised value of the ith VI is superior to limit value vii_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. Thus, the calculation of vii_EV+ is an absolute value:(17)vii_EV+=∑j=1nμij∗gijxj+μi0∗−vii_EV.Furthermore, because different VIs have different dimensions, it is necessary to normalise the degree to which the value expectation is met.gijxj 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 gijxj=1, parameter μi0∗+∑j=1nμij∗ in equation (18) represents the maximum value of the ith VI to be realised. The objective function of the mathematical model under the condition of maximum cost is expressed as(18)maxW=∑i=1&i≠kmvi_wi′⋅∑j=1nμij∗gijqj+μio∗−vii_EV∑j=1nμij∗+μio∗.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. Thus, the objective function of the mathematical model under the condition of minimum cost is expressed as(19)max∑j=1nμkj∗gkjqj+μko∗−vik_EV.In equations (18) and (19), because the optimisation configuration scheme for GQPs is constrained in the feasible region, when operator S is “>” or “≥,” μij∗=μij∗¯, and when operator S is “<” or “≤,” μij∗=μij∗¯.The 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. Thus, the two optimal configuration schemes are considered as the upper and lower bounds of the set of optimal configuration schemes for GQPs.Figure 4
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. The 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.


## 6. 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 Table3.Table 3
Value expectations declared by stakeholders for DiDi.
Value indicators
Value expectations (VEs)
Stakeholders related to VEs
v
i
1: Market Share
v
p
1
=
v
i
1
,
70
%
,
>
DiDi app provider
v
i
2: Daily Order Volume
v
p
2
=
v
i
2
,
0.2
million
,
>
PSP
v
i
3: Average Income per Order
v
p
3
=
v
i
3
,
25
Yuan
,
>
MSP
v
i
4: Operation Cost
v
p
4
=
v
i
4
,
2.55
million Yuan
,
<
DiDi app provider
v
i
5: Average Daily Income
v
p
5
=
v
i
5
,
320
Yuan
,
>
Taxi drivers
v
i
6: Favourable Rate
v
p
6
=
v
i
6
,
50
%
,
>
Individual travellers
PSP: payment service provider; MSP: map service provider.Next, we need to determine the relative importance ratings of the six VIs in Table3. As described in Section 3.2, we adopt an FAHP; the detailed description of the FAHP is shown in Figure 5. Then, relative importance ratings VIW = {vi_w1,vi_w2,…,vi_w6} = {0.211, 0.183, 0.139, 0.124, 0.145, 0.198} are obtained.Figure 5
Detailed description of the FAHP.Next are the generation of the GQPs of DiDi and the identification of value constraints on the GQPs. The results are shown in Table4.Table 4
GQPs and their value constraints.
GQPs
Value constraints on GQPs
q
1: Average Travel Cost
ctq
1 = [1.4 Yuan/km, 2.0 Yuan/km]
q
2: Maximum Waiting Time during Peak Period
ctq
2 = [5 min, 20 min]
q
3: Quantity of Available Taxis
ctq
3 = [3500 vehicles, 5000 vehicles]
q
4: Drivers’ Service Attitude
ctq
4 = {1, 2, 3, 4, 5}
q
5: Security Guarantee Level
ctq
5 = {1, 2, 3}
q
6: Positioning Accuracy
ctq
6 = {10 m, 50 m}Then, the designers need to identify the one-to-one basic type of quantitative mapping between each quality parameterqj and impact degree vii_d of each VI. Because of space limitations, only a partial set of influence degree relation functions is provided in Table 5.Table 5
Partial influence degree relation functions.
Functions
Expressions
Value range of independent variables
v
i
1
_
d
=
g
11
q
1
v
i
1
_
d
=
e
7
/
e
7
−
1
⋅
e
−
7
⋅
q
1
−
1.4
/
2.0
−
1.4
−
1
/
e
7
−
1
q
1 ∈ [1.4, 2.0]
v
i
1
_
d
=
g
12
q
2
v
i
1
_
d
=
−
1
/
e
6
−
1
⋅
e
6
⋅
q
2
−
5
/
20
−
5
+
e
6
/
e
6
−
1
q
2 ∈ [5, 20]
v
i
1
_
d
=
g
13
q
3
v
i
1
_
d
=
1
/
5000
⋅
q
3
q
3 ∈ [3500, 5000]
v
i
1
_
d
=
g
14
q
4
v
i
1
_
d
=
0
,
q
4
=
1
0.25
,
q
4
=
2
0.5
,
q
4
=
3
0.75
,
q
4
=
4
1
,
q
4
=
5
q
4 ∈ [1, 2, 3, 4, 5]
v
i
1
_
d
=
g
15
q
5
v
i
1
_
d
=
0
,
q
5
=
1
0.7
,
q
5
=
2
1
,
q
5
=
3
q
5 ∈ [1, 2, 3]
v
i
1
_
d
=
g
16
q
6
v
i
1
_
d
=
1
/
5000
⋅
q
3
q
6 ∈ [10, 50]Next, the designers need to provide the relevant data samples, as shown in Tables6 and 7. Based on the given input-output sample sets, using the FLAR model, the objective function can be transformed into a linear programming model. The fuzzy coefficients that result from substituting the data into six linear programming models are shown in Table 8.Table 6
GQPs in sample sets.
q
1
q
2
q
3
q
4
q
5
q
6
Sample 1
1.5
7
4000
5
2
10
Sample 2
2.0
18
1500
4
3
15
Sample 3
1.5
9
3500
4
1
20
Sample 4
1.7
12
2500
3
1
30
Sample 5
1.6
6
4500
5
3
15
Sample 6
2.0
10
3000
2
1
25
Sample 7
1.5
11
3200
3
2
30
Sample 8
1.9
15
2000
4
2
15
Sample 9
1.7
12
3200
3
1
20
Sample 10
1.5
11
3200
3
2
20
Sample 11
1.8
18
1500
4
3
25
Sample 12
1.5
9
3500
3
2
30Table 7
Value expectations in sample sets.
p
v
i
1
∗
p
v
i
2
∗
p
v
i
3
∗
p
v
i
4
∗
p
v
i
5
∗
p
v
i
6
∗
Sample 1
(0.91, 0.03)
(28.5, 1)
(25, 1)
(275, 5)
(340, 5)
(0.77, 0.02)
Sample 2
(0.45, 0.02)
(17.5, 0.2)
(32, 2)
(165, 5)
(325, 5)
(0.4, 0.02)
Sample 3
(0.75, 0.03)
(20.5, 0.5)
(21, 1)
(205, 5)
(280, 5)
(0.43, 0.02)
Sample 4
(0.53, 0.03)
(12.8, 0.5)
(22, 2)
(145, 5)
(300, 5)
(0.18, 0.02)
Sample 5
(0.88, 0.03)
(29, 0.5)
(28, 1)
(320, 5)
(390, 5)
(0.7, 0.02)
Sample 6
(0.5, 0.03)
(12.5, 0.3)
(24.5, 2)
(165, 5)
(292, 5)
(0.14, 0.02)
Sample 7
(0.75, 0.03)
(22, 0.5)
(23, 1)
(200, 5)
(305, 5)
(0.45, 0.02)
Sample 8
(0.6, 0.03)
(15, 0.5)
(29, 2)
(165, 5)
(345, 5)
(0.36, 0.02)
Sample 9
(0.62, 0.02)
(14.5, 0.5)
(22, 2)
(175, 5)
(300, 5)
(0.2, 0.02)
Sample 10
(0.77, 0.02)
(22, 0.5)
(23, 1)
(215, 5)
(305, 5)
(0.5, 0.02)
Sample 11
(0.5, 0.02)
(15, 0.2)
(29, 2)
(160, 5)
(325, 5)
(0.35, 0.02)
Sample 12
(0.78, 0.02)
(25, 0.5)
(23, 1)
(220, 5)
(305, 5)
(0.5, 0.02)Table 8
Fuzzy coefficients.
μ
i
j
∗
i = 1
i = 2
i = 3
i = 4
i = 5
i = 6
j = 0
c
0.0000
3.3319
0.0000
0.0000
0.0000
0.0000
s
0.0076
0.0914
0.0000
5.0000
5.0000
0.0053
j = 1
c
0.4090
9.3727
23.3333
0.5828
161.4414
0.3521
s
0.0000
0.3658
2.0000
0.0000
0.0000
0.0000
j = 2
c
0.2698
4.9006
0.0000
4.4202
118.3024
0.2310
s
0.0225
0.0000
0.0000
0.0000
0.0000
0.0125
j = 3
c
0.2903
11.9931
0.0000
0.7669
0.0000
0.0000
s
0.0000
0.3448
0.0000
0.0000
0.0000
0.0000
j = 4
c
0.1817
3.3942
4.6666
1.3006
61.2664
0.1523
s
0.0000
0.0069
0.0000
0.0000
0.0000
0.0000
j = 5
c
0.0988
5.3985
4.5238
3.0279
60.3799
0.2014
s
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
j = 6
c
0.0308
0.2407
0.0000
0.8908
0.0000
0.1479
s
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000In Table8, 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 q2 and Quantity of Available Taxis q3. As q3 changes, q2 also changes. This correlation can be expressed as q2 = −0.004 × q3 + 23.42.UsingVIW and μij∗ 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 are normalised by column, and the relationship matrix of VIs versus GQPs is obtained as follows:(20)P=0.31940.21070.22670.14190.07720.02410.26550.13880.33970.09620.15290.00690.71740.00000.00000.14350.13910.00000.05300.40220.06980.11840.27550.08110.40220.29470.00000.15270.15040.00000.32450.21300.00000.14040.18570.1364.P
ij represents the coefficient between the ith VI and jth GQP. The importance rating of the GQPs can be obtained by calculation as follows:(21)QW=0.3448,0.2046,0.1187,0.1321,0.1563,0.0434.Next, we need to generate an optimal configuration scheme for GQPs. Theλ-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.Table 9
Confidence interval (CI) corresponding to the fuzzy coefficient.
CI ofμij∗
i = 1
i = 2
i = 3
i = 4
i = 5
i = 6
j = 0
lb
−0.00608
3.25878
0.0000
−4.0000
−4.0000
−0.00424
ub
0.00608
3.40502
0.0000
4.0000
4.0000
0.00424
j = 1
lb
0.4090
9.08006
21.7333
0.5828
161.4414
0.3521
ub
0.4090
9.66534
24.9333
0.5828
161.4414
0.3521
j = 2
lb
0.2518
4.9006
0.0000
4.4202
118.3024
0.2210
ub
0.2878
4.9006
0.0000
4.4202
118.3024
0.2410
j = 3
lb
0.2903
11.7173
0.0000
0.7669
0.0000
0.0000
ub
0.2903
12.2690
0.0000
0.7669
0.0000
0.0000
j = 4
lb
0.1817
3.3887
4.6666
1.3006
61.2664
0.1523
ub
0.1817
3.3997
4.6666
1.3006
61.2664
0.1523
j = 5
lb
0.0988
5.3985
4.5238
3.0279
60.3799
0.2014
ub
0.0988
5.3985
4.5238
3.0279
60.3799
0.2014
j = 6
lb
0.0308
0.2407
0.0000
0.8908
0.0000
0.1479
ub
0.0308
0.2407
0.0000
0.8908
0.0000
0.1479
CI: the confidence interval; lb: the lower bound of the confidence interval; ub: the upper bound of the confidence interval.By substituting the upper and lower bounds of theλ-cut set into the nonlinear programming model, two nonlinear programming models that consist of precise parameters are obtained:(22)maxW=∑i=1&i≠46vi_wi′⋅∑j=16μijgijqj+μi0−vii_EV∑j=16μij+μi0,s.t.∑j=16μ1jg1jqj+μ10≥0.7,∑j=16μ2jg2jqj+μ20≥20,∑j=16μ3jg3jqj+μ30≥25,∑j=16μ4jg4jqj+μ40≤300,∑j=16μ5jg5jqj+μ50≥320,∑j=16μ6jg6jqj+μ60≥0.5,q2=−0.004q3+23.42,1.4≤q1≤2.0,5≤q2≤20,3500≤q3≤5000,10≤q6≤50,q3∈1,2,3,4,5,q4∈1,2,3,(23)minW=∑j=16μ4jg4jqj+μ40−300,s.t.∑j=16μ1jg1jqj+μ10≥0.7,∑j=16μ2jg2jqj+μ20≥20,∑j=16μ3jg3jqj+μ30≥25,∑j=16μ4jg4jqj+μ40≤300,∑j=16μ5jg5jqj+μ50≥320,∑j=16μ6jg6jqj+μ60≥0.5,q2=−0.004q3+23.42,1.4≤q1≤2.0,5≤q2≤20,3500≤q3≤5000,10≤q6≤50,q3∈1,2,3,4,5,q4∈1,2,3.By solving equations (22) and (23), two optimal configuration schemes Q1 = (1.5, 8.8, 3647.5, 5, 3, 50) and Q2 = (1.6, 9.4, 3500, 5, 3, 50) can be obtained. Therefore, the set of optimal configuration schemes for GQPs for DiDi is as follows:(i)
q1-Average Travel Cost (Yuan/km): [1.5, 1.6](ii)
q2-Maximum Waiting Time during Peak Period (min): [8.8, 9.4](iii)
q3-Quantify of Available Taxis (vehicle): [3500, 3648](iv)
q4-Driver’s Service Attitude (1∼5): [5, 5](v)
q5-Security Guarantee Level (1∼3): [3, 3](vi)
q6-Positioning Accuracy (m): [50, 50]In the above case, DiDi is in the initial stage of operation, and its business goal is to open up the market. At this time, its business strategy is to increase the cost of investment to provide high-value and high-quality services at a more favourable price to attract more individual travellers and gain more market share. From the above set of optimal configuration schemes for GQPs, we know that the value range of “Average Travel Cost” is [1.5, 1.6], which means that DiDi’s price is relatively favourable and the value range of “Maximum Waiting Time during Peak Period” is [8.8, 9.4], which means that the individual traveller’s waiting time is relatively short. The value range of “Driver’s Service Attitude” is [5, 5] and the value range of “Security Guarantee Level” is [3, 3]. The values of these two quality parameters have reached their respective maximum values, and they all have a greater impact on “Market Share.” By contrast, the value range of “Quantify of Available Taxis” is [3500, 3648] and the value range of “Positioning Accuracy” is [50, 50]. The value range of these two GQPs is not ideal, but their influence on “Market Share” is small. Overall, the configuration scheme for the above GQPs is in line with the design requirements of transboundary services.


## 7. 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 real-world 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.There are two issues that still need to be solved in our VQD-QCD. One is the lack of related data. The 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. The adjustment scheme of the value expectations can help to reconduct the generative design and obtain a reasonable configuration scheme. Therefore, 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.



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*Source: 9478083-2020-02-24.xml*