# Sustainable Strategic Alliance Partner Selection Using a Neutrosophic-Based Decision-Making Model: A Case Study in Passive Component Manufacturing

Authors: Huai-Wei Lo; Dong-Shang Chang; Lee-Te Huang
Journal: Complexity
 (2022)

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## Abstract

The electronics manufacturing industry is in an era of collaborative thinking and rapid change, as the rise of strategic alliances (SAs) plays a critical role in supply chain management. Strategic alliance (SA) collaboration is one of the most common strategies in the electronics industry, helping companies to complement each other. Most organizations or alliances operate together to produce more beneficial technologies for mutual benefit based on the sustainability thinking, such as in the areas of 5G, electric vehicles, aerospace, and smart healthcare. As the prompt evolution of information technology and electronics has a deep impact on global business activities, selecting partners based on a sustainability perspective is an urgent task. This paper proposes a complete sustainable SA partner selection framework to select the optimal partners. A neutrosophic-based decision-making model is used in the analysis. The neutrosophic ITARA technique is proposed to generate a set of criteria objective weights, and the neutrosophic TOPSIS technique is applied to determine the performance and priority of sustainable SA partners. This study introduces neutrosophic fuzzy logic to reflect the uncertainty in complex problems. Real-world data from a multinational passive component manufacturing company are used for case demonstration and analysis. The framework and methodology proposed in this study have many contributions to the electronics industry, including the establishment of assessment criteria, the identification of criteria, and the provision of partner selection practices. For academic research, the proposed model can be replicated in other areas of assessment and selection issues.


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## Body

## 1. Introduction

Due to the lack of material, financial, technical, or managerial resources, companies form alliances with other organizations to collaborate so that they can share resources with each other and promote sustainable development [1]. However, many studies have illustrated the functions, benefits, risks, or developmental limitations of business alliances [2]. Chang et al. [3] state that the goal of strategic alliances (SAs) is to integrate the strengths or resources of multiple companies so that supply chain management systems can realize resource sharing and market diversification. Gnyawali and Ryan Charleton [4] show that the benefits that companies gain from alliances include new functions, skills, and knowledge resources. On the other hand, through the formation of alliances, it is possible to obtain access to new products and market opportunities that they cannot obtain internally. In general, the formation of SAs involves formal legal or private informal partnerships where supply chain partners can assist each other’s strengths and weaknesses in order to decrease the operational risks of the companies.In a highly competitive global market, companies are increasingly using SAs and acquisitions and mergers to acquire external knowledge (e.g., Toyota with Mazda, Panasonic, and SoftBank). As a result, SAs are also seen as a means of accumulating resources and participating in the codevelopment of technologies, products, systems, and services. Understanding the factors that contribute to successful SAs among organizations has become an important field of inquiry among practitioners and researchers [5]. With the current boom in new technologies such as 5G, electric vehicles, aerospace, smart healthcare, and Industry 4.0, many electronics manufacturing industries are forming SAs to develop these areas together.Different from the general manufacturing industry, the electronics manufacturing industry is classified as one of the energy-intensive industries (EIIs), and the electronic component manufacturing industry is one of its subsectors. The “electronic component manufacturing industry” is upstream of various computer and information industries, following the electronic component research and development and design industries, and is engaged in the manufacture of basic components for computer, communication, information, home electronic equipment, and other related products, and can be divided into four categories according to product characteristics: semiconductor manufacturing, passive electronic component manufacturing, printed circuit board manufacturing, and other electronic component manufacturing [6, 7]. Taiwan’s electronic component manufacturing industry has developed early and has a complete upstream, midstream, and downstream all-inclusive industrial chain. The upstream side (raw materials) includes ceramic substrates, alumina substrates, conductive pastes, and electrode metals. The midstream side (manufacturing) includes resistors, capacitors, and inductors. The downstream side (product application) includes modems, gateways, routers, and hubs. In the process of business development, various strategies can be successful or unsuccessful at different stages. How to maintain a competitive advantage and continue to grow is the most important issue for business survival.However, while the electronic component manufacturing industry has brought the development of economic and industrial clusters to the region, the negative emissions and waste from production activities can cause environmental damage [6]. As international organizations and environmental groups become more conscious of sustainability, many economic, environmental, and social criteria and regulations are being developed to require companies to operate in a manner that minimizes negative impacts on the environment and people’s lives. If the notion of sustainable development is leaded into the selection of SA partners, energy consumption, harmful pollution, waste emissions, and corporate social responsibility (CSR) in the supply chain can be significantly controlled.Therefore, the sustainable performance of SA partners plays a key role in the administration of any industry. The selection of a sustainable SA partner is based on a set of sustainability criteria to assess the performance of the alliance partner in order to select the optimal partner to become a member of the supply chain. However, the assessment and selection process involves several complex criteria or indicators, and a multiple criteria decision-making (MCDM) is the most appropriate way to approach this issue. The main aims of this study can be divided into the following three items.(i)
To construct an assessment framework for sustainable SA partner selection.(ii)
To determine the discriminatory power of the criteria in the assessment system, i.e., the criteria weights.(iii)
To consolidate the performance of the alliance partners assessed and prioritize them.Since sustainable SA partner selection is a difficult and complex problem, it is difficult to use crisp value to reflect the actual feelings and judgments of experts. Therefore, neutrosophic fuzzy logic (here, single-valued trapezoidal neutrosophic numbers, SVTNNs is adopted) is introduced to reflect the ambiguity of the actual environment in the paper. Furthermore, the uncertainty of the experts in the assessment is measured by three parameters such as truth, falsity, and indeterminacy. The implementation process of this study can be divided into two phases: first, a framework for assessing the sustainability strategy of alliance partners in passive component manufacturing is proposed, which consists of six dimensions, which can be subdivided into 29 criteria. In the second phase, we develop a hybrid model based on neutrosophic theory, the neutrosophic ITARA technique to gain objective weights of sustainability criteria, and apply the neutrosophic TOPSIS technique to determine the performance and prioritization of sustainable SA partners. Our proposed neutrosophic ITARA improves the practicality of original ITARA. Neutrosophic ITARA not only introduces the aspiration level (AL) concept into the ITARA calculation process but also uses neutrosophic fuzzy sets to interpret uncertainty information. In addition, the neutrosophic TOPSIS extends the concept of TOPSIS in determining the variation of each alternative with respect to the normalized reference ideal, using the ideal and nonideal solutions to map the relative position of each assessed item. The improved neutrosophic TOPSIS not only overcomes the practical limitations of TOPSIS but also facilitates the examination of the attributes where the assessed items are underperforming. The proposed model is valid and reliable for assessing sustainable SA partners. This study provides insight into which criteria are discriminatory to the assessment system, and the company or organization can focus on these criteria to strengthen them. In addition, the results of the neutrosophic TOPSIS can be used to observe which criteria are underperforming in their current state, and alternative partners can develop improvement strategies based on these underperforming criteria to enhance the sustainability performance of the organization. In short, this study has the following features and contributions:(i)
This paper proposes a sustainable SA partner assessment framework to discuss the selection of the passive component manufacturing partners. However, only a few studies have measured the performance of alternative partners from a perspective of substainability. The proposed framework incorporates the concept of sustainability to make the assessment framework more comprehensive.(ii)
The proposed model developed (integrated neutrosophic, ITARA, and TOPSIS) is novel since it has not been proposed in other partner selection studies. Neutrosophic ITARA can generate an objective set of criterion weights based on the assessed performance data of SA partners, and it does not require the release of a questionnaire for the pairwise comparison of criteria such as the analytic hierarchy process (AHP) and best-worst method (BWM). Moreover, neutrosophic TOPSIS improves on the original TOPSIS method and results in a more reliable ranking of alternative partners.(iii)
The research framework of this paper is reproducible and not limited to being used by any certain industry. Only minor adjustments to industry-appropriate assessment criteria are required.The structure and content of the other sections of this paper are described below. Section2 reviews the literature on SA partners and presents the proposed assessment framework system. Section 3 describes the methodology used in this study, which includes SVTNNs, neutrosophic ITARA, and neutrosophic TOPSIS. Section 4 illustrates the feasibility and effectiveness of the proposed model using a real case of a multinational passive component manufacturer. Section 5 discusses the advantages and contributions of this paper. Section 6 concludes the full discussion and provides future research directions.


## 2. Literature Review

SAs are an important form of cooperation among companies or organizations, and there is a lot of literature on the selection and assessment of the SA partners. By forming SAs, the partners can pool their strengths and existing resources to achieve their targets, reduce risks, share knowledge, and gain access to potential markets [8]. In the last two decades, the topics of SAs have extended from conceptual development to a more rigorous expert-based decision support system.However, despite the popularity of SAs across all industries and sectors, there are still a large number of failed alliance operations [3]. In addition to inherent risks, one of the most frequently cited reasons for alliance failure is incompatibility among partners. Selecting the suitable partners can generate important competitive advantages and enhance the chances of success of SA operations. Therefore, selecting the right SA partners is an important task in the performance of an industry alliance. Finding the right partners requires careful screening, which can be a time-consuming and complicated procedure. It also takes time to understand the expectations and goals of the partners. The following subsections present the proposed assessment framework and research gaps.


### 2.1. Proposed Sustainable SA Partner Assessment Framework

This section reviews a large body of past research on SA partners and develops an assessment framework by the collaboration of several experts in the field. The sustainable SA partner assessment framework proposed in this paper is based on a perspective of sustainability, with several key dimensions added to form a comprehensive and complete assessment system. The dimensions can be composed of economy resource (E), environmental protection (G), social (S), innovation capability (I), organizational management (O), and risk factor (R). The six dimensions can be subdivided into 29 criteria that adequately reflect the key factors of SA partners, as shown in Tables 1–6. Table 1 presents the criteria of economic sustainability, including firm size (E1), financial strength (E2), material cost/selling price (E3), mergers/acquisitions (E4), and joint investment (E5), which are highly related to corporate economic activity.Table 1
The economy resource dimension and its criteria.
DimensionCriterionDescriptionReferencesEconomy resource (E)Firm size (E1)Corporate capital, turnover, number of employees, and market share, among other factors.Elia et al. [19]; Padovani et al. [20]Financial strength (E2)Information on corporate assets and liabilities, profit and loss, solvency, internal controls, board of directors’ functions, and business status.Cardoni et al. [21]; Padovani et al. [20]Material cost/selling price (E3)All direct and indirect fixed and variable costs of materials, labor, equipment, plants, operations, marketing, and net/gross profit margins.Gaustad et al. [22]; Lo et al. [7]Mergers/acquisitions (E4)Assessing whether the company can merge with other companies or has the value to do so.Yu et al. [23]; Cacciolatti et al. [12]Joint investment (E5)The willingness of the companies to invest their respective existing and superior resources in the joint venture in order to achieve joint capital, shared risk, and shared revenue.Cacciolatti et al. [12]; Vendrell-Herrero et al. [24]Table 2
The environmental protection dimension and its criteria.
DimensionCriterionDescriptionReferencesEnvironmental protection (G)Environmental certification (G1)The company should comply with the environmental regulations of international organizations and governments and obtain several environmental certifications and certificates.Thorne et al. [9]; Ge et al. [10]Green resource integration (G2)The company should respect the natural environment and protect the ecology in the green production system.Huang and Li [11]Pollution discharge treatment (G3)The company should actively implement environmental policies to reduce pollutant emissions and improve the efficiency of its energy use.Chang et al. [3]Clean energy use (G4)The company should strive to develop efficient and clean technologies for the production of passive components and promote the use of energy that does not pollute the environment.Cacciolatti et al. [12]Recycling/renewable capacity (G5)In the R&D and production process, enterprises should stress the importance of the recycling and reclamation of materials and consumables.D’Amato et al. [13]Table 3
The social dimension and its criteria.
DimensionCriterionDescriptionReferencesSocial (S)Worker education and safety and health (S1)Attaching importance to the education, training, and physical health of our employees. The work environment controls the concentration of harmful substances and measures the ergonomics of workers’ actions.Mani et al. [30]; Gul [31]Information sharing (S2)The company in the SA partnership can publish all production process information in a timely and accurate manner on a common information platform.Russo and Cesarani [32]; Lee [33]Social contribution (S3)The company should serve the public selflessly and assume greater CSR. The company shall comply with ethical norms and promote economic development in order to improve social well-being and improve the quality of life of society.Muñoz and Kimmitt [34]; Chang et al. [3]Stakeholders’ rights protection (S4)Valuing the interests and rights of SA partners and all stakeholders in the supply chain.Bhaumik et al. [35]; Nguyen et al. [36]Local employment opportunities (S5)The company can bring more employment opportunities to local residents and promote fairness to maintain the employment rights of people.Fernando et al. [37]; Burke and Stephens [38]Table 4
The innovation capability dimension and its criteria.
DimensionCriterionDescriptionReferencesInnovation capability (I)Core technical patent (I1)The company currently holds patents of key core technologies. The strategy of developing patents is to develop potential markets to ensure the company’s competitive advantage.Sun et al. [25]Product’s life cycle (I2)The company develops products that go through an introductory phase, a growth phase, a maturity phase, and a decline phase. Usually, companies expect to produce products with a longer life cycle.da Costa et al. [26]Manufacturing process capability (I3)Under fixed production conditions and stable control, whether the company’s manufacturing process matches the quality required by customers.Gunasekaran et al. [27]R&D capability (I4)Whether the company has the leading technologies and knowledge based on R&D, a clear understanding of market needs, and the ability to innovate products.Martínez-Noya and Narula [28]Supply chain integration (I5)The company’s ability to integrate the supply chain, including all product processes such as incoming materials, production, inventory, and sales.Nguyen and Tran [29]Table 5
The organizational management dimension and its criteria.
DimensionCriterionDescriptionReferencesOrganizational management (O)Trust and commitment (O1)A stable foundation for SA cohesion, trust, and termination penalties can be effective tools to motivate commitment and increase alliance effectiveness.Alaaraj et al. [14]Partners’ complementarity (O2)Different resources, capabilities and technologies can be integrated and managed to enhance the complementary nature of the SA.Mindruta et al. [15]; Hu et al. [16]Corporate branded image (O3)The perception and impression of the company’s brand fully reflect its values. The excellent brand image of the company increases profits and creates more channels to increase the market share of products.Singh et al. [17]CRM capability (O4)The service level of the company to meet the needs of customers. The main purpose is to use a high-performance information management system to analyze customer needs and process orders quickly.Aldaihani and Ali [18]Table 6
The risk factor dimension and its criteria.
DimensionCriterionDescriptionReferencesRisk factor (R)External legitimacy (R1)The company and alliance partners must obtain legalization from the local government before they can operate and trade in transnational economic organizations, and must avoid violating legal and criminal liabilities.Zhang et al. [39]Geographical fit (R2)When organizing economic activities in different regions, the company must evaluate cultural differences and business operations of the region in advance in order to avoid losses and reputational damage to the company.Huertas-García et al. [40]Collaborating stability (R3)The ambition of the company is to achieve the common goals of the SA.Li and Nguyen [41]Government policy (R4)The company operates in accordance with and supports the policies, laws, and regulations set by the local government.Byun et al. [42]Potential competitor (R5)The company should collect timely intelligence and information to assess potential competitors; otherwise, it may be threatened or even eliminated from the market.Kim [43]Table2 presents the dimension of environmental sustainability, which focuses on the perspective of environmental protection and is composed of environmental certification (G1), green resource integration (G2), pollution discharge treatment (G3), clean energy use (G4), and recycling/renewable capacity (G5).Table3 introduces the relevant indicators of social sustainability, including worker education and safety and health (S1), information sharing (S2), social contribution (S3), stakeholders’ rights protection (S4), and local employment opportunities (S5).The passive component manufacturing pays special attention to the innovation and R&D capabilities of partners, so innovation capability is a dimension in the evaluation system. In Table4, the criteria are core technical patent (I1), product’s life cycle (I2), manufacturing process capability (I3), R&D capability (I4), and supply chain integration (I5).Organizational management is a common and important topic of strategic alliances. Table5 shows the important organizational management key indicators, which include trust and commitment (O1), partners’ complementarity (O2), corporate branded image (O3), and customer relationship management (CRM) capability (O4).The last dimension is the risk factor. In practice, risk control is one of the keys to the success or failure of a strategic alliance. Businesses must understand whether the alliance can afford to take the potential risks. According to Table6, this dimension can be divided into external legitimacy (R1), geographical fit (R2), collaborating stability (R3), government policy (R4), and potential competitor (R5) criteria.


### 2.2. Research Gap

In the keenly competitive global environment, seeking mutually beneficial partners is a key factor to maintain the competitiveness of enterprises. There have been many researchers evaluating partners for different industries. Wang et al. [44] proposed a hybrid model that combines grey theory and data envelopment analysis (DEA) to explore the partner selection issues in the global aerospace and defense industry. Their study examined the financial performance of the world’s 35 largest aerospace and defense companies. Wang et al. [45] also used DEA to evaluate the operational performance of 20 IC packaging and testing enterprises. The findings suggest that what causes alliances to fail is that each partner tries to maximize personal interests rather than their cooperative interests. Chang et al. [3] developed a green SA evaluation framework to select the most suitable marketing partners for the biopharmaceutical industry. Their research focused on five dimensions of performance, including economic resource, innovation capability, organizational management, risk factors, and environmental protection. A hybrid BWM and TOPSIS model was used in their study. The study shows that innovation capability is the most important factor in SA for the biopharmaceutical industry. Tang and Hsu [46] applied a hierarchy structural fuzzy ANP (H-S FANP) approach to assess key factors of marketing SA development in the mobile telecommunication industry. Their study pointed out that H-S FANP can effectively identify the interaction of key factors. In addition to the above literature, there are many approaches to discussing SA selection and evaluation issues. The examples include statistical probability theory [1], multiple linear regression [5, 9, 12], and combined AHP with TOPSIS [8].In terms of SA evaluation criteria, most of the research still focuses on the marketing capabilities, financial indicators, and innovation capabilities of alternatives. However, only a few articles incorporate green awareness as an assessment perspective. In order to make up for this research gap, this study proposes a more comprehensive evaluation framework, which summarizes the economic resource, environmental protection, social, innovation capability, organizational management, and risk factor dimensions. In addition, this study proposes a novel neutrosophic fuzzy-based MCDM model that not only effectively measures the integration performance of partners but also takes into account broader information uncertainty.


## 2.1. Proposed Sustainable SA Partner Assessment Framework

This section reviews a large body of past research on SA partners and develops an assessment framework by the collaboration of several experts in the field. The sustainable SA partner assessment framework proposed in this paper is based on a perspective of sustainability, with several key dimensions added to form a comprehensive and complete assessment system. The dimensions can be composed of economy resource (E), environmental protection (G), social (S), innovation capability (I), organizational management (O), and risk factor (R). The six dimensions can be subdivided into 29 criteria that adequately reflect the key factors of SA partners, as shown in Tables 1–6. Table 1 presents the criteria of economic sustainability, including firm size (E1), financial strength (E2), material cost/selling price (E3), mergers/acquisitions (E4), and joint investment (E5), which are highly related to corporate economic activity.Table 1
The economy resource dimension and its criteria.
DimensionCriterionDescriptionReferencesEconomy resource (E)Firm size (E1)Corporate capital, turnover, number of employees, and market share, among other factors.Elia et al. [19]; Padovani et al. [20]Financial strength (E2)Information on corporate assets and liabilities, profit and loss, solvency, internal controls, board of directors’ functions, and business status.Cardoni et al. [21]; Padovani et al. [20]Material cost/selling price (E3)All direct and indirect fixed and variable costs of materials, labor, equipment, plants, operations, marketing, and net/gross profit margins.Gaustad et al. [22]; Lo et al. [7]Mergers/acquisitions (E4)Assessing whether the company can merge with other companies or has the value to do so.Yu et al. [23]; Cacciolatti et al. [12]Joint investment (E5)The willingness of the companies to invest their respective existing and superior resources in the joint venture in order to achieve joint capital, shared risk, and shared revenue.Cacciolatti et al. [12]; Vendrell-Herrero et al. [24]Table 2
The environmental protection dimension and its criteria.
DimensionCriterionDescriptionReferencesEnvironmental protection (G)Environmental certification (G1)The company should comply with the environmental regulations of international organizations and governments and obtain several environmental certifications and certificates.Thorne et al. [9]; Ge et al. [10]Green resource integration (G2)The company should respect the natural environment and protect the ecology in the green production system.Huang and Li [11]Pollution discharge treatment (G3)The company should actively implement environmental policies to reduce pollutant emissions and improve the efficiency of its energy use.Chang et al. [3]Clean energy use (G4)The company should strive to develop efficient and clean technologies for the production of passive components and promote the use of energy that does not pollute the environment.Cacciolatti et al. [12]Recycling/renewable capacity (G5)In the R&D and production process, enterprises should stress the importance of the recycling and reclamation of materials and consumables.D’Amato et al. [13]Table 3
The social dimension and its criteria.
DimensionCriterionDescriptionReferencesSocial (S)Worker education and safety and health (S1)Attaching importance to the education, training, and physical health of our employees. The work environment controls the concentration of harmful substances and measures the ergonomics of workers’ actions.Mani et al. [30]; Gul [31]Information sharing (S2)The company in the SA partnership can publish all production process information in a timely and accurate manner on a common information platform.Russo and Cesarani [32]; Lee [33]Social contribution (S3)The company should serve the public selflessly and assume greater CSR. The company shall comply with ethical norms and promote economic development in order to improve social well-being and improve the quality of life of society.Muñoz and Kimmitt [34]; Chang et al. [3]Stakeholders’ rights protection (S4)Valuing the interests and rights of SA partners and all stakeholders in the supply chain.Bhaumik et al. [35]; Nguyen et al. [36]Local employment opportunities (S5)The company can bring more employment opportunities to local residents and promote fairness to maintain the employment rights of people.Fernando et al. [37]; Burke and Stephens [38]Table 4
The innovation capability dimension and its criteria.
DimensionCriterionDescriptionReferencesInnovation capability (I)Core technical patent (I1)The company currently holds patents of key core technologies. The strategy of developing patents is to develop potential markets to ensure the company’s competitive advantage.Sun et al. [25]Product’s life cycle (I2)The company develops products that go through an introductory phase, a growth phase, a maturity phase, and a decline phase. Usually, companies expect to produce products with a longer life cycle.da Costa et al. [26]Manufacturing process capability (I3)Under fixed production conditions and stable control, whether the company’s manufacturing process matches the quality required by customers.Gunasekaran et al. [27]R&D capability (I4)Whether the company has the leading technologies and knowledge based on R&D, a clear understanding of market needs, and the ability to innovate products.Martínez-Noya and Narula [28]Supply chain integration (I5)The company’s ability to integrate the supply chain, including all product processes such as incoming materials, production, inventory, and sales.Nguyen and Tran [29]Table 5
The organizational management dimension and its criteria.
DimensionCriterionDescriptionReferencesOrganizational management (O)Trust and commitment (O1)A stable foundation for SA cohesion, trust, and termination penalties can be effective tools to motivate commitment and increase alliance effectiveness.Alaaraj et al. [14]Partners’ complementarity (O2)Different resources, capabilities and technologies can be integrated and managed to enhance the complementary nature of the SA.Mindruta et al. [15]; Hu et al. [16]Corporate branded image (O3)The perception and impression of the company’s brand fully reflect its values. The excellent brand image of the company increases profits and creates more channels to increase the market share of products.Singh et al. [17]CRM capability (O4)The service level of the company to meet the needs of customers. The main purpose is to use a high-performance information management system to analyze customer needs and process orders quickly.Aldaihani and Ali [18]Table 6
The risk factor dimension and its criteria.
DimensionCriterionDescriptionReferencesRisk factor (R)External legitimacy (R1)The company and alliance partners must obtain legalization from the local government before they can operate and trade in transnational economic organizations, and must avoid violating legal and criminal liabilities.Zhang et al. [39]Geographical fit (R2)When organizing economic activities in different regions, the company must evaluate cultural differences and business operations of the region in advance in order to avoid losses and reputational damage to the company.Huertas-García et al. [40]Collaborating stability (R3)The ambition of the company is to achieve the common goals of the SA.Li and Nguyen [41]Government policy (R4)The company operates in accordance with and supports the policies, laws, and regulations set by the local government.Byun et al. [42]Potential competitor (R5)The company should collect timely intelligence and information to assess potential competitors; otherwise, it may be threatened or even eliminated from the market.Kim [43]Table2 presents the dimension of environmental sustainability, which focuses on the perspective of environmental protection and is composed of environmental certification (G1), green resource integration (G2), pollution discharge treatment (G3), clean energy use (G4), and recycling/renewable capacity (G5).Table3 introduces the relevant indicators of social sustainability, including worker education and safety and health (S1), information sharing (S2), social contribution (S3), stakeholders’ rights protection (S4), and local employment opportunities (S5).The passive component manufacturing pays special attention to the innovation and R&D capabilities of partners, so innovation capability is a dimension in the evaluation system. In Table4, the criteria are core technical patent (I1), product’s life cycle (I2), manufacturing process capability (I3), R&D capability (I4), and supply chain integration (I5).Organizational management is a common and important topic of strategic alliances. Table5 shows the important organizational management key indicators, which include trust and commitment (O1), partners’ complementarity (O2), corporate branded image (O3), and customer relationship management (CRM) capability (O4).The last dimension is the risk factor. In practice, risk control is one of the keys to the success or failure of a strategic alliance. Businesses must understand whether the alliance can afford to take the potential risks. According to Table6, this dimension can be divided into external legitimacy (R1), geographical fit (R2), collaborating stability (R3), government policy (R4), and potential competitor (R5) criteria.


## 2.2. Research Gap

In the keenly competitive global environment, seeking mutually beneficial partners is a key factor to maintain the competitiveness of enterprises. There have been many researchers evaluating partners for different industries. Wang et al. [44] proposed a hybrid model that combines grey theory and data envelopment analysis (DEA) to explore the partner selection issues in the global aerospace and defense industry. Their study examined the financial performance of the world’s 35 largest aerospace and defense companies. Wang et al. [45] also used DEA to evaluate the operational performance of 20 IC packaging and testing enterprises. The findings suggest that what causes alliances to fail is that each partner tries to maximize personal interests rather than their cooperative interests. Chang et al. [3] developed a green SA evaluation framework to select the most suitable marketing partners for the biopharmaceutical industry. Their research focused on five dimensions of performance, including economic resource, innovation capability, organizational management, risk factors, and environmental protection. A hybrid BWM and TOPSIS model was used in their study. The study shows that innovation capability is the most important factor in SA for the biopharmaceutical industry. Tang and Hsu [46] applied a hierarchy structural fuzzy ANP (H-S FANP) approach to assess key factors of marketing SA development in the mobile telecommunication industry. Their study pointed out that H-S FANP can effectively identify the interaction of key factors. In addition to the above literature, there are many approaches to discussing SA selection and evaluation issues. The examples include statistical probability theory [1], multiple linear regression [5, 9, 12], and combined AHP with TOPSIS [8].In terms of SA evaluation criteria, most of the research still focuses on the marketing capabilities, financial indicators, and innovation capabilities of alternatives. However, only a few articles incorporate green awareness as an assessment perspective. In order to make up for this research gap, this study proposes a more comprehensive evaluation framework, which summarizes the economic resource, environmental protection, social, innovation capability, organizational management, and risk factor dimensions. In addition, this study proposes a novel neutrosophic fuzzy-based MCDM model that not only effectively measures the integration performance of partners but also takes into account broader information uncertainty.


## 3. Methodology

The architecture of the analysis process for passive component SA partner assessment is shown in Figure1. The methodology consists of three implementation procedures, namely, SVTNNs, neutrosophic ITARA, and neutrosophic TOPSIS. First, assessment criteria and alternative partners are identified, and assessment data for all alternative partners are generated through an actual survey. These data are used to obtain final scores using the SVTNNs conversion rule. Neutrosophic ITARA is then used to generate weights for the criteria with their importance ranking. Finally, neutrosophic TOPSIS is used to integrate the performance of the alternative partners and to determine their priority. The calculation process is described in detail below.Figure 1
The analysis process chart.


### 3.1. Basic Concepts and Definitions of the SVTNN

Zadeh [47] first proposed the concept of fuzzy sets (FSs), mainly to explore the theory of information fuzziness and the uncertainty of the assessment environment. Then, Atanassov [48] conducted an extended study on fuzzy sets by proposing intuitionistic fuzzy sets (IFSs). However, in order to reflect experts’ judgment more precisely, Smarandache [49] proposed neutrosophic logic that combines the three parameters of truth (Tθ˜), falsity (Fθ˜), and indeterminacy (Iθ˜) to fully interpret the uncertainty in the expert’s assessment. Decision-making models based on neutrosophic set theory have been proposed by many researchers [50–54], and they believe that neutrosophic set theory is effective and practical in practice. The SVTNN is one of the methods of neutrosophic set theory, which overcomes some drawbacks of traditional intuitionistic fuzzy numbers. SVTNNs have two advantages. That is, they contain three fuzzy parameters (truth, falsity, and indeterminacy) to measure multifaceted uncertainty and use trapezoidal fuzzy numbers to encompass more latent information. SVTNNs can be explicated by the following definitions [55]:Definition 1.
Tθ˜, Fθ˜, and Iθ˜ have a fixed range, which indicates that all three values are in [0, 1], and can also be expressed in percentage form. A regular SVTNN (θ˜) has 7 elements, which are represented as θ˜=θ1,θ2,θ3,θ4,Tθ˜,Fθ˜,Iθ˜. It belongs to a special neutrosophic set in the real number set R, where μθ˜, λθ˜, and νθ˜ are expressed as truth-membership (TM), falsity-membership (FM), and indeterminacy-membership (IM). The three membership functions can be defined by(1)μθ˜x=x−θ1Tθ˜θ2−θ1θ1≤x≤θ2,Tθ˜θ2≤x≤θ3,θ4−xTθ˜θ4−θ3θ3≤x≤θ4,0otherwise.(2)λθ˜x=θ2−x+Fθ˜x−θ1θ2−θ1θ1≤x≤θ2,Fθ˜θ2≤x≤θ3,x−θ3+Fθ˜θ4−xθ4−θ3θ3≤x≤θ4,1otherwise.(3)νθ˜x=θ2−x+Iθ˜x−θ1θ2−θ1θ1≤x≤θ2,Iθ˜θ2≤x≤θ3,x−θ3+Iθ˜θ4−xθ4−θ3θ3≤x≤θ4,1otherwise..
An SVTNN can be broken down into two parts. The first part is the general form of trapezoidal fuzzy numbersθ1,θ2,θ3,θ4, the minimum value of the fuzzy numbers is θ1, and the maximum value is θ4. In addition, θ2 and θ3 are the intermediate values, where it is not required θ2 to be equal to θ3. The second part is neutrosophic logic Tθ˜,Fθ˜,Iθ˜. Tθ˜, Fθ˜, and Iθ˜ denote the truth, falsity, and indeterminacy of the trapezoidal fuzzy numbers, respectively. Tθ˜, Fθ˜, and Iθ˜ are independent, so the sum of Tθ˜, Fθ˜, and Iθ˜ is not required to be equal to 1.Definition 2.
SVTNN provides three useful indexes, which are final score (scθ), accuracy (lθ), and certainty (cθ) indexes, as in(4)scθ=θ1+2θ2+2θ3+θ42+Tθ˜−Fθ˜−Iθ˜18,(5)lθ=θ1+2θ2+2θ3+θ4Tθ˜−Fθ˜6,(6)cθ=θ1+2θ2+2θ3+θ4Tθ˜6.Definition 3.
Suppose that there are two SVTNNs here, namelysu˜=su1,su2,su3,su4,Tsu˜,Fsu˜,Isu˜ and sv˜=sv1,sv2,sv3,sv4,Tsv˜,Fsv˜,Isv˜; therefore, su˜ and sv˜ can be compared with each other, which is defined as follows:(i)
Supposescsu>scsv, then su˜>sv˜, and it indicates that su˜ is absolutely better than sv˜.(ii)
Supposescsu=scsv and lsu>lsv, then su˜>sv˜, and it indicates that su˜ is better than sv˜.(iii)
Supposescsu=scsv, then sv˜>su˜, and it indicates that su˜ is worse than sv˜.
Supposescsu=scsv, lsu=lsv, and csu>csv, then su˜>sv˜. Obviously, su˜ is better than sv˜. Suppose csu<csv, then sv˜>su˜. When csu=csv, it indicates that su˜ and sv˜ are the same.


### 3.2. Determining the Weights of the Criteria: Neutrosophic ITARA

There are many different methods to generate the weights of the criteria, which can be broadly classified into two types, namely, subjective and objective weighting methods. Subjective weighting methods are obtained through pairwise comparisons of criteria by experts or decision makers, such as AHP, analytic network process (ANP), decision making trial and evaluation laboratory (DEMATEL), and BWM. On the other hand, objective weighting methods are applied to train the appropriate weights of criteria from existing performance data, including CRITIC, entropy, and ITARA. The ITARA technique proposed by Hatefi [56] is a relatively new technique, which determines the weights by measuring the dispersion of the data. The greater the dispersion of data, the greater the ability of the criterion to discriminate how good the alternative partners are, and therefore the greater the weight assigned to it. Dispersion logic (DL) and indifference threshold (IT) are the two core parameters of ITARA. DL determines the dispersion of two adjacent data, while IT is the minimum allowed degree of difference.Unfortunately, conventional ITARA only takes into account the distance between two adjacent partners but ignores the difference between the data itself and the AL. Suppose that there are 5 alternative partners with a rating of3,3,2,1,1 and 10,10,9,8,8 (on a scale of 1 to 10) for 2 criteria. Although the deviations for the two sets of data are the same, the distances from the AL (10) are different. However, through the conventional ITARA, it assigns equal weights to both criteria. Therefore, this paper refers to the study of Lo et al. [57] to improve the conventional ITARA and incorporate SVTNNs to convert expert qualitative judgments into quantitative data. The steps of implementing the neutrosophic ITARA are detailed as follows.Step 1. Collect the performance data of the alternative partners to build the initial neutrosophic assessment matrixθ˜.In this paper,m alternative partners (Ai, i = 1, 2, …, m) are assessed under n assessment criteria (Cj, j = 1, 2, …, n), respectively. The initial assessment matrix obtained is shown in equation (7). Due to the inclusion of the concept of AL, the AL (daspire, j) is added as a benchmarking basis. The assessment team assesses the performance of the alternative partners based on the interpretation variables set in Table 7 and then measures the uncertainty of each assessment based on Table 8.(7)θ˜=θ˜11θ˜12⋯θ˜1nθ˜21θ˜22⋯θ˜2n⋮⋮⋱⋮θ˜m1θ˜m2⋯θ˜mnθ˜aspire,1θ˜aspire,2⋯θ˜aspire,nm+1×n.Step 2. Convert the linguistic variables into crisp values to form the matrixscθ.The elements in the neutrosophic assessment matrixθ˜ are converted into crisp values (final scores) by (4) to form the matrix scθ:(8)scθ=scθ11scθ12⋯scθ1nscθ21scθ22⋯scθ2n⋮⋮⋱⋮scθm1scθm2⋯scθmnscθaspire,1scθaspire,2⋯scθaspire,nm+1×n.Step 3. Determine the ITj for each criterion.In this step, we develop a reasonableITj, j = 1, 2, …, n. The ITj reflects the experts’ allowable range for the degree of dispersion.Step 4. Create a normalized assessment matrixAThe normalization procedure is performed by (9) so that the values of the elements in the normalized assessment matrix A (10) fall in the range of 0 to 1.(9)aij=scθij∑i=1mscθij,(10)A=aijm+1×n.Here,ITj is also converted to NITj by normalization:(11)NITj=ITij∑i=1mscθij,j=1,2,…,n.Step 5. Arrange the elements of matrixA (in ascending order).The elements of matrixA are arranged in ascending order to form a matrix β, as in equation (12). The AL βaspire,j must be the maximum, so it will be arranged as the last.(12)β=β11β12⋯β12β21β22⋯β2n⋮⋮⋱⋮βm1βm2⋯βmnβaspire,1βaspire,2⋯βaspire,nm+1×n.Step 6. Calculate the degree of dispersionγijThe dispersion of two adjacent alternative partners can be defined by equation (13). Similarly, the AL βaspire,j must be subtracted from the previous data.(13)γij=βi+1,j−βij.Step 7. Consider the difference betweenγij and NITjWhenγij>NITj, it indicates that the dispersion of the two adjacent alternative partners is greater than the acceptable range for the decision makers. Therefore, δij is used to represent the difference between γij and NITj. Conversely, when γij≤NITj, it indicates that γij is not significant. Therefore, δij is set to 0. The summary of the above can be shown in(14)δij=γij−NITj,γij>NITj,0,γij≤NITj..Step 8. Generate a set of objective weights for the criteria.The equationvj=∑imδijp1/p is a method to calculate multidimensional distances, and usually, the p values range from 1 to ∞. The Euclidean distance (p = 2) is used to define the distance between alternative partners, as shown in(15)vj=∑imδij21/2.vj is further normalized to conform to the concept of MCDM so that wj≥0 and ∑j=1nwj=1:(16)wj1=vj∑j=1nvj.On the other hand, Lo et al. [57] proposed to incorporate ITARA by increasing the coefficient of variation (cv) as an index reflecting the overall dispersion (Equation (17)) so that the final objective criterion weight is shown in equation (18). ε is generally set to 0.5.(17)wj2=cvj∑j=1ncvj,(18)wj∗=εwj1+1−εwj2.Table 7
Grade scale of performance assessment [3].
Linguistic variablesCodeFuzzy numbersVery poorVP(0, 1, 1, 2)PoorP(2, 3, 3, 4)FairF(4, 5, 5, 6)GoodG(6, 7, 7, 8)Very goodVG(8, 9, 9, 10)Table 8
Linguistic variables and corresponding fuzzy numbers in the neutrosophic part [58].
Linguistic variablesCodeFuzzy numbersNo confidenceN(0, 0, 0)Low confidenceL(0.6, 0.2, 0.2)Fairly low confidenceFL(0.7, 0.1, 0.1)Medium confidenceM(0.8, 0.1, 0)Fairly high confidenceFH(0.8, 0.2, 0.2)High confidenceH(0.9, 0.1, 0.1)Absolutely high confidenceAH(1, 0, 0)


### 3.3. Calculation of the Total Performance Scores of the Alternative Partners: Neutrosophic TOPSIS

This study integrates TOPSIS with neutrosophic logic theory to reflect the practical assessment of environmental uncertainty and uses the AL as the benchmark for the highest rating. The detailed TOPSIS procedure is described as follows.Step 1. Use the matrixscθ in Section 3.2 as the initial assessment matrix.Step 2. Build the normalized assessment matrixF of neutrosophic TOPSIS.The conventional normalization approach is to take the largest valuation of the alternative partners as the denominator, but this is equivalent to choosing only one relatively good apple in a basket. Therefore, this study introduces the AL concept into Step 2. Here, we add the AL and the worst level (WL) to the performance matrix. The normalized assessment matrixF of TOPSIS is created:(19)F=fijm+2×n,wherefij=scθij/scθaspire,j and scθaspire,j = 10 (the highest level of the assessment scale).Step 3. Construct a weighted normalized assessment matrixX.Taking into account the different degrees of the discriminative power of the criteria, the weight values generated by neutrosophic ITARA (wj∗) are multiplied with the normalized assessment matrix F, which is calculated as in equation (20). The weighted normalized assessment matrix X is obtained as in equation (21).(20)xij=fij⋅wj∗,(21)X=xijm+2×n.Step 4. Define positive and negative ideal solutions (PIS and NIS)The values of PIS and NIS of the alternative partners should be 1 and 0 after normalization. The PIS and NIS of the alternative partners are shown:(22)ρj+=1⋅w1,1⋅w2,…,1⋅wn=w1,w2,…,wn,(23)ρj−=0.1⋅w1,0.1⋅w2,…,0.1⋅wn.Step 5. Calculate the difference between the PIS and NIS of the alternative partners.Equations (24) and (25) are used to calculate the separation (Euclidean distance squared) between the PIS and NIS of the alternative partner i.(24)di∗=∑j=1nρj+−xij∗∗2,(25)di−=∑j=1nxij∗∗−ρj−2.Step 6. Calculate the closeness coefficient (CCi) of the alternative partners.The closeness coefficient CCi is a reliable ranking index. According to Kuo [59], this ranking index takes into account the distance of all alternative partners from PIS and NIS to overcome the shortcomings of the ranking index proposed by traditional TOPSIS, then, CCi is shown:(26)CCi=w+di−∑i=1mdi−−w−di∗∑i=1mdi∗,−1≤CCi≤10≤w+≤10≤w−≤1,i=1,2,…,m,wherew+ and w− indicate the importance of PIS and NIS. Generally speaking, we set 0.5 to indicate equal importance to these two reference indicators. On the other hand, when CCi is greater than 0, it indicates alternative partner i has higher performance. Conversely, when the CCi is less than 0, it indicates that partner i has a relatively low performance.


## 3.1. Basic Concepts and Definitions of the SVTNN

Zadeh [47] first proposed the concept of fuzzy sets (FSs), mainly to explore the theory of information fuzziness and the uncertainty of the assessment environment. Then, Atanassov [48] conducted an extended study on fuzzy sets by proposing intuitionistic fuzzy sets (IFSs). However, in order to reflect experts’ judgment more precisely, Smarandache [49] proposed neutrosophic logic that combines the three parameters of truth (Tθ˜), falsity (Fθ˜), and indeterminacy (Iθ˜) to fully interpret the uncertainty in the expert’s assessment. Decision-making models based on neutrosophic set theory have been proposed by many researchers [50–54], and they believe that neutrosophic set theory is effective and practical in practice. The SVTNN is one of the methods of neutrosophic set theory, which overcomes some drawbacks of traditional intuitionistic fuzzy numbers. SVTNNs have two advantages. That is, they contain three fuzzy parameters (truth, falsity, and indeterminacy) to measure multifaceted uncertainty and use trapezoidal fuzzy numbers to encompass more latent information. SVTNNs can be explicated by the following definitions [55]:Definition 1.
Tθ˜, Fθ˜, and Iθ˜ have a fixed range, which indicates that all three values are in [0, 1], and can also be expressed in percentage form. A regular SVTNN (θ˜) has 7 elements, which are represented as θ˜=θ1,θ2,θ3,θ4,Tθ˜,Fθ˜,Iθ˜. It belongs to a special neutrosophic set in the real number set R, where μθ˜, λθ˜, and νθ˜ are expressed as truth-membership (TM), falsity-membership (FM), and indeterminacy-membership (IM). The three membership functions can be defined by(1)μθ˜x=x−θ1Tθ˜θ2−θ1θ1≤x≤θ2,Tθ˜θ2≤x≤θ3,θ4−xTθ˜θ4−θ3θ3≤x≤θ4,0otherwise.(2)λθ˜x=θ2−x+Fθ˜x−θ1θ2−θ1θ1≤x≤θ2,Fθ˜θ2≤x≤θ3,x−θ3+Fθ˜θ4−xθ4−θ3θ3≤x≤θ4,1otherwise.(3)νθ˜x=θ2−x+Iθ˜x−θ1θ2−θ1θ1≤x≤θ2,Iθ˜θ2≤x≤θ3,x−θ3+Iθ˜θ4−xθ4−θ3θ3≤x≤θ4,1otherwise..
An SVTNN can be broken down into two parts. The first part is the general form of trapezoidal fuzzy numbersθ1,θ2,θ3,θ4, the minimum value of the fuzzy numbers is θ1, and the maximum value is θ4. In addition, θ2 and θ3 are the intermediate values, where it is not required θ2 to be equal to θ3. The second part is neutrosophic logic Tθ˜,Fθ˜,Iθ˜. Tθ˜, Fθ˜, and Iθ˜ denote the truth, falsity, and indeterminacy of the trapezoidal fuzzy numbers, respectively. Tθ˜, Fθ˜, and Iθ˜ are independent, so the sum of Tθ˜, Fθ˜, and Iθ˜ is not required to be equal to 1.Definition 2.
SVTNN provides three useful indexes, which are final score (scθ), accuracy (lθ), and certainty (cθ) indexes, as in(4)scθ=θ1+2θ2+2θ3+θ42+Tθ˜−Fθ˜−Iθ˜18,(5)lθ=θ1+2θ2+2θ3+θ4Tθ˜−Fθ˜6,(6)cθ=θ1+2θ2+2θ3+θ4Tθ˜6.Definition 3.
Suppose that there are two SVTNNs here, namelysu˜=su1,su2,su3,su4,Tsu˜,Fsu˜,Isu˜ and sv˜=sv1,sv2,sv3,sv4,Tsv˜,Fsv˜,Isv˜; therefore, su˜ and sv˜ can be compared with each other, which is defined as follows:(i)
Supposescsu>scsv, then su˜>sv˜, and it indicates that su˜ is absolutely better than sv˜.(ii)
Supposescsu=scsv and lsu>lsv, then su˜>sv˜, and it indicates that su˜ is better than sv˜.(iii)
Supposescsu=scsv, then sv˜>su˜, and it indicates that su˜ is worse than sv˜.
Supposescsu=scsv, lsu=lsv, and csu>csv, then su˜>sv˜. Obviously, su˜ is better than sv˜. Suppose csu<csv, then sv˜>su˜. When csu=csv, it indicates that su˜ and sv˜ are the same.


## 3.2. Determining the Weights of the Criteria: Neutrosophic ITARA

There are many different methods to generate the weights of the criteria, which can be broadly classified into two types, namely, subjective and objective weighting methods. Subjective weighting methods are obtained through pairwise comparisons of criteria by experts or decision makers, such as AHP, analytic network process (ANP), decision making trial and evaluation laboratory (DEMATEL), and BWM. On the other hand, objective weighting methods are applied to train the appropriate weights of criteria from existing performance data, including CRITIC, entropy, and ITARA. The ITARA technique proposed by Hatefi [56] is a relatively new technique, which determines the weights by measuring the dispersion of the data. The greater the dispersion of data, the greater the ability of the criterion to discriminate how good the alternative partners are, and therefore the greater the weight assigned to it. Dispersion logic (DL) and indifference threshold (IT) are the two core parameters of ITARA. DL determines the dispersion of two adjacent data, while IT is the minimum allowed degree of difference.Unfortunately, conventional ITARA only takes into account the distance between two adjacent partners but ignores the difference between the data itself and the AL. Suppose that there are 5 alternative partners with a rating of3,3,2,1,1 and 10,10,9,8,8 (on a scale of 1 to 10) for 2 criteria. Although the deviations for the two sets of data are the same, the distances from the AL (10) are different. However, through the conventional ITARA, it assigns equal weights to both criteria. Therefore, this paper refers to the study of Lo et al. [57] to improve the conventional ITARA and incorporate SVTNNs to convert expert qualitative judgments into quantitative data. The steps of implementing the neutrosophic ITARA are detailed as follows.Step 1. Collect the performance data of the alternative partners to build the initial neutrosophic assessment matrixθ˜.In this paper,m alternative partners (Ai, i = 1, 2, …, m) are assessed under n assessment criteria (Cj, j = 1, 2, …, n), respectively. The initial assessment matrix obtained is shown in equation (7). Due to the inclusion of the concept of AL, the AL (daspire, j) is added as a benchmarking basis. The assessment team assesses the performance of the alternative partners based on the interpretation variables set in Table 7 and then measures the uncertainty of each assessment based on Table 8.(7)θ˜=θ˜11θ˜12⋯θ˜1nθ˜21θ˜22⋯θ˜2n⋮⋮⋱⋮θ˜m1θ˜m2⋯θ˜mnθ˜aspire,1θ˜aspire,2⋯θ˜aspire,nm+1×n.Step 2. Convert the linguistic variables into crisp values to form the matrixscθ.The elements in the neutrosophic assessment matrixθ˜ are converted into crisp values (final scores) by (4) to form the matrix scθ:(8)scθ=scθ11scθ12⋯scθ1nscθ21scθ22⋯scθ2n⋮⋮⋱⋮scθm1scθm2⋯scθmnscθaspire,1scθaspire,2⋯scθaspire,nm+1×n.Step 3. Determine the ITj for each criterion.In this step, we develop a reasonableITj, j = 1, 2, …, n. The ITj reflects the experts’ allowable range for the degree of dispersion.Step 4. Create a normalized assessment matrixAThe normalization procedure is performed by (9) so that the values of the elements in the normalized assessment matrix A (10) fall in the range of 0 to 1.(9)aij=scθij∑i=1mscθij,(10)A=aijm+1×n.Here,ITj is also converted to NITj by normalization:(11)NITj=ITij∑i=1mscθij,j=1,2,…,n.Step 5. Arrange the elements of matrixA (in ascending order).The elements of matrixA are arranged in ascending order to form a matrix β, as in equation (12). The AL βaspire,j must be the maximum, so it will be arranged as the last.(12)β=β11β12⋯β12β21β22⋯β2n⋮⋮⋱⋮βm1βm2⋯βmnβaspire,1βaspire,2⋯βaspire,nm+1×n.Step 6. Calculate the degree of dispersionγijThe dispersion of two adjacent alternative partners can be defined by equation (13). Similarly, the AL βaspire,j must be subtracted from the previous data.(13)γij=βi+1,j−βij.Step 7. Consider the difference betweenγij and NITjWhenγij>NITj, it indicates that the dispersion of the two adjacent alternative partners is greater than the acceptable range for the decision makers. Therefore, δij is used to represent the difference between γij and NITj. Conversely, when γij≤NITj, it indicates that γij is not significant. Therefore, δij is set to 0. The summary of the above can be shown in(14)δij=γij−NITj,γij>NITj,0,γij≤NITj..Step 8. Generate a set of objective weights for the criteria.The equationvj=∑imδijp1/p is a method to calculate multidimensional distances, and usually, the p values range from 1 to ∞. The Euclidean distance (p = 2) is used to define the distance between alternative partners, as shown in(15)vj=∑imδij21/2.vj is further normalized to conform to the concept of MCDM so that wj≥0 and ∑j=1nwj=1:(16)wj1=vj∑j=1nvj.On the other hand, Lo et al. [57] proposed to incorporate ITARA by increasing the coefficient of variation (cv) as an index reflecting the overall dispersion (Equation (17)) so that the final objective criterion weight is shown in equation (18). ε is generally set to 0.5.(17)wj2=cvj∑j=1ncvj,(18)wj∗=εwj1+1−εwj2.Table 7
Grade scale of performance assessment [3].
Linguistic variablesCodeFuzzy numbersVery poorVP(0, 1, 1, 2)PoorP(2, 3, 3, 4)FairF(4, 5, 5, 6)GoodG(6, 7, 7, 8)Very goodVG(8, 9, 9, 10)Table 8
Linguistic variables and corresponding fuzzy numbers in the neutrosophic part [58].
Linguistic variablesCodeFuzzy numbersNo confidenceN(0, 0, 0)Low confidenceL(0.6, 0.2, 0.2)Fairly low confidenceFL(0.7, 0.1, 0.1)Medium confidenceM(0.8, 0.1, 0)Fairly high confidenceFH(0.8, 0.2, 0.2)High confidenceH(0.9, 0.1, 0.1)Absolutely high confidenceAH(1, 0, 0)


## 3.3. Calculation of the Total Performance Scores of the Alternative Partners: Neutrosophic TOPSIS

This study integrates TOPSIS with neutrosophic logic theory to reflect the practical assessment of environmental uncertainty and uses the AL as the benchmark for the highest rating. The detailed TOPSIS procedure is described as follows.Step 1. Use the matrixscθ in Section 3.2 as the initial assessment matrix.Step 2. Build the normalized assessment matrixF of neutrosophic TOPSIS.The conventional normalization approach is to take the largest valuation of the alternative partners as the denominator, but this is equivalent to choosing only one relatively good apple in a basket. Therefore, this study introduces the AL concept into Step 2. Here, we add the AL and the worst level (WL) to the performance matrix. The normalized assessment matrixF of TOPSIS is created:(19)F=fijm+2×n,wherefij=scθij/scθaspire,j and scθaspire,j = 10 (the highest level of the assessment scale).Step 3. Construct a weighted normalized assessment matrixX.Taking into account the different degrees of the discriminative power of the criteria, the weight values generated by neutrosophic ITARA (wj∗) are multiplied with the normalized assessment matrix F, which is calculated as in equation (20). The weighted normalized assessment matrix X is obtained as in equation (21).(20)xij=fij⋅wj∗,(21)X=xijm+2×n.Step 4. Define positive and negative ideal solutions (PIS and NIS)The values of PIS and NIS of the alternative partners should be 1 and 0 after normalization. The PIS and NIS of the alternative partners are shown:(22)ρj+=1⋅w1,1⋅w2,…,1⋅wn=w1,w2,…,wn,(23)ρj−=0.1⋅w1,0.1⋅w2,…,0.1⋅wn.Step 5. Calculate the difference between the PIS and NIS of the alternative partners.Equations (24) and (25) are used to calculate the separation (Euclidean distance squared) between the PIS and NIS of the alternative partner i.(24)di∗=∑j=1nρj+−xij∗∗2,(25)di−=∑j=1nxij∗∗−ρj−2.Step 6. Calculate the closeness coefficient (CCi) of the alternative partners.The closeness coefficient CCi is a reliable ranking index. According to Kuo [59], this ranking index takes into account the distance of all alternative partners from PIS and NIS to overcome the shortcomings of the ranking index proposed by traditional TOPSIS, then, CCi is shown:(26)CCi=w+di−∑i=1mdi−−w−di∗∑i=1mdi∗,−1≤CCi≤10≤w+≤10≤w−≤1,i=1,2,…,m,wherew+ and w− indicate the importance of PIS and NIS. Generally speaking, we set 0.5 to indicate equal importance to these two reference indicators. On the other hand, when CCi is greater than 0, it indicates alternative partner i has higher performance. Conversely, when the CCi is less than 0, it indicates that partner i has a relatively low performance.


## 4. A Real Case as a Data Demonstration

This study uses a multinational passive component manufacturer to illustrate the proposed neutrosophic-based DM model. Section4 presents the problem description of the case study, followed by a description of the implementation processes of neutrosophic ITARA and TOPSIS in the case.


### 4.1. Background Description and Data Collection

The passive component manufacturing industry has developed early compared to other electronic industries, initially producing in the original equipment manufacturer (OEM) mode, and later shifting to the original design manufacturer (ODM) mode in order to increase added value and grasp key customers. After the rise of the semiconductor industry, passive components have almost become a traditional industry in the electronics industry, playing the role of driving the peripheral and equipment industries. The downstream application manufacturers are mainly computer equipment manufacturers, followed by the communication products market. The main products of passive components are capacitors (storing and releasing electrical energy in the form of static electricity), resistors (reducing voltage and limiting current to regulate circuit characteristics), inductors (generating electromagnetic flux to prevent electromagnetic interference), oscillators, and filters. After experiencing slow demand and oversupply in the communications and information market in 2000, the computer-related equipment, communications, and consumer electronics industries have been recovering since 2003, and the passive component boom has rebounded locally and internationally. The capacity utilization rate of various companies has gradually increased, and the companies have expanded their territories by expanding their production capacity and merging and acquiring with SAs in the industry.In recent years, the case company has a deep understanding of the importance of technological capability and has been investing a fixed percentage of its annual revenue in technological research and development and innovation since 2000, devoting itself to various special product developments such as miniaturization, cost-efficiency optimization, green environmental protection, and independent research and development of materials to comply the trend of 3C products that are light, thin, and short with multifunctional integration. The passive components produced by the case company are widely used in various electronic products, from computer information, communication devices, consumer electronics, and even applications across electric vehicles, smart healthcare, and Industry 4.0. In the future, the case company expects to establish a SA to integrate the supply chain for electric vehicle production. Unfortunately, there is not yet a complete “sustainability concept” system for assessing SA partners, but rather a focus on the R&D and profitability of the alternative partners. Traditionally, SA decisions have been made mostly through meetings of senior executives to determine goals. Therefore, the case company needs a complete system for assessing sustainable SA partners and using scientific and computational tools to support SA strategy formulation.The case company has a DM team consisting of senior executives, which includes the chairman, CEO, general manager, and division managers. The DM team assessed the performance of the six alternative partner companies based on the assessment framework developed in Section2. Table 9 presents the joint assessment of the DM team. For example, based on the linguistic variables in Tables 7 and 8, A1 is rated as good (G) and absolutely high confidence (AH) on the scale of criterion E1. Next, we convert the elements in Table 9 into SVTNNs, as in Table 10. According to the above example, {G, AH} can be converted into one SVTNN, i.e., {(6, 7, 7, 8), (1, 0, 0)}, where 6 is the fuzzy lower bound, 8 is the fuzzy upper bound, and 7 is the fuzzy intermediate value (because it is a trapezoidal fuzzy number, there are two 7s). In addition, the truth is 1 and the falsity and indeterminacy are 0. According to equation (4), the SVTNNs can be converted into final scores as shown in Table 11. Subsequent neutrosophic ITARA and TOPSIS calculations are based on this table as initial input.Table 9
Performance data of the six alternative partners (linguistic variables).
CriterionAlternativeA1A2A3A4A5A6E1{G, AH}{G, FH}{F, H}{G, FH}{VG, M}{VG, H}E2{P, H}{VG, M}{VG, H}{G, H}{G, AH}{F, M}E3{VG, H}{F, H}{VG, M}{G, H}{G, FH}{P, H}E4{F, M}{G, AH}{G, FH}{F, FH}{G, H}{F, H}E5{G, AH}{VG, H}{P, H}{F, H}{P, H}{G, AH}G1{F, H}{P, H}{G, FH}{G, FH}{G, H}{G, H}G2{G, H}{F, FH}{F, AH}{F, M}{G, H}{G, M}G3{VG, H}{F, H}{G, M}{F, H}{G, H}{P, H}G4{F, H}{G, M}{P, H}{VG, M}{G, H}{G, FH}G5{VG, M}{F, H}{VG, FH}{P, H}{VG, M}{G, AH}S1{G, M}{VG, FH}{G, AH}{G, AH}{G, AH}{VG, FH}S2{P, FL}{G, H}{VG, H}{F, AH}{G, H}{P, M}S3{G, M}{G, M}{VG, M}{VG, M}{G, AH}{VG, M}S4{P, H}{G, FH}{F, H}{P, H}{G, AH}{VG, M}S5{VG, FH}{G, M}{VG, M}{G, M}{G, AH}{P, H}I1{G, H}{VG, FH}{F, H}{VG, AH}{G, M}{F, M}I2{VG, FH}{P, H}{F, H}{G, AH}{VG, H}{VG, H}I3{G, M}{G, M}{VG, H}{G, M}{G, AH}{G, AH}I4{G, M}{F, FL}{P, FH}{VG, H}{G, FL}{VG, L}I5{VG, FH}{G, M}{VG, H}{G, M}{VG, H}{G, M}O1{G, H}{F, H}{G, AH}{G, FH}{G, H}{G, FH}O2{F, M}{G, M}{F, H}{G, AH}{VG, FH}{G, H}O3{G, H}{G, AH}{VG, M}{P, H}{VG, M}{G, H}O4{G, H}{VG, M}{G, AH}{VG, H}{F, H}{VG, H}R1{G, FH}{F, H}{G, H}{G, AH}{VG, H}{G, AH}R2{P, H}{VG, M}{G, H}{VG, H}{G, FH}{F, H}R3{VG, H}{G, FH}{F, H}{P, H}{VG, M}{VG, H}R4{G, H}{VG, H}{VG, M}{G, FH}{G, AH}{P, H}R5{G, FH}{P, H}{G, AH}{G, AH}{VG, M}{G, AH}Table 10
Performance data of the six alternative partners (SVTNNs).
CriterionAlternativeA1A2A3A4A5A6E1{(6, 7, 7, 8), (1, 0, 0)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(8, 9, 9, 10), (0.9, 0.1, 0.1)}E2{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(8, 9, 9, 10), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (1, 0, 0)}{(4, 5, 5, 6), (0.8, 0.1, 0)}E3{(8, 9, 9, 10), (0.9, 0.1, 0.1)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(6, 7, 7, 8), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}E4{(4, 5, 5, 6), (0.8, 0.1, 0)}{(6, 7, 7, 8), (1, 0, 0)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(4, 5, 5, 6), (0.8, 0.2, 0.2)}{(6, 7, 7, 8), (0.9, 0.1, 0.1)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}E5{(6, 7, 7, 8), (1, 0, 0)}{(8, 9, 9, 10), (0.9, 0.1, 0.1)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (1, 0, 0)}⋮⋮⋮⋮⋮⋮⋮R5{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (1, 0, 0)}{(6, 7, 7, 8), (1, 0, 0)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(6, 7, 7, 8), (1, 0, 0)}Table 11
Performance data of the six alternative partners (final scores).
CriterionAlternativeA1A2A3A4A5A6E17.05.64.55.68.18.1E22.78.18.16.37.04.5E38.14.58.16.35.62.7E44.57.05.64.06.34.5E57.08.12.74.52.77.0⋮⋮⋮⋮⋮⋮⋮R55.62.77.07.08.17.0


### 4.2. Using Neutrosophic ITARA to Generate the Objective Weights

Table12 shows the initial assessment matrix for the sustainability alliance partners (which has been converted to Table 11), with each alternative partner having a performance score under each criterion. The data volume of the initial assessment matrix scθ is 6 × 29 pieces of data, which are used to generate the objective weights of the criteria.Table 12
The initial assessment matrixscθ.
E1E2E3E4E5⋯R5A17.02.78.14.57.0⋯5.6A25.68.14.57.08.1⋯2.7A34.58.18.15.62.7⋯7.0A45.66.36.34.04.5⋯7.0A58.17.05.66.32.7⋯8.1A68.14.52.74.57.0⋯7.0AL1010101010⋯10Sum48.946.745.341.942.0⋯47.4IT0.50.50.50.50.5⋯0.5The sum of the final scores of the alternative partners for each criterion can be found in Table12. The members of the DM team are asked to jointly develop an allowed difference, IT, for each criterion, which can be set to a different value for each criterion. Then, the objective weighting and ranking of the criteria can be calculated according to the neutrosophic ITARA process in Section 3.2, as shown in Table 13. The top five criteria are environmental certification (G1), information sharing (S2), joint investment (E5), stakeholder’ rights protection (S4), and green resource integration (G2)Table 13
Calculation results of neutrosophic ITARA.
CriterionE1E2E3E4E5G1G2G3G4G5S1S2S3S4S5I1I2I3I4I5O1O2O3O4R1R2R3R4R5vj0.0380.0510.0530.0620.0670.0860.0780.0630.0550.0590.0450.0670.0290.0560.0720.0410.0590.0300.0560.0290.0570.0580.0710.0390.0340.0530.0600.0600.063wj10.0240.0320.0330.0390.0420.0540.0490.0390.0350.0370.0280.0420.0180.0350.0450.0260.0370.0190.0350.0180.0360.0360.0450.0240.0220.0330.0380.0380.04cvj0.2720.3670.3820.3460.4640.3790.3270.4040.3810.360.1610.4660.1690.4740.3260.3070.360.1870.40.1840.2690.2860.3270.2330.2560.3820.3780.3390.332wj20.0290.0390.040.0360.0490.040.0340.0420.040.0380.0170.0490.0180.050.0340.0320.0380.020.0420.0190.0280.030.0340.0240.0270.040.040.0360.035wj∗0.0260.0350.0370.0380.0460.0470.0420.0410.0370.0370.0230.0460.0180.0430.040.0290.0370.0190.0390.0190.0320.0330.040.0240.0240.0370.0390.0370.037Rank2319171131561412262294722132710282120824251691815


### 4.3. Using Neutrosophic TOPSIS to Integrate the Performance of Alternative Partners

The assessment and selection process of sustainable SA partners cannot be discussed using traditional cost-benefit analysis (CBA) because it involves a number of criteria other than cost or benefit in addition to many qualitative criteria that cannot be measured using instruments or equipment tools. As a result of the extensive literature review, MCDM has excellent analytical capabilities in dealing with MCDM issues, and it can meet the development needs of decision-makers/operators in order to support companies in formulating appropriate improvement strategies. Due to the ambiguity of the information and the uncertainty of the assessment environment, this study combines the neutrosophic fuzzy technique into TOPSIS, in addition to the AL and the WL as the basis for the assessment of the alternative partners, avoiding the consideration of the relative preference solution of the current solution. The procedure can be performed according to Section3.3.Table14 presents the input data of neutrosophic TOPSIS, which is actually the same as the initial data of neutrosophic ITARA, with the difference that neutrosophic TOPSIS adds the AL and the WL as the two parameters of the calculation. Table 15 presents the results of the neutrosophic TOPSIS analysis, which shows the difference between the AL and the WL (d∗ and d−) for each partner, with A5 being the partner closest to the AL and furthest from the WL, with a gap of 0.069 and 0.128, respectively. It is worth mentioning that the AL and the WL are appropriate as a basis for judging the alternative partners so that it is possible to distinguish which partner is relatively good and which is relatively bad. In this case, the closeness coefficient obtained for A4 is negative, −0.002, which means that it is relatively poor among the available partners. The order of preference of the alternative partners is A5 >≻ A3 >≻ A1 >≻ A6 >≻ A2 >≻ A4.Table 14
The initial assessment matrix of the neutrosophic TOPSIS.
E1E2E3E4E5⋯R5A17.02.78.14.57.0⋯5.6A25.68.14.57.08.1⋯2.7A34.58.18.15.62.7⋯7.0A45.66.36.34.04.5⋯7.0A58.17.05.66.32.7⋯8.1A68.14.52.74.57.0⋯7.0AL1010101010⋯10WL00000⋯0Table 15
The analysis results of the neutrosophic TOPSIS.
Alternative partnerd∗d-CCRankA10.0880.1150.0023A20.0890.1130.0005A30.0860.1180.0062A40.0910.111−0.0026A50.0690.1280.0231A60.0900.1140.0004AL00.1910.107WL0.1910-0.135


## 4.1. Background Description and Data Collection

The passive component manufacturing industry has developed early compared to other electronic industries, initially producing in the original equipment manufacturer (OEM) mode, and later shifting to the original design manufacturer (ODM) mode in order to increase added value and grasp key customers. After the rise of the semiconductor industry, passive components have almost become a traditional industry in the electronics industry, playing the role of driving the peripheral and equipment industries. The downstream application manufacturers are mainly computer equipment manufacturers, followed by the communication products market. The main products of passive components are capacitors (storing and releasing electrical energy in the form of static electricity), resistors (reducing voltage and limiting current to regulate circuit characteristics), inductors (generating electromagnetic flux to prevent electromagnetic interference), oscillators, and filters. After experiencing slow demand and oversupply in the communications and information market in 2000, the computer-related equipment, communications, and consumer electronics industries have been recovering since 2003, and the passive component boom has rebounded locally and internationally. The capacity utilization rate of various companies has gradually increased, and the companies have expanded their territories by expanding their production capacity and merging and acquiring with SAs in the industry.In recent years, the case company has a deep understanding of the importance of technological capability and has been investing a fixed percentage of its annual revenue in technological research and development and innovation since 2000, devoting itself to various special product developments such as miniaturization, cost-efficiency optimization, green environmental protection, and independent research and development of materials to comply the trend of 3C products that are light, thin, and short with multifunctional integration. The passive components produced by the case company are widely used in various electronic products, from computer information, communication devices, consumer electronics, and even applications across electric vehicles, smart healthcare, and Industry 4.0. In the future, the case company expects to establish a SA to integrate the supply chain for electric vehicle production. Unfortunately, there is not yet a complete “sustainability concept” system for assessing SA partners, but rather a focus on the R&D and profitability of the alternative partners. Traditionally, SA decisions have been made mostly through meetings of senior executives to determine goals. Therefore, the case company needs a complete system for assessing sustainable SA partners and using scientific and computational tools to support SA strategy formulation.The case company has a DM team consisting of senior executives, which includes the chairman, CEO, general manager, and division managers. The DM team assessed the performance of the six alternative partner companies based on the assessment framework developed in Section2. Table 9 presents the joint assessment of the DM team. For example, based on the linguistic variables in Tables 7 and 8, A1 is rated as good (G) and absolutely high confidence (AH) on the scale of criterion E1. Next, we convert the elements in Table 9 into SVTNNs, as in Table 10. According to the above example, {G, AH} can be converted into one SVTNN, i.e., {(6, 7, 7, 8), (1, 0, 0)}, where 6 is the fuzzy lower bound, 8 is the fuzzy upper bound, and 7 is the fuzzy intermediate value (because it is a trapezoidal fuzzy number, there are two 7s). In addition, the truth is 1 and the falsity and indeterminacy are 0. According to equation (4), the SVTNNs can be converted into final scores as shown in Table 11. Subsequent neutrosophic ITARA and TOPSIS calculations are based on this table as initial input.Table 9
Performance data of the six alternative partners (linguistic variables).
CriterionAlternativeA1A2A3A4A5A6E1{G, AH}{G, FH}{F, H}{G, FH}{VG, M}{VG, H}E2{P, H}{VG, M}{VG, H}{G, H}{G, AH}{F, M}E3{VG, H}{F, H}{VG, M}{G, H}{G, FH}{P, H}E4{F, M}{G, AH}{G, FH}{F, FH}{G, H}{F, H}E5{G, AH}{VG, H}{P, H}{F, H}{P, H}{G, AH}G1{F, H}{P, H}{G, FH}{G, FH}{G, H}{G, H}G2{G, H}{F, FH}{F, AH}{F, M}{G, H}{G, M}G3{VG, H}{F, H}{G, M}{F, H}{G, H}{P, H}G4{F, H}{G, M}{P, H}{VG, M}{G, H}{G, FH}G5{VG, M}{F, H}{VG, FH}{P, H}{VG, M}{G, AH}S1{G, M}{VG, FH}{G, AH}{G, AH}{G, AH}{VG, FH}S2{P, FL}{G, H}{VG, H}{F, AH}{G, H}{P, M}S3{G, M}{G, M}{VG, M}{VG, M}{G, AH}{VG, M}S4{P, H}{G, FH}{F, H}{P, H}{G, AH}{VG, M}S5{VG, FH}{G, M}{VG, M}{G, M}{G, AH}{P, H}I1{G, H}{VG, FH}{F, H}{VG, AH}{G, M}{F, M}I2{VG, FH}{P, H}{F, H}{G, AH}{VG, H}{VG, H}I3{G, M}{G, M}{VG, H}{G, M}{G, AH}{G, AH}I4{G, M}{F, FL}{P, FH}{VG, H}{G, FL}{VG, L}I5{VG, FH}{G, M}{VG, H}{G, M}{VG, H}{G, M}O1{G, H}{F, H}{G, AH}{G, FH}{G, H}{G, FH}O2{F, M}{G, M}{F, H}{G, AH}{VG, FH}{G, H}O3{G, H}{G, AH}{VG, M}{P, H}{VG, M}{G, H}O4{G, H}{VG, M}{G, AH}{VG, H}{F, H}{VG, H}R1{G, FH}{F, H}{G, H}{G, AH}{VG, H}{G, AH}R2{P, H}{VG, M}{G, H}{VG, H}{G, FH}{F, H}R3{VG, H}{G, FH}{F, H}{P, H}{VG, M}{VG, H}R4{G, H}{VG, H}{VG, M}{G, FH}{G, AH}{P, H}R5{G, FH}{P, H}{G, AH}{G, AH}{VG, M}{G, AH}Table 10
Performance data of the six alternative partners (SVTNNs).
CriterionAlternativeA1A2A3A4A5A6E1{(6, 7, 7, 8), (1, 0, 0)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(8, 9, 9, 10), (0.9, 0.1, 0.1)}E2{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(8, 9, 9, 10), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (1, 0, 0)}{(4, 5, 5, 6), (0.8, 0.1, 0)}E3{(8, 9, 9, 10), (0.9, 0.1, 0.1)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(6, 7, 7, 8), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}E4{(4, 5, 5, 6), (0.8, 0.1, 0)}{(6, 7, 7, 8), (1, 0, 0)}{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(4, 5, 5, 6), (0.8, 0.2, 0.2)}{(6, 7, 7, 8), (0.9, 0.1, 0.1)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}E5{(6, 7, 7, 8), (1, 0, 0)}{(8, 9, 9, 10), (0.9, 0.1, 0.1)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(4, 5, 5, 6), (0.9, 0.1, 0.1)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (1, 0, 0)}⋮⋮⋮⋮⋮⋮⋮R5{(6, 7, 7, 8), (0.8, 0.2, 0.2)}{(2, 3, 3, 4), (0.9, 0.1, 0.1)}{(6, 7, 7, 8), (1, 0, 0)}{(6, 7, 7, 8), (1, 0, 0)}{(8, 9, 9, 10), (0.8, 0.1, 0)}{(6, 7, 7, 8), (1, 0, 0)}Table 11
Performance data of the six alternative partners (final scores).
CriterionAlternativeA1A2A3A4A5A6E17.05.64.55.68.18.1E22.78.18.16.37.04.5E38.14.58.16.35.62.7E44.57.05.64.06.34.5E57.08.12.74.52.77.0⋮⋮⋮⋮⋮⋮⋮R55.62.77.07.08.17.0


## 4.2. Using Neutrosophic ITARA to Generate the Objective Weights

Table12 shows the initial assessment matrix for the sustainability alliance partners (which has been converted to Table 11), with each alternative partner having a performance score under each criterion. The data volume of the initial assessment matrix scθ is 6 × 29 pieces of data, which are used to generate the objective weights of the criteria.Table 12
The initial assessment matrixscθ.
E1E2E3E4E5⋯R5A17.02.78.14.57.0⋯5.6A25.68.14.57.08.1⋯2.7A34.58.18.15.62.7⋯7.0A45.66.36.34.04.5⋯7.0A58.17.05.66.32.7⋯8.1A68.14.52.74.57.0⋯7.0AL1010101010⋯10Sum48.946.745.341.942.0⋯47.4IT0.50.50.50.50.5⋯0.5The sum of the final scores of the alternative partners for each criterion can be found in Table12. The members of the DM team are asked to jointly develop an allowed difference, IT, for each criterion, which can be set to a different value for each criterion. Then, the objective weighting and ranking of the criteria can be calculated according to the neutrosophic ITARA process in Section 3.2, as shown in Table 13. The top five criteria are environmental certification (G1), information sharing (S2), joint investment (E5), stakeholder’ rights protection (S4), and green resource integration (G2)Table 13
Calculation results of neutrosophic ITARA.
CriterionE1E2E3E4E5G1G2G3G4G5S1S2S3S4S5I1I2I3I4I5O1O2O3O4R1R2R3R4R5vj0.0380.0510.0530.0620.0670.0860.0780.0630.0550.0590.0450.0670.0290.0560.0720.0410.0590.0300.0560.0290.0570.0580.0710.0390.0340.0530.0600.0600.063wj10.0240.0320.0330.0390.0420.0540.0490.0390.0350.0370.0280.0420.0180.0350.0450.0260.0370.0190.0350.0180.0360.0360.0450.0240.0220.0330.0380.0380.04cvj0.2720.3670.3820.3460.4640.3790.3270.4040.3810.360.1610.4660.1690.4740.3260.3070.360.1870.40.1840.2690.2860.3270.2330.2560.3820.3780.3390.332wj20.0290.0390.040.0360.0490.040.0340.0420.040.0380.0170.0490.0180.050.0340.0320.0380.020.0420.0190.0280.030.0340.0240.0270.040.040.0360.035wj∗0.0260.0350.0370.0380.0460.0470.0420.0410.0370.0370.0230.0460.0180.0430.040.0290.0370.0190.0390.0190.0320.0330.040.0240.0240.0370.0390.0370.037Rank2319171131561412262294722132710282120824251691815


## 4.3. Using Neutrosophic TOPSIS to Integrate the Performance of Alternative Partners

The assessment and selection process of sustainable SA partners cannot be discussed using traditional cost-benefit analysis (CBA) because it involves a number of criteria other than cost or benefit in addition to many qualitative criteria that cannot be measured using instruments or equipment tools. As a result of the extensive literature review, MCDM has excellent analytical capabilities in dealing with MCDM issues, and it can meet the development needs of decision-makers/operators in order to support companies in formulating appropriate improvement strategies. Due to the ambiguity of the information and the uncertainty of the assessment environment, this study combines the neutrosophic fuzzy technique into TOPSIS, in addition to the AL and the WL as the basis for the assessment of the alternative partners, avoiding the consideration of the relative preference solution of the current solution. The procedure can be performed according to Section3.3.Table14 presents the input data of neutrosophic TOPSIS, which is actually the same as the initial data of neutrosophic ITARA, with the difference that neutrosophic TOPSIS adds the AL and the WL as the two parameters of the calculation. Table 15 presents the results of the neutrosophic TOPSIS analysis, which shows the difference between the AL and the WL (d∗ and d−) for each partner, with A5 being the partner closest to the AL and furthest from the WL, with a gap of 0.069 and 0.128, respectively. It is worth mentioning that the AL and the WL are appropriate as a basis for judging the alternative partners so that it is possible to distinguish which partner is relatively good and which is relatively bad. In this case, the closeness coefficient obtained for A4 is negative, −0.002, which means that it is relatively poor among the available partners. The order of preference of the alternative partners is A5 >≻ A3 >≻ A1 >≻ A6 >≻ A2 >≻ A4.Table 14
The initial assessment matrix of the neutrosophic TOPSIS.
E1E2E3E4E5⋯R5A17.02.78.14.57.0⋯5.6A25.68.14.57.08.1⋯2.7A34.58.18.15.62.7⋯7.0A45.66.36.34.04.5⋯7.0A58.17.05.66.32.7⋯8.1A68.14.52.74.57.0⋯7.0AL1010101010⋯10WL00000⋯0Table 15
The analysis results of the neutrosophic TOPSIS.
Alternative partnerd∗d-CCRankA10.0880.1150.0023A20.0890.1130.0005A30.0860.1180.0062A40.0910.111−0.0026A50.0690.1280.0231A60.0900.1140.0004AL00.1910.107WL0.1910-0.135


## 5. Discussion

Due to the raging COVID-19 epidemic, the operation of global industrial chains was disrupted in one fell swoop. Now, even in the postepidemic era, business owners are thinking about how to improve operational flexibility, reallocate production resources, or significantly reduce their reliance on a single factor of production. Fortunately, due to the development of trends in 5G, electric vehicles, aerospace, smart healthcare, and Industry 4.0, many passive component makers have increased their revenue due to the surge in demand in the electronics market. The case company mainly produces passive components related products. They understand that developing SAs is an important means to enhance the competitiveness of the company, and the benefits brought by successful SAs are long-term and sustainable.As far as we know, few previous studies in the literature have examined the assessment framework of SA partners for passive component manufacturing, especially the sustainability assessment criteria that have not been well proposed. In this study, we propose a model for assessing sustainable SA partners to bring a comprehensive assessment framework and approach to the industry. First, through an extensive literature review and expert interviews, six dimensions and 29 criteria were identified. Next, neutrosophic ITARA was used to obtain the criteria weights and neutrosophic TOPSIS was applied to prioritize the alternative partners.According to the neutrosophic ITARA results in Table13, environmental certification (G1) is the most discriminating criterion, with a weight value of 0.047. This result indicates that the performance of the G1 criterion varies considerably among the alternative partners. Since companies have different competitive strategies and environmental regimes, investment in the criteria may vary. In different countries, there are many different environmental certifications, such as JIS, NRTL, VDE, RoHS, and CE. As environmental protection issues gradually become the focus of international attention, governments and private enterprises are paying more and more attention to green materials, green processes, or green products, and therefore gradually setting up standards and regulations, and giving rise to green-related certifications or environmental labels, and enterprises obtaining green-related certifications or environmental labels are relatively gaining the recognition and trust of customers and general consumers in terms of green protection. Besides, other criteria that are among the top five in importance are communication and information sharing (S2), joint investment (E5), stakeholders’ rights protection (S4), and green resource integration (G2) are all criteria of particular importance to alternative partners, as improved performance on these indicators can significantly improve overall performance.In the ranking of the alternative partners, A5 is currently the optimal performing SA partner. A5 is a multinational manufacturer of high-frequency antennas for GPS, automotive navigation cables, NFC, and more. The partner has a wide sales channel and masters the technology of high-frequency antenna production. In recent years, the case company wants to develop new technologies and sales channels for electric vehicle components, and A5’s support in this part can make a great contribution and help the case company’s future business development. In addition to A5, A3 is the second-ranked alternative partner, and the case company can determine how many companies it needs to include in the SA based on its competitive strategy.Since G1 is the most discriminating criterion in this case, a sensitivity analysis is performed to detect the influence of this criterion on the analysis results. The weight of G1 is set in the range of 0.01 to 0.09, and the interval unit of each change is 0.01. Other criteria are assigned in proportion to the neutrosophic ITARA weights. Table16 is the ranking of alternative partners by performing nine sensitivity analyses. A5 still belongs to the top one alternative partner in the nine analysis results. According to Figure 2, the ranking status of the alternatives can be clearly seen. Except for A5 and A3, the rest of the alternative partners will change with the weight of G1, which shows the necessity of formulating the criteria weights.Table 16
The ranking of alternative partners by performing nine sensitivity analyses.
Run 1Run 2Run 3Run 4Run 5Run 6Run 7Run 8Run 9G1 weight0.010.020.030.040.050.060.070.080.09A1443334445A2334456666A3222222222A4666665554A5111111111A6555543333Figure 2
Line graph of sensitivity analysis results.This study compared six neutrosophic-based MCDM methods to illustrate their differences, including neutrosophic simple additive weighting (SAW), neutrosophic additive ratio assessment (ARAS), neutrosophic weighted aggregated sum product assessment (WASPAS), neutrosophicvlse kriterijumska optimizacija i kompromisno resenje in Serbian (VIKOR), neutrosophic original TOPSIS, and our proposed model. Table 17 presents the calculation results of the six methods and the ranking of alternative partners. With the exception of neutrosophic VIKOR, the ranking results for the other five methods are the same. In this paper, our model extends the concept of original TOPSIS in determining the variation of each alternative with respect to the normalized reference ideal, using the AL and WL solutions to map the relative position of each assessed partner. Compared with the other five methods, our model can obtain more potential gap information of alternative partners. In addition, the proposed model not only overcomes the practical limitations of the original TOPSIS but also facilitates the examination of the attributes with which the assessed partners are underperforming.Table 17
Comparison of six neutrosophic-based MCDM methods.
Neutrosophic SAWNeutrosophic ARASNeutrosophic WASPASNeutrosophic VIKORNeutrosophic TOPSIS (original)Neutrosophic TOPSIS (our model)SAWRankKRankQRankRRankCCRankCCRankA10.58130.16330.56430.95550.56530.0023A20.57250.16050.55850.99560.55850.0005A30.60020.16820.58320.70230.58020.0062A40.57260.16060.55560.50020.5496-0.0026A50.66710.18710.65910.35010.64910.0231A60.57740.16240.55840.83140.55840.0004


## 6. Conclusion and Future Work

This paper presents a systematic and sustainable SA partner assessment model that provides a tool for selecting and assessing SA partners in passive component manufacturing industries. This hybrid MCDM model not only reduces the subjectivity of management decisions but also measures the uncertainty of information. There is no academic research that comprehensively examines the recruitment of SA members in passive component manufacturing industries. This paper integrates several state-of-the-art approaches, including neutrosophic fuzzy logic, neutrosophic ITARA, and neutrosophic TOPSIS techniques to consider various realistic factors such as the consideration of information uncertainty and the introduction of the aspiration level concept. According to neutrosophic ITARA calculations, environmental certification (G1) is the most discriminative criterion. On the other hand, the order of preference of the alternative partners is A5 >≻ A3 >≻ A1 >≻ A6 >≻ A2 >≻ A4.Our study illustrates the validity and reliability of the proposed model. It should bring several benefits to the case company:(i)
Identifying the most appropriate SA partners for passive component manufacturers;(ii)
Providing criteria for sustainability assessment of partners; and(iii)
Helping analysts to be more systematic in the DM process.The model concept proposed in this study is novel, but there are still some limitations to overcome. The proposed model can be programmed in collaboration with academics from information backgrounds to jointly develop software for SA selection to facilitate its application by more academic researchers and industry managers. In addition, the interdependence among the criteria has not been discussed in this paper, and in the future, the DEMATEL technique can be combined to determine the mutual influential relationships of criteria.



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*Source: 9483256-2022-04-23.xml*