Bilateral Matching Decision Making of Partners of Manufacturing Enterprises Based on BMIHFIBPT Integration Methods: Evaluation Criteria of Organizational Quality-Specific Immunity

Abstract

This study aims to examine how the bilateral matching decision making of manufacturing enterprises that are seeking partners in the manufacturing supply chain can be improved by taking into consideration evaluation criteria for organizational quality-specific immunity. This study constructs an evaluation indicator system to measure organizational quality-specific immunity based on immune theory. The system’s evaluation criteria are based on the key components of organizational quality-specific immunity. We also construct bilateral matching evaluation and decision-making models using interval-valued hesitant fuzzy information and bidirectional projection technology (BMIHFIBPT). The interval-valued bilateral fuzzy bidirectional projection technology is applied to solve a combination satisfaction and matching optimization model. Empirical analysis is carried out to assess both the supply and demand sides of representative manufacturing enterprises in the manufacturing supply chain, match the main supply and demand bodies of two subjects, and help manufacturing enterprises select the optimal cooperation partners. The empirical analysis results indicate that the bilateral matching evaluation and decision-making models based on BMIHFIBPT can overcome the lack of information to some extent and help solve interval-valued hesitant fuzzy decision-making problems. In turn, the models can provide a basis for manufacturing enterprises to effectively select the best cooperation partners and conduct bilateral matching decision making in the manufacturing supply chain area that supports organizational quality-specific immunity.

1. Introduction

Today’s increasingly fierce and complex competitive environment poses unprecedented challenges to manufacturing enterprises’ development. Quality plays a vital role in staying competitive. Quality management thus not only offers many benefits for enterprises but also involves huge security risks [1]. In recent years, the quality management problems of manufacturing enterprises have become increasingly prominent. Many well-known manufacturing enterprises have experienced quality crises and faced criticism by the public and media. Takata Airbags had an issue with an abnormal gas generator rupture. After the incident came to light, more than 60 million vehicles globally were affected and recalled. The recall incident brought huge losses to Takada, which declared bankruptcy in June 2017. In 2016, Samsung was caught in the “Battery Gate” incident. Within a month of the release of the Galaxy Note7 mobile phone, more than 30 explosions and fires occurred due to battery defects. Samsung permanently stopped production and sales of the Galaxy Note7, and the event became one of the most shameful events in the company’s history. Quality management problems cause serious economic losses for manufacturing enterprises, affecting in turn the survival and development of other manufacturing enterprises in the supply chain.

Quality is key to manufacturing enterprises’ survival. There are many manufacturing enterprises in the manufacturing supply chain. These enterprises mainly select partners based on features of quality, for example, their ability to jointly complete quality tasks and performance in the manufacturing supply chain [2,3,4,5], maintain resilience [6,7,8,9,10,11], strengthen quality management practice and sustainability [12,13,14,15,16,17,18,19], achieve sustainable development [20,21], and promote green quality management and green technology innovation [22,23,24,25]. Organizational quality-specific immunity is the comprehensive embodiment of the organizational quality of a manufacturing enterprise in the manufacturing supply chain [26,27,28,29,30,31,32,33,34,35]. The stronger the organizational quality-specific immunity of a manufacturing enterprise, the easier it is for that enterprise to be selected as a partner.

Therefore, in view of the importance of evaluating organizational quality-specific immunity, this study uses immune theory as an entry point to construct relevant evaluation criteria. We introduce bidirectional projection technology to the bilateral matching decision-making method and consider both the supply and demand sides. We use data from the cooperation partners of representative manufacturing enterprises in the manufacturing supply chain as the interval-value hesitant fuzzy information. This study further carries out bilateral (two-sided) matching decision making according to the proposed evaluation criteria for organizational quality-specific immunity. The process involves applying integration methods to create bilateral matching decision-making models that incorporate interval-valued hesitant fuzzy information and bidirectional projection technology (BMIHFIBPT). The resulting bilateral matching decision-making models and methods will provide the foundation basis for effective selection of partners in the manufacturing supply chain based on organizational quality-specific immunity, providing practical guidance as well as scientific contribution to the field.

2. Literature Review

2.1. Bilateral Matching Decision-Making Models and Methods

Bilateral matching decision making is closely related to management science, and various types of bilateral matching decision-making models and methods are widely used in the field of management science and engineering, mainly in the fields of human resources management, price and material management, e-commerce management, enterprise operation management, and risk investment management [36,37,38,39,40,41,42,43]. However, limited relevant empirical research has applied the various types of bilateral matching decision-making models and methods to the supply chain quality management and supply chain operation management fields. The models and methods available to support bilateral matching decision making mainly stem from models and methods related to emerging technology, operational optimization, statistical and artificial intelligence, simulation, and bilateral matching based on the specific preference information of the bilateral subjects [36,37,38,39,40,41,42,43].

Several representative emerging technology models and methods are as follows [36,37,38,39,40,41,42,43]: two-sided matching decision models based on advantage sequences, two-sided matching game analysis methods, two-sided matching models based on the matching efforts of a bilateral platform, two-sided matching decision-making methods based on triangular intuitionistic fuzzy number information, intuitionistic fuzzy two-sided matching methods considering regret aversion and matching aspiration, two-sided game matching methods with uncertain preference ordinals, decision-making models and methods based on two-sided matching dynamic games, and decision-making methods for stable two-sided matching based on linguistic preference information.

Several representative models and methods for operational optimization, statistical and artificial intelligence, and simulation are as follows [44,45,46]: intuitionistic fuzzy two-sided matching models, multi-objective stable matching methods with distributional constraints, and dynamic matching methods with unknown preferences.

Several representative models and methods for bilateral matching based on specific preference information from bilateral subjects are as follows [47,48,49,50]: network visualization of stable matching methods, dynamic two-sided matching methods based on uncoordinated preference information, multiple decision-making matching models based on the characteristics and circumstances of two-sided (bilateral) subjects, and strict two-sided matching methods based on complete preference ordinal information.

2.2. Organizational Quality-Specific Immunity

Quality accidents are not uncommon. Such issues reveal not only a regulatory mechanism with loopholes but also an imperfect quality management system. In the process of business development, quality accidents are the “symptoms” of enterprises with a quality-related disease, and enterprises infected by that disease will soon see their competitiveness drop, at the very least. The quality management departments and quality management personnel in an enterprise constitute the quality management immune system of an enterprise. Their function is to prevent disease from occurring in the enterprise, perpetually maintaining the enterprise’s health, and to provide proper treatment the moment the enterprise starts to fall sick. Seeking out and eliminating “quality accident-inducing factors” is an effective means by which the quality management immune system can prevent an enterprise from getting sick.

Lv and Wang [51,52,53] were the first to apply immune theory to organizational management. Their work explores organizational adaptability and has led to inspiring results about general organizational immunity from the perspective of immunization [54]. They assert that organizational immunity consists of specific immunities and non-specific immunities. Specific immunities, which emerge as the organization establishes key behaviours, help to prevent “viruses” in the enterprise [55]. At the heart of general organizational immunity, i.e., perhaps the most important element in determining the rise or fall of an enterprise, is organizational quality [56]. Organizational quality-specific immunity, in turn, is fostered by specificity, adaptability, initiative attributes, and the characteristics of acquired cultivation and fostering nurture. These features enhance the efficiency and learning effectiveness of the immune system, saving immune response time if the issue arises again, essentially immunizing the enterprise. The main components of organizational quality-specific immunity are thus quality monitoring and cognition, quality defence, quality memory, and immune homeostasis. These components complement each other, allowing for coordinating development in the formation of an orderly dynamic benign cycle [57].

Existing empirical studies on organizational quality-specific immunity have drawn on relevant theoretical analysis frameworks and conceptual framework models to conduct data surveys, questionnaires, interviews, statistical investigations, and case studies. Luca et al. [58] point out that quality management is becoming an increasingly important factor in determining an enterprise’s level of economic and technological development. Improving quality is an urgent need for enterprises seeking to survive and develop in the current competitive environment. Luca et al. also note the key success factors for implementing quality improvement measures and propose a performance measurement system to evaluate those factors. Kaynak and Hartley [59] and Tari et al. [60] confirm that quality management practice has a significant positive impact on the product quality and operational efficiency of the company. In biological and immune theory, each time the organism completes the immune response, its immune cells are enhanced; the organism is thus preserved by immunological memory. Considering organizational quality management from the perspective of immune theory, when an enterprise faces a threat to organizational quality due to internal abnormalities or changes in the external environment, its immune system should identify and respond to the threat and then commit the event to memory; doing so ensures that, next time, the enterprise can mobilize available resources in a timely and reasonable manner to remove similar risks or harm, ensuring healthy and sustainable development [61].

Wang et al. draw on the theory of medical immunity to study the adaptability of enterprises. They divide the concept of organizational immunity into two dimensions: non-specific immunities and specific immunities. Non-specific immunities are determined by three major components: organizational structure, institutional rules, and company culture. Specific immunities, in comparison, are determined by organizational monitoring and surveillance, organizational defence, and organizational memory [61]. Li et al. [62] propose the product quality management model for supply chains based on the characteristics and mechanisms of the biological immune response. With the biological immune system as a parallel, their supply chain quality management model has four stages: immune recognition, learning, memory, and immune effects. Based on that model, the quality identification mechanism and control methods are effective. Passing through the supply chain thus has a positive effect on ensuring product quality and safety.

Liu et al., Shi et al., and Dai and Ding [63,64,65,66,67,68] indicate that just as organizational quality-specific immunity is at the core of general organizational quality immunity, the latter is at the core of overall organizational immunity. In summary, they find that organizational quality-specific immunity has three main components: organizational quality monitoring and cognition; organizational quality defence, clearance, and repair; and organizational quality memory and immune self-stability. They propose a path towards quality performance improvement based on empirical analysis of the factors that affect quality defect management from the perspective of immune theory. Wang and Li [54], also on the basis on immune theory, consider enterprises’ immune recognition ability and use it as a mediator variable to construct a multi-media model. They use the resulting AMOS model to analyse the influencing factors of and risks to immunity to enhance enterprises’ ability to resist breaches of immunity. In summary, research has indicated that an enterprise’s intrinsic ability to recognize risks to its own survival is equivalent to an immune system’s ability to recognize threats to the body’s health. Dai and Ding [68] draw on the basic ideas of immune theory in their analysis of the relationships between organizational immunity and the internal control of an enterprise. Based on their findings, they design an internal control evaluation indicator system and construct an evaluation model, which has broadened the research thoughts in the field.

Scholars have expressed concern about the application of immune theory in the field of quality management. The scope of its application remains very limited, and the existing research has not been in depth. At present, the domestic and international investment in the effort to understand quality management as an artificial immune system is insufficient. Few independent empirical analyses have focused on fusing the concept of organizational immunity with quality management. Theoretical and empirical research and evaluations of organizational quality management and organizational quality-specific immunity are relatively rare. Further, no studies have specifically used organizational quality-specific immunity to determine evaluation criteria in conjunction with integration methods and bilateral matching decision-making models based on BMIHFIBPT to solve the problem, on both the supply and demand sides, of matching manufacturing enterprises for cooperation.

3. Evaluation Indicator System Construction of Organizational Quality-Specific Immunity

Organizational quality-specific immunity reduces quality fluctuation and quality loss, addressing present and potential quality problems. Metaphorically, it can fight a stubborn disease, eliminate the virus, and generate the antigens to protect quality, in the longer term ensuring the re-activation and effectiveness of quality-protecting antibodies. Considering the function of organizational quality-specific immunity, and based on the relevant theories and previous literature review [63,64,65,66,67,68], the present study selects the following components for its evaluation indicator system: organizational quality monitoring and cognition; organizational quality defence, clearance, and repair (both hard and soft features); and organizational quality memory and immune self-stability. These components correspond to the respective scales and evaluation indicators shown in

Table 1. Evaluation indicator system for organizational quality-specific immunity.

Construction Dimension		Scales and Evaluation Indicators
Organizational quality monitoring and cognition		External environmental monitoring of organizational quality
		Internal environmental monitoring of organizational quality
		Internal activities and behaviour monitoring of organizational quality
		Value judgement
		Cognitive motivation (intrinsic motivation, extrinsic motivation)
		Cognitive diversity
Organizational quality defence, clearance, and repair	Organizational quality defence, clearance, and repair of soft features	Leadership
		Employee participation
		Supplier relationship management
		Customer request
	Organizational quality defence, clearance, and repair of hard features	Product design
		Process management
		Statistical control and feedback
Organizational quality memory and immune self-stability		Learning
		Record
		Summary
		Save
		Spread and diffusion
		Communication control and supervision

.

4. Bilateral Matching Decision-Making Models Based on Interval-Valued Hesitant Fuzzy Information and Bidirectional Projection Technology (BMIHFIBPT)

In recent years, multi-criteria decision making has been widely used in the field of economic and management [69,70,71,72,73,74,75,76,77,78,79]. Bilateral matching decision making is an important branch of multi-criteria decision making. In bilateral matching (two-sided matching), two subjects (with different finite sets) are matched by a specific algorithm to each other in order to achieve the satisfaction of both parties [80,81,82,83,84]. At present, bilateral matching decision making is becoming an important component of management decision theory. Many economic and management activities entail matching one or more members of two groups, such as the matching of venture capital parties with start-ups [85,86,87]. Roth [88] first proposed the concept of bilateral matching in a study of marriage matching, in which Roth analyses actual cases of bilateral matching. Bilateral matching decision-making theory has since received extensive attention from scholars. Fan and Yue [17] consider the highest acceptability order of bilateral subjects and propose a strict bilateral matching decision-making method based on the complete preference information. Chen et al. [89] examine the dynamic matching decision-making problem based on uncertainty preference sequence information. On the basis of the theory of constructing the ordinal deviation, they apply the evidence fusion method to solve the problem with the help of uncertainty preference sequence information.

However, because the evaluation information of both subjects is uncertain, and because the decision-making environment and situation are complex, the subjects’ preference information is often hesitant, fuzzy, and vague [90]. Therefore, how to overcome the lack of decision-making information is a problem worthy of attention. Interval-valued hesitant fuzzy sets have excellent expressive advantages in dealing with hesitant fuzzy information [90]. The present study therefore utilizes interval-valued hesitant fuzzy sets and bidirectional projection technology to measure fuzzy information and effectively solve the problem of bilateral matching decision making. The bilateral matching decision-making method used in this study firstly deals with the interval-valued hesitant fuzzy preference information. It then adopts the bidirectional projection technology to obtain the vector projection formed by different intervals. The TOPSIS method is also used to obtain the closeness of match, which can express the preference of both subjects. Finally, the optimization model is constructed. We then incorporate the closeness into the optimization model to solve the problem.

In our hesitant and fuzzy environment, sets $A_p\left(p=2,3,\dots ,m\right)$$$ and $B_q\left(q=2,3,\dots ,n\right)$ represent manufacturing enterprises in the manufacturing supply chain. Manufacturing enterprises in these sets all want partners in the supply chain. Manufacturing enterprises in set $A_p\left(p=2,3,\dots ,m\right)$ want to select a partner with suitable partners in the scope of set $B_q\left(q=2,3,\dots ,n\right)$. Set $X$ is a non-empty set, such that $R=\left\{\langle x,g_R\left(x_i\right)\rangle |x_i\in X,i=1,2,\dots ,n\right\}$ refers to interval-valued hesitant fuzzy sets (IVHFSs) in $X$. $g_R\left(x_i\right)$ refers to interval-valued hesitant fuzzy elements (IVHFEs). The element $x$ is from the scope of $X$, which belongs to the membership degree of $R$. $l$ is the number and quantity of elements in interval-valued hesitant fuzzy elements. Manufacturing enterprises in set $A_p\left(p=2,3,\dots ,m\right)$ in the manufacturing supply chain present interval-valued hesitant fuzzy preference evaluation information for the potential partners (manufacturing enterprises in set $B_q\left(q=2,3,\dots ,n\right)$). That information forms interval-valued hesitant fuzzy preference matrix $G={\lfloor g_{ij}\rfloor }_{m*n}$. Correspondingly, the potential partners (manufacturing enterprises in set $B_q\left(q=2,3,\dots ,n\right)$ present interval-valued hesitant fuzzy preference evaluation information for manufacturing enterprises in set $A_p\left(p=2,3,\dots ,m\right)$, and that information forms interval-valued hesitant fuzzy preference matrix $H={\lfloor h_{ij}\rfloor }_{n*m}$ [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100].

(1)

The construction of bilateral matching decision-making models of partners of manufacturing enterprises based on BMIHFIBPT integration methods

The main model construction principles, procedures, and steps of the bilateral matching decision-making models of partners of manufacturing enterprises based on BMIHFIBPT integration methods are as follows [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]:

The interval-valued hesitant fuzzy decision matrix is normalized by the obtained interval-valued hesitant fuzzy information and assembled by the bidirectional projection method to ensure scientific and effective results.

Assuming $G^{\prime }={\left[g^{\prime }{}_{ij}\right]}_{m\times n}$ as a standardized interval-valued hesitant fuzzy decision matrix, the positive and negative ideal fuzzy elements are $g^{+}=(g_1^{+},g_2^{+},\cdots ,g_l^{+})$ and $g^{-}=(g_1^{-},g_2^{-},\cdots ,g_l^{-})$ respectively.

$$\begin{array}{l}{g}^{+}=(g_1^{+},g_2^{+},\cdots ,g_l^{+})=(<[{\gamma }_1^{L^{+}},{\gamma }_1^{U^{+}}],[{\gamma }_2^{L^{+}},{\gamma }_2^{U^{+}}],\cdots ,[{\gamma }_l^{L^{+}},{\gamma }_l^{U^{+}}]>)\\ =(<[\underset{1\le i\le m}{\max {\gamma }_{i1}^L,}\underset{1\le i\le m}{\max {\gamma }_{i1}^U}],[\underset{1\le i\le m}{\max {\gamma }_{i2}^L,}\underset{1\le i\le m}{\max {\gamma }_{i2}^U}],\cdots ,[\underset{1\le i\le m}{\max {\gamma }_{il}^L,}\underset{1\le i\le m}{\max {\gamma }_{il}^U}]\end{array}$$

(1)

$$\begin{array}{l}{g}^{-}=(g_1^{-},g_2^{-},\cdots ,g_l^{-})=(<[{\gamma }_1^{L^{-}},{\gamma }_1^{U^{-}}],[{\gamma }_2^{L^{-}},{\gamma }_2^{U^{-}}],\cdots ,[{\gamma }_l^{L^{-}},{\gamma }_l^{U^{-}}]>)\\ =(<[\underset{1\le i\le m}{\min {\gamma }_{i1}^L,}\underset{1\le i\le m}{\min {\gamma }_{i1}^U}],[\underset{1\le i\le m}{\min {\gamma }_{i2}^L,}\underset{1\le i\le m}{\min {\gamma }_{i2}^U}],\cdots ,[\underset{1\le i\le m}{\min {\gamma }_{il}^L,}\underset{1\le i\le m}{\min {\gamma }_{il}^U}]\end{array}$$

(2)

Let ${\mathrm{g}}_p$ and ${\mathrm{g}}_q$ be two interval-valued hesitant fuzzy elements after standardization $(IVHFE)$, so $g_p=(<[{\gamma }_{p1}^L,{\lambda }_{p1}^U],[{\gamma }_{p2}^L,{\lambda }_{p2}^U],\cdots ,[{\gamma }_{pl}^L,{\lambda }_{pl}^U]>)$, and $g_q=(<[{\gamma }_{q1}^L,{\lambda }_{q1}^U],[{\gamma }_{q2}^L,{\lambda }_{q2}^U],\cdots ,[{\gamma }_{ql}^L,{\lambda }_{ql}^U]>)$. Then, the correlation coefficients of ${\mathrm{g}}_p$ and ${\mathrm{g}}_q$ are:

$$K_{IVHFE}(g_p,g_q)=\frac{C_{IVHFE}(h_p,h_q)}{\sqrt{E_{IVHFE}(h_p)}\times \sqrt{E_{IVHFE}(h_q)}}$$

(3)

where:

$$C_{IVHFE}(h_p,h_q)=\frac{1}{2}{\displaystyle \sum _{i=1}^l({\gamma }_{pi}^L}{\gamma }_{qi}^L+{\gamma }_{pi}^U{\gamma }_{qi}^U)$$

(4)

$$E_{IVHFE}(h_p)=\frac{1}{2}{\displaystyle \sum _{i=1}^l[{({\gamma }_{pi}^L)}^2+{({\gamma }_{pi}^U)}^2]}$$

(5)

$$E_{IVHFE}(h_q)=\frac{1}{2}{\displaystyle \sum _{i=1}^l[{({\gamma }_{qi}^L)}^2+{({\gamma }_{qi}^U)}^2]}$$

(6)

The vector formed by the interval-valued hesitant fuzzy elements ${\mathrm{g}}_p$ and ${\mathrm{g}}_q$ are:

$$h_p{h}_q=(<[\min {\gamma }_1^L,\max {\gamma }_1^U],[\min {\gamma }_2^L,\max {\gamma }_2^U],\cdots ,[\min {\gamma }_l^L,\max {\gamma }_l^U]>)$$

(7)

where:

$$\min {\gamma }_i^L=\min (\left|{\gamma }_{qi}^L-{\gamma }_{pi}^L\right|,\left|{\gamma }_{qi}^U-{\gamma }_{pi}^U\right|),\mathrm{and}\max {\gamma }_i^L=\max (\left|{\gamma }_{qi}^L-{\gamma }_{pi}^L\right|,\left|{\gamma }_{qi}^U-{\gamma }_{pi}^U\right|),i=1,2,\cdots ,n.$$

Let the interval-valued hesitant fuzzy element be $g^{\prime }$, the positive and negative ideal interval-valued hesitant fuzzy elements be $g^{+},g^{-}$, and the positive ideal interval-valued hesitant fuzzy element and negative ideal interval-valued hesitant fuzzy element be $g^{+}{g}^{-}$. The positive and negative ideal interval-valued hesitant fuzzy elements and interval-valued hesitant fuzzy elements form the vector $g^{\prime }{g}^{+}$, $g^{\prime }{g}^{-}$. Then, the bidirectional projection formed by $g^{\prime }{g}^{-}$ on $g^{+}{g}^{-}$ is:

$$\begin{array}{ll}{\mathrm{Pr}}_{g^{-}{g}^{+}}^{g^{-}{g}^{\prime }}& =\left|g^{-}{g}^{\prime }\right|K_{IVHFE}(g^{-}{g}^{\prime },g^{-}{g}^{+})\\ & =\frac{C_{IVHFE}(g^{-}{g}^{\prime },g^{-}{g}^{+})}{\sqrt{E_{IVHFE}(g^{-}{g}^{+})}}\end{array}$$

(8)

The bidirectional projection formed by $g^{+}{g}^{-}$ on $g^{\prime }{g}^{+}$ is:

$$\begin{array}{ll}{\mathrm{Pr}}_{g^{\prime }{g}^{+}}^{g^{-}{g}^{+}}& =\left|g^{-}{g}^{+}\right|K_{IVHFE}(g^{-}{g}^{+},g^{\prime }{g}^{+})\\ & =\frac{C_{IVHFE}(g^{-}{g}^{+},g^{\prime }{g}^{+})}{\sqrt{E_{IVHFE}(g^{\prime }{g}^{+})}}\end{array}$$

(9)

Based on the closeness formula of TOPSIS and other methods, the interval-valued hesitant fuzzy information is further assembled effectively, and the following formula is constructed:

$$D=\frac{{\mathrm{Pr}}_{h^{-}{h}^{+}}^{h^{-}{h}^{\prime }}}{{\mathrm{Pr}}_{h^{-}{h}^{+}}^{h^{-}{h}^{\prime }}+{\mathrm{Pr}}_{h^{\prime }{h}^{+}}^{h^{-}{h}^{+}}}$$

(10)

Thus, the principal matching closeness matrices of two-sided subjects $D_A={[a_{ij}]}_{m\times n}$ and $D_B={[b_{ij}]}_{m\times n}$ for matching are constructed.

(2)

The optimization solution of bilateral matching decision-making models of partners of manufacturing enterprises based on BMIHFIBPT integration methods

The main principles, procedures, and steps of the optimization solution of bilateral matching decision-making models of partners of manufacturing enterprises based on BMIHFIBPT integration methods are as follows [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]:

The bilateral matching decision-making optimization model is constructed based on the principal matching closeness matrices of two-sided subjects $D_A={[a_{ij}]}_{m\times n}$ and $D_B={[b_{ij}]}_{m\times n}$.

$$\begin{array}{l}\max Z={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m[\lambda (\frac{a_{ij}+b_{ij}}{2})+(1-\lambda )\sqrt{a_{ij}\times b_{ij}}]x_{ij}}}\\ s.t.{\displaystyle \sum _{j=1}^m{x}_{ij}\le 1,i=1,2,\cdots ,n}\\ {\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{x}_{ij}\le 1,j=1,2,\cdots ,m}\end{array}$$

(11)

where $x_{ij}$ is the 0–1 variable, $x_{ij}=0$ indicates that the two subjects do not match, and $x_{ij}=1$ indicates that the two subjects match each other. $\lambda$ is the adjustment parameter, $0\le \lambda \le 1$, and the value of $\lambda$ is determined by the specific needs of the actual problem. $\lambda =0$ and $\lambda =1$ indicate that the actual problem satisfies the preference consistency and complementarity, respectively. In this study, the combination of satisfaction matching analysis method is used to solve the optimization model.

$$c_{ij}=\lambda (\frac{a_{ij}+b_{ij}}{2})+(1-\lambda )\sqrt{a_{ij}\times b_{ij}},\lambda \in [0,1]$$

(12)

(3)

The processes of the bilateral matching decision-making model of partners of manufacturing enterprises based on BMIHFIBPT integration methods

The processes of the bilateral matching decision-making model of partners of manufacturing enterprises based on BMIHFIBPT integration methods are as follows [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]:

Step 1: Based on the matching subjects’ preference information, obtain the interval-valued hesitant fuzzy decision matrices $G={[g_{ij}]}_{m\times n}$ and $H={[h_{ij}]}_{n\times m}$ respectively.

Step 2: Use the optimistic criterion or the pessimistic criterion to consistently process the interval-valued hesitant fuzzy decision matrices G and H and arrange the order of the elements to obtain the normalized interval-valued hesitant fuzzy element matrices $G^{\prime }={[g^{\prime }{}_{ij}]}_{m\times n}$ and $H^{\prime }={[h^{\prime }{}_{ij}]}_{n\times m}$.

Step 3: Apply Equations (1) and (2) to construct the positive and negative ideal fuzzy elements $g^{+},g^{-}$ and $h^{+},h^{-}$ according to the normalized interval-valued hesitant fuzzy element matrix.

Step 4: Use Equations (8) and (9) to calculate the bidirectional projection matrices $G_{{}_1}^{*}={[{({\mathrm{Pr}}_{g^{-}{g}^{+}}^{g^{-}{g}^{\prime }})}_{ij}]}_{m\times n}$, $G_2^{*}={[{({\mathrm{Pr}}_{g^{\prime }{g}^{+}}^{g^{-}{g}^{+}})}_{ij}]}_{m\times n}$, and $H_{{}_1}^{*}={[{({\mathrm{Pr}}_{h^{-}{h}^{+}}^{h^{-}{h}^{\prime }})}_{ij}]}_{n\times m}$, $H_2^{*}={[{({\mathrm{Pr}}_{h^{\prime }{h}^{+}}^{h^{-}{h}^{+}})}_{ij}]}_{n\times m}$ respectively.

Step 5: Use Equation (10) to calculate the closeness and obtain the closeness matrices $D_A={[a_{ij}]}_{m\times n}$ and $D_B={[b_{ij}]}_{m\times n}$.

Step 6: Use Equation (11) to obtain the matching degree matrix $C={[c_{ij}]}_{m\times n}$ and further construct the optimization model.

Step 7: Use Lingo software to solve the optimization model and analyse the results to obtain bilateral matching decision-making schemes.

In summary, the bilateral matching decision-making model to help manufacturing enterprises choose partners based on BMIHFIBPT integration methods is shown in Figure 1.

5. Empirical Analysis

Quality management is the key means to ensuring the manufacturing supply chain continues to develop steadily. Therefore, as the main actors in the manufacturing supply chain, manufacturing enterprises place great emphasis on quality management in the production and operation management scope. With good quality management, products will satisfy customers and core competitiveness will improve, and the cooperation and partnerships among enterprises will become closer and closer. However, to achieve satisfactory matching results and make optimal decisions, managers must be able to identify the most mature enterprises, namely, those enterprises that have established and operate an organizational quality-specific immune system. In turn, managers must also be able to achieve bilateral matching between their own enterprise and these parties. To serve this aim, the present study selects 11 large-sized manufacturing enterprises in the eastern region of China as the evaluation targets. The selected manufacturing enterprises have a quality management system certification, are good at constructing immunity mechanisms to deal with quality risk events, and display an organizational quality-specific immunity performance that has placed them in leading positions in the same industry. The reputation, product market share, assets, profit, competitiveness, finances, production and operation management performance, rank, and scale of all these enterprises are typical and representative. All 11 manufacturing enterprises are state-owned and state-holding enterprises over 20 years old. We selected and invited 80 managers of the 11 manufacturing enterprises in total. All the managers have a master’s degree; have been working in a position in manufacturing enterprises for more than 20 years; and are familiar with quality management, production operation, and management of enterprises.

We collected data by extensive on-site questionnaire distribution, field interviews, and survey investigations. There are seven large-sized manufacturing enterprises ($A_1,A_2,A_3,A_4,A_5,A_6,A_7$) and four other large-sized manufacturing enterprises ($B_1,B_2,B_3,B_4$). All 11 manufacturing enterprises are seeking partners in the manufacturing supply chain with the aim of forming long-term cooperation relationships and close partnerships in the quality management scope. All the enterprises are also core actors in the same supply chain. Based on the organizational quality-specific immunity components (i.e., organizational quality monitoring and cognition; organizational quality defence, clearance, and repair, both soft and hard features; and organizational quality memory and immune self-stability), the evaluation indicator system for organizational quality-specific immunity is constructed. We use organizational quality-specific immunity to determine the evaluation criteria. Based on immune theory, organizational quality-specific immunity is the focus of the benchmarking reference system, decision-making scale, and basis. Organizational quality-specific immunity, as discussed above, is vital to both the supply and demand sides of manufacturing enterprises in the manufacturing supply chain. Therefore, it must be a central consideration in selecting optimal partners and in bilateral matching decision making.

The organizational quality-specific immunity components of the selected manufacturing enterprises are organizational quality monitoring and cognition; organizational quality defence, clearance, and repair (soft and hard features); and organizational quality memory and immune self-stability. Both parties completed a preference evaluation of the above evaluation indicators. Namely, all 80 senior managers of the manufacturing enterprises filled out the evaluation survey items and on-site evaluation questionnaires on their decision making with interval-valued hesitant fuzzy information and decision-making preferences according to the evaluation criteria of organizational quality-specific immunity. In the process of preference evaluation, the subjects’ preference information was often hesitant, fuzzy, and vague. By processing the interval-valued hesitant fuzzy information, we determined the best-matched manufacturing enterprises, i.e., the enterprise pairs with optimal cooperative and coordination potential.

Step 1: According to the preference information presented by both subjects, the interval-valued hesitant fuzzy preference matrices $G={[g_{ij}]}_{m\times n}$ and $H={[h_{ij}]}_{n\times m}$ are obtained, as shown in

Table 2. Interval-valued hesitant fuzzy preference matrix 1.

	${\mathit{B}}_1$	${\mathit{B}}_2$	${\mathit{B}}_3$	${\mathit{B}}_4$
$A_1$	$\{[0.3,0.4],[0.6,0.8]\}$	$\{[0.1,0.3],[0.5,0.6]\}$	$\{[0.3,0.5]\}$	$\{[0.5,0.7],[0.8,0.9]\}$
$A_2$	$\{[0.5,0.6]\}$	$\{[0.1,0.2],[0.4,0.5]\}$	$\{[0.2,0.4],[0.5,0.6],[0.7,0.8]\}$	$\{[0.4,0.5],[0.5,0.8]\}$
$A_3$	$\{[0.1,0.3],[0.3,0.6]\}$	$\{[0.3,0.4],[0.5,0.6]\}$	$\{[0.2,0.3],[0.4,0.6]\}$	$\{[0.3,0.5],[0.6,0.8]\}$
$A_4$	$\{[0.4,0.6],[0.8,0.9]\}$	$\{[0.2,0.3],[0.5,0.7]\}$	$\{[0.2,0.3],[0.6,0.8]\}$	$\{[0.5,0.6],[0.8,0.9]\}$
$A_5$	$\{[0.1,0.3],[0.2,0.4]\}$	$\{[0.7,0.8]\}$	$\{[0.1,0.2],[0.5,0.7]\}$	$\{[0.3,0.5]\}$
$A_6$	$\{[0.3,0.4],[0.7,0.9]\}$	$\{[0.4,0.7]\}$	$\{[0.6,0.7],[0.7,0.9]\}$	$\{[0.2,0.4],[0.7,0.8]\}$
$A_7$	$\{[0.2,0.3],[0.5,0.6]\}$	$\{[0.3,0.5],[0.8,0.9]\}$	$\{[0.3,0.4]\}$	$\{[0.5,0.7]\}$

and

Table 3. Interval-valued hesitant fuzzy preference matrix 2.

	${\mathit{A}}_1$		${\mathit{A}}_2$		${\mathit{A}}_3$		${\mathit{A}}_4$
$B_1$	$\{[0.4,0.5],[0.7,0.8]\}$		$\{[0.2,0.6]\}$		$\{[0.6,0.7]\}$		$\{[0.1,0.3],[0.4,0.5],[0.7,0.9]\}$
$B_2$	$\{[0.3,0.4],[0.6,0.8]\}$		$\{[0.1,0.2],[0.5,0.9]\}$		$\{[0.3,0.8]\}$		$\{[0.1,0.4],[0.5,0.7]\}$
$B_3$	$\{[0.1,0.2],[0.4,0.6]\}$		$\{[0.2,0.4],[0.6,0.7]\}$		$\{[0.2,0.5]\}$		$\{[0.1,0.2],[0.4,0.5],[0.5,0.7]\}$
$B_4$	$\{[0.3,0.5],[0.6,0.9]\}$		$\{[0.1,0.4],[0.5,0.7]\}$		$\{[0.6,0.7]\}$		$\{[0.5,0.6],[0.8,0.9]\}$
	${\mathit{A}}_{\mathbf{5}}$		${\mathit{A}}_{\mathbf{6}}$		${\mathit{A}}_{\mathbf{7}}$
$B_1$	$\{[0.2,0.3],[0.5,0.6]\}$		$\{[0.3,0.6]\}$		$\{[0.1,0.2],[0.3,0.4],[0.5,0.6]\}$
$B_2$	$\{[0.1,0.4],[0.7,0.8]\}$		$\{[0.7,0.8]\}$		$\{[0.2,0.3],[0.5,0.7]\}$
$B_3$	$\{[0.1,0.3],[0.4,0.5],[0.8,0.9]\}$		$\{[0.2,0.5]\}$		$\{[0.5,0.6],[0.7,0.8]\}$
$B_4$	$\{[0.2,0.4],[0.6,0.7]\}$		$\{[0.6,0.9]\}$		$\{[0.3,0.5],[0.8,0.9]\}$

.

Step 2: By consistently processing the lengths of the matrices $G$ and $H$, we arranged the order of the elements (this study uses the optimistic criteria to process the length) to obtain the normalized interval-valued hesitant fuzzy element matrices $G^{\prime }={[g^{\prime }{}_{ij}]}_{m\times n}$ and $H^{\prime }={[h^{\prime }{}_{ij}]}_{n\times m}$, as shown in

Table 4. Interval-valued hesitant fuzzy preference matrix 3.

	${\mathit{B}}_1$	${\mathit{B}}_2$	${\mathit{B}}_3$	${\mathit{B}}_4$
$A_1$	$\{[0.3,0.4],[0.6,0.8]\}$	$\{[0.1,0.3],[0.5,0.6]\}$	$\{[0.3,0.5],[0.3,0.5],[0.3,0.5]\}$	$\{[0.5,0.7],[0.8,0.9]\}$
$A_2$	$\{[0.5,0.6],[0.5,0.6]\}$	$\{[0.1,0.2],[0.4,0.5]\}$	$\{[0.2,0.4],[0.5,0.6],[0.7,0.8]\}$	$\{[0.4,0.5],[0.5,0.8]\}$
$A_3$	$\{[0.1,0.3],[0.3,0.6]\}$	$\{[0.3,0.4],[0.5,0.6]\}$	$\{[0.2,0.3],[0.4,0.6],[0.4,0.6]\}$	$\{[0.3,0.5],[0.6,0.8]\}$
$A_4$	$\{[0.4,0.6],[0.8,0.9]\}$	$\{[0.2,0.3],[0.5,0.7]\}$	$\{[0.2,0.3],[0.6,0.8],[0.6,0.8]\}$	$\{[0.5,0.6],[0.8,0.9]\}$
$A_5$	$\{[0.1,0.3],[0.2,0.4]\}$	$\{[0.7,0.8],[0.7,0.8]\}$	$\{[0.1,0.2],[0.5,0.7],[0.5,0.7]\}$	$\{[0.3,0.5],[0.3,0.5]\}$
$A_6$	$\{[0.3,0.4],[0.7,0.9]\}$	$\{[0.4,0.7],[0.4,0.7]\}$	$\{[0.6,0.7],[0.7,0.9],[0.7,0.9]\}$	$\{[0.2,0.4],[0.7,0.8]\}$
$A_7$	$\{[0.2,0.3],[0.5,0.6]\}$	$\{[0.3,0.5],[0.8,0.9]\}$	$\{[0.3,0.4],[0.3,0.4],[0.3,0.4]\}$	$\{[0.5,0.7],[0.5,0.7]\}$

and

Table 5. Interval-valued hesitant fuzzy preference matrix 4.

	${\mathit{A}}_1$	${\mathit{A}}_2$		${\mathit{A}}_3$		${\mathit{A}}_4$
$B_1$	$\{[0.4,0.5],[0.7,0.8]\}$	$\{[0.2,0.6],[0.2,0.6]\}$		$\{[0.6,0.7]\}$		$\{[0.1,0.3],[0.4,0.5],[0.7,0.9]\}$
$B_2$	$\{[0.3,0.4],[0.6,0.8]\}$	$\{[0.1,0.2],[0.5,0.9]\}$		$\{[0.3,0.8]\}$		$\{[0.1,0.4],[0.5,0.7],[0.5,0.7]\}$
$B_3$	$\{[0.1,0.2],[0.4,0.6]\}$	$\{[0.2,0.4],[0.6,0.7]\}$		$\{[0.2,0.5]\}$		$\{[0.1,0.2],[0.4,0.5],[0.5,0.7]\}$
$B_4$	$\{[0.3,0.5],[0.6,0.9]\}$	$\{[0.1,0.4],[0.5,0.7]\}$		$\{[0.6,0.7]\}$		$\{[0.5,0.6],[0.8,0.9],[0.8,0.9]\}$
	${\mathit{A}}_{\mathbf{5}}$		${\mathit{A}}_{\mathbf{6}}$		${\mathit{A}}_{\mathbf{7}}$
$B_1$	$\{[0.2,0.3],[0.5,0.6],[0.5,0.6]\}$		$\{[0.3,0.6]\}$		$\{[0.1,0.2],[0.3,0.4],[0.5,0.6]\}$
$B_2$	$\{[0.1,0.4],[0.7,0.8],[0.7,0.8]\}$		$\{[0.7,0.8]\}$		$\{[0.2,0.3],[0.5,0.7],[0.5,0.7]\}$
$B_3$	$\{[0.1,0.3],[0.4,0.5],[0.8,0.9]\}$		$\{[0.2,0.5]\}$		$\{[0.5,0.6],[0.7,0.8],[0.7,0.8]\}$
$B_4$	$\{[0.2,0.4],[0.6,0.7],[0.6,0.7]\}$		$\{[0.6,0.9]\}$		$\{[0.3,0.5],[0.8,0.9],[0.8,0.9]\}$

.

Step 3: We use Equations (1)–(7) to construct positive and negative ideal fuzzy elements $g^{+},g^{-}$ and $h^{+},h^{-}$, respectively, according to the normalized interval-valued hesitant fuzzy element matrix:

$$\begin{array}{l}{g}^{+}=(\{[0.5,0.6],[0.8,0.9]\},\{[0.7,0.8],[0.8,0.9]\},\{[0.6,0.7],[0.7,0.9],\\ [0.7,0.9]\},\{[0.5,0.7],[0.8,0.9]\})\end{array}$$

$$\begin{array}{l}{g}^{-}=(\{[0.1,0.3],[0.2,0.4]\},\{[0.1,0.2],[0.4,0.5]\},\{[0.1,0.2],[0.3,0.4],\\ [0.3,0.4]\},\{[0.2,0.4],[0.3,0.5]\})\end{array}$$

$$\begin{array}{l}{h}^{+}=(\{[0.4,0.5],[0.7,0.9]\},\{[0.2,0.6],[0.6,0.9]\},\{[0.6,0.8]\},\{[0.5,0.6],[0.8,0.9],\\ [0.8,0.9]\},\{[0.2,0.4],[0.7,0.8],[0.8,0.9]\},\{[0.7,0.9]\},\{[0.5,0.6],[0.8,0.9],[0.8,0.9]\})\end{array}$$

$$\begin{array}{l}{h}^{-}=(\{[0.1,0.2],[0.4,0.6]\},\{[0.1,0.2],[0.2,0.6]\},\{[0.2,0.5]\},\{[0.1,0.2],[0.4,0.5],\\ [0.5,0.7]\},\{[0.1,0.3],[0.4,0.5],[0.5,0.6]\},\{[0.2,0.5]\},\{[0.1,0.2],[0.3,0.4],[0.5,0.6]\})\end{array}$$

Step 4: We use Equations (8) and (9) to calculate the bidirectional projection matrices $G_{{}_1}^{*}={[{({\mathrm{Pr}}_{g^{-}{g}^{+}}^{g^{-}{g}^{\prime }})}_{ij}]}_{m\times n}$, $G_2^{*}={[{({\mathrm{Pr}}_{g^{\prime }{g}^{+}}^{g^{-}{g}^{+}})}_{ij}]}_{m\times n}$, and $H_{{}_1}^{*}={[{({\mathrm{Pr}}_{h^{-}{h}^{+}}^{h^{-}{h}^{\prime }})}_{ij}]}_{n\times m}$, $H_2^{*}={[{({\mathrm{Pr}}_{h^{\prime }{h}^{+}}^{h^{-}{h}^{+}})}_{ij}]}_{n\times m}$ respectively.

$$G_1^{*}=\left[\begin{array}{l}0.4190.0970.2150.543\\ 0.4040.0710.4250.295\\ 0.1300.2230.2340.304\\ 0.6250.1660.4550.516\\ 0.0160.6650.2830.083\\ 0.5030.3880.8120.295\\ 0.2440.4300.1230.331\end{array}\right]$$

$$G_2^{*}=\left[\begin{array}{l}0.6080.7160.7820.063\\ 0.5500.7210.7130.511\\ 0.6440.7200.8060.510\\ 0.2830.6950.6840.212\\ 0.6560.4000.7490.535\\ 0.5890.6200.0810.427\\ 0.6360.5940.7920.451\end{array}\right]$$

$$H_1^{*}=\left[\begin{array}{l}0.3890.1850.5190.1130.0800.1050.023\\ 0.2830.2300.3540.1610.3560.4090.255\\ 0.1790.3060.2670.1240.2060.2830.594\\ 0.3540.2510.5190.6200.2290.3980.622\end{array}\right]$$

$$H_2^{*}=\left[\begin{array}{l}0.2120.3540.2830.5850.4220.4530.707\\ 0.4240.3500.2850.5940.2860.3540.682\\ 0.4260.4000.3540.6200.3160.4530.567\\ 0.3000.4470.7050.3190.4020.3530.392\end{array}\right]$$

Step 5: We use Equation (10) to calculate the closeness and obtain the closeness matrices $D_A={[a_{ij}]}_{m\times n}$ and $D_B={[b_{ij}]}_{m\times n}$.

$$D_A^{}=\left[\begin{array}{l}0.4080.1190.2160.896\\ 0.4230.0900.3730.366\\ 0.1680.2360.2250.370\\ 0.6880.1930.4000.709\\ 0.0240.6240.2740.134\\ 0.4610.3850.9100.409\\ 0.2770.4200.1350.424\end{array}\right]D_B^{}=\left[\begin{array}{l}0.6470.4030.2960.541\\ 0.3430.3970.4330.360\\ 0.6570.5540.4300.424\\ 0.1620.2130.1670.660\\ 0.1590.5650.3950.363\\ 0.1880.5360.3850.530\\ 0.0320.2720.5120.613\end{array}\right]$$

Step 6: We use Equation (11) to obtain the matching degree matrix $C={[c_{ij}]}_{m\times n}$ and further construct the optimization model.

$$\eta =\left[\begin{array}{l}0.5140.2190.2530.696\\ 0.3810.1890.4020.363\\ 0.3320.3620.3110.396\\ 0.3340.2030.2580.684\\ 0.0620.5940.3290.221\\ 0.2940.4540.5920.466\\ 0.0940.3380.2630.510\end{array}\right]$$

Step 7: We bring the matching degree matrix $\eta$ into the optimization model (11), further solving and obtaining the optimization model with the help of Lingo software:

$$X_{11}=1,X_{12}=0,X_{13}=0,X_{14}=0,X_{21}=0,X_{22}=0,X_{23}=0,X_{24}=0,X_{31}=0,X_{32}=0,X_{33}=0,X_{34}=0,X_{41}=0,X_{42}=0,X_{43}=0,X_{44}=1,X_{51}=0,X_{52}=1,X_{53}=0,X_{54}=0,X_{61}=0,X_{62}=0,X_{63}=1,X_{64}=0,X_{71}=0,X_{72}=0,X_{73}=0,X_{74}=0.$$

The results are as follows: $A_1\leftrightarrow B_1$, $A_4\leftrightarrow B_4$, $A_5\leftrightarrow B_2$, $A_6\leftrightarrow B_3$, and for the manufacturing enterprises $A_2$, $A_3$, and $A_7$, there are no suitable manufacturing enterprises to match.

6. Conclusions and Discussion

6.1. Conclusions

Decision-making science has undergone continuous development and improvement and is now widely used in many different fields. This study, taking immune theory as a starting point, has applied decision-making science to the organizational quality management field in the context of manufacturing enterprises. The study constructs an evaluation indicator system for organizational quality-specific immunity. The components of organizational quality-specific immunity act as the evaluation criteria. This study further integrates interval-valued hesitant fuzzy information and bidirectional projection technology into bilateral matching decision making, constructing the bilateral matching evaluation and decision-making models based on interval-valued hesitant fuzzy information and bidirectional projection technology (BMIHFIBPT). To use the interval-valued hesitant fuzzy evaluation information to solve the combination satisfaction and matching optimization model, we apply the score formation of left interval value and right interval value, the interval-valued hesitant fuzzy preference, the interval-valued hesitant fuzzy decision-making matrices, the interval-valued hesitant fuzzy elements and closeness, and the interval-valued bilateral fuzzy bidirectional projection technology. We conduct empirical analysis to reflect the supply and demand sides of representative manufacturing enterprises in the manufacturing supply chain, match the main bodies of two parties and subjects, and help manufacturing enterprises achieve optimal bilateral matching. The empirical analysis results indicate that bilateral matching decision-making models that incorporate interval-valued hesitant fuzzy information and bidirectional projection technology (BMIHFIBPT) via integration methods can offer the following: a bilateral matching evaluation and decision-making process for both supply- and demand-side partners; interval-valued hesitant fuzzy evaluation and decision information; and bidirectional projection technology, which possesses the consistency, feasibility, operability, and rationality to solve the interval-valued hesitant fuzzy decision-making problems. Thus, this study provides a basis for manufacturing enterprises in the manufacturing supply chain area to effectively select the best partners based on organizational quality-specific immunity. Bilateral matching evaluation and decision-making models and methods are embedded to provide a reference for manufacturing enterprises to make optimal decisions. These models and methods offer effectiveness, accuracy, robustness, and convenience in selecting the optimal supply–demand matching relationships, determining coordination and cooperation partners on the basis of organizational quality-specific immunity, and achieving satisfactory matching evaluation and optimal coupling decisions by operating the organizational quality-specific immune system.

6.2. Discussion

Bilateral subjects usually give vague, fuzzy, and hesitant preference information [90]. This vague, fuzzy, and hesitant ambiguity emerges in the process of bilateral matching decision making as well [89,90,91,92,93,94]. The ability to deal with vague, fuzzy, and hesitant ambiguity in bilateral matching decision making has important theoretical value and practical significance. Using the methods and models of the relevant literature [36,37,38,39,40,41,42,43], consistent empirical research results and bilateral matching decision-making results were obtained. Compared with existing studies [44,45,46,47,48,49,50], the present study offers the following advantages due to its research methods and models: First, the bilateral matching decision-making models and the methods based on interval-valued hesitant fuzzy information and bidirectional projection technology are different from the bilateral matching decision-making models and methods based on complete preference order information, which effectively help determine the evaluation criteria of organizational quality-specific immunity. The bilateral matching decision-making methods based on interval-valued hesitant fuzzy information and bidirectional projection are determined by the interval-valued hesitant fuzzy information given by the subjects; these methods build on existing methods [44,45,46]. After processing the length of the interval-valued hesitant fuzzy decision matrix and arranging the order of elements, the normalized interval-valued hesitant fuzzy element matrix is obtained, and the positive and negative ideal fuzzy elements are constructed. The bidirectional projection value matrix is calculated using bidirectional projection technology, and reference is made to TOPSIS. The TOPSIS method is used to calculate the closeness and obtain the closeness matrix. The satisfaction and matching optimization model is thus solved, and the best solution is obtained. Through empirical analysis, this study indicates that the bi-level and bidirectional projection decision-making method with interval-valued hesitant fuzzy information and bidirectional projection technology can solve the problem of matching enterprises on both the demand and supply sides based on organizational quality-specific immunity components. The method, in other words, can select optimal and sustainable partners for representative manufacturing enterprises in the manufacturing supply chain on the basis of organizational quality-specific immunity. The research results show that bilateral matching evaluation models can be achieved using integration methods and bilateral matching decision-making methods that incorporate interval-valued hesitant fuzzy information and bidirectional projection technology based on a biological perspective and an empirical point of view.

With the help of analogy, we can use immune theory to map the operations of organizational quality management and, as a result, generate an understanding of how to achieve organizational quality-specific immunity. There is potential for further application of interval-valued hesitant fuzzy information in decision-making problems in the field of organizational quality management. The results of the present empirical analysis in the field of organizational quality management drew on immune theory, which offers new ideas and methodological systems. The organizational quality-specific immunity evaluation criteria, based on the results, can also inform theoretical frameworks to help manufacturing enterprises effectively select partners based on organizational quality-specific immunity with a view to forming close and long-term relationships in the manufacturing supply chain.

6.3. Research Limitations and Prospects

This study is only a preliminary exploration of the application of interval-valued hesitant fuzzy information and bidirectional projection technology to find optimal partners for manufacturing enterprises in the manufacturing supply chain based on organizational quality-specific immunity. The proposed bilateral (two-sided) matching decision-making models that incorporate interval-valued hesitant fuzzy information and bidirectional projection technology via integration methods are only evaluation instruments; they are only part of an approach for the selection of optimal partners of manufacturing enterprises. While the models will ensure the suitability of two partners, the models do not offer an explanation in terms of other partners and subjects in the manufacturing supply chain. The original data on which the models are based were mainly derived from the subjective responses of manufacturing enterprises’ managers gathered via on-site questionnaire distribution, field interviews, and survey investigations. In future research, we will carry out longitudinal tracking in order to obtain longitudinal tracking time series data with the aim of combining objective data with subjective data for the models and methods. Incorporating objective data, as well as introducing more partners and subjects of manufacturing enterprises in the manufacturing supply chain, will further improve the proposed bilateral matching decision-making models based on the evaluation criteria of organizational quality-specific immunity.