A New Hybrid Decision-Making Model for Promoting Sustainable Social Rental Housing

Abstract

The realization of sustainable social rental housing is regarded as an important policy to solve the housing burden, but social rental housing is often unsustainable. This study assesses the sustainability of social rental housing. However, the decision-making models, such as the classical decision-making hierarchy (AHP) used in the current study, conflict with the resolution of the complex influence of the relationship between evaluation dimensions/criteria. Based on this, we construct a new hybrid multi-attribute decision-making model (MADM) combining the Fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL), Fuzzy DEMATEL-based analytic network process (DANP) and the modified VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for the sustainability assessment of government-led social rental housing (SRH) using Taiwanese experts as the subject of the investigation. The Fuzzy DEMATEL found that economic sustainability (D₁), as the core dimension, affects environmental (D₃) and social sustainability (D₂). Furthermore, criteria with the “cause” position, including the reasonable development model (C₂), the provision of living facilities and services needed (C₅), the adoption of environmentally friendly technology and equipment (C₁₀), guaranteed rent and lease (C₁), the acquisition of working skill and employment opportunities (C₆) and space planning and design (C₃), should receive more attention from decision makers because improving these can further enhance the sustainability of the overall scheme. Combined with the DANP weight and modified VIKOR, we also indicate that these criteria should be optimized to make the evaluation more sustainable for a selected social housing case in Taiwan. The research also further proposes management strategy implications.

1. Introduction

The world’s urban population is expected to grow from 3.6 billion in 2011 to 6.3 billion in 2050, with 94% of the growth occurring in developing countries [1]. In developing countries, approximately 828 million people reside in slums and substandard housing [2]. The shortage of affordable housing has become a structural problem [3,4]. As one of the most basic human needs, housing is a key component of sustainable development for communities [5] and one of the most important public priorities of 202 affecting sustainable urban development [6]. Failure to properly solve housing problems may increase spatial inequality [7] and become a potential determinant of intergenerational discrimination in society [8]. Fast-developing countries such as China [9] and more developed European countries [10] have observed severe housing problems—high housing prices and associated affordability for low-income groups. To address this challenge, social housing (hereinafter referred to as SH) has been regarded as a panacea for solving this problem and has been proposed as an agenda by many governments for improving the housing conditions of low-income families.

Promoting SH toward sustainability has received considerable attention since 1998 and is central to sustainable development policymaking [11]. For example, social housing projects in Brazil are the ultimate goal of sustainable development [12]. However, social housing developments are often not sustainable, especially with the low cost and affordability inherent in SH developments. Therefore, economic sustainability often becomes a more important consideration for decision makers in public and private sector organizations [13]. Given this, it can be observed that most affordable housing facilities are built on the outskirts of cities and towns [14] but often suffer from underdeveloped key infrastructure, such as roads or living facilities, resulting in public housing application rates being too low [15]. Problems with architectural design, including poor durability, affect residents’ quality of life and lead to environmental degradation [9], which tends to isolate them and create high social segregation [16]. On the other hand, the lack of consideration of inclusive policies to create a supportive community environment in the past when designing social housing [17] promotes the vacancy of social housing, leads to the deterioration of the surrounding environment and stigmatizes social housing [7]. Carter and Fortune [11] surveyed social housing landlords and found that social housing does not pay equal attention to achieving sustainability. Therefore, it is necessary to actively balance economic, social and environmental goals in promoting SH toward sustainable development [18].

How to promote social housing toward sustainable development has received increasing attention, especially the establishment of a sustainable social housing evaluation framework from the perspective of post-evaluation. This helps relevant stakeholders to propose corresponding strategies for evaluating current programs/states [19] to achieve the most sustainable outcomes [20] while ensuring that the public administration allocates available resources [21]. Many construction projects have evaluation systems such as Leadership in Energy and Environmental Design (LEED) in the United States, Building Research Establishment’s Environmental Assessment Method (BREEAM) in the United Kingdom, Comprehensive Assessment System for Built Environment Efficiency (CASBEE) in Japan and GBTool in Canada. Because of the disproportionate consideration of environmental sustainability, the consideration of social and economic dimensions in SH has been inadequate [22]. On the other hand, although the academic field proposes a more flexible and comprehensive evaluation framework, its decision-modeling method also faces some practical challenges. More prominently, traditional linear statistics [8,9,13,14,18,23,24,25] and classical methods such as the Analytic Hierarchy Process (AHP) are widely used [6,15,26,27,28], but the lack of careful consideration of the interaction relationship between assessment dimensions/criteria is still unfavorable, especially the frequent interaction between different dimensions/criteria in sustainability assessment obtaining academic consensus [29,30,31]. Although a few social housing evaluation studies adopt the advanced Analytic Network Process (ANP) [32,33], initially solving the problem of mutual influence, the weight matrix constructed without obtaining the mutual relationship in a systematic way is still not convincing enough [34,35]. Although more advanced decision-making methods have been applied to explore the interplay between low-cost housing and environmental sustainability [36], the study lacks a comprehensive social and economic assessment. The decision-making evaluation of the introduction of relationships into actual cases is also insufficient, and these deficiencies are the key research cores of this study.

By clarifying the interrelationships between dimensions/criteria and identifying their causal attributes, decision makers can think about allocating resources under limited resources to make achieving sustainability easier [37,38]. Adabre [14] stated that exploring the interrelationships between key social housing is critical for building a sustainable social housing model, especially in achieving the United Nations Sustainable Development Goal 11, which emphasizes that all people need sustainable and affordable housing by 2030. Based on this, this study intends to construct a new hybrid multi-attributable decision-making model (MADM), including multiple decision-making evaluation methods from the perspective of ex-post evaluation. This model is carried out in government-led social rental housing. When building new communities or cities for housing, sustainable development should be part of urban development plans, and the role of government among all stakeholders is crucial in the pursuit of sustainability [39]. In this study, under the background of Taiwan, which has actively promoted social housing policies in recent years, we investigate the views of relevant experts in the region on the mutual influence of social housing to achieve sustainable evaluation and conduct a sustainability assessment of a social housing project that has been promoted in this area. We evaluate the performance of the model to check its feasibility and then propose measures for improvement.

In short, the proposed MADM fully considers the influence of the relationship of the evaluation dimension/criterion from the basis of system dynamics, i.e., after using the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method to obtain the influence relationship, it is introduced into Go to the traditional ANP to obtain the DANP weight of the evaluation dimension/criterion. Then, this weight is combined with the modified VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) to evaluate the performance of the case and its gap to achieve the ideal level for proposing an improvement strategy combined with the influence relationship of DEMATEL. This kind of N-HMADM has gradually attracted attention and application in the assessment of urban sustainability in recent years [30,40] because this method not only improves the lack of assessment criteria/dimensions of the previous classic AHP, but the consideration of the mutual influence relationship among them also optimizes the inadequacy of traditional ANP to construct the influence relationship matrix [37,38]. The modified VIKOR can also propose the performance evaluation ranking of cases based on different perspectives that tend to be the least regretful of individual cases or groups and improve the shortcomings of traditional VIKOR that can only evaluate multiple projects [41]. Moreover, the influence relationship of DEMATEL can also be combined. This can provide decision-makers with the identification of the best improvement direction and countermeasures to achieve sustainable development. To our knowledge, this study is also the first to apply this novel model to the sustainability assessment of social housing, filling the gaps in the current literature and providing new ideas for assessment decisions.

In the next section, we review relevant literature and propose an assessment framework for social rental housing toward sustainability. Following this is the presentation of the modelling procedures of the proposed model, MADM, with a case study in Section 3. Section 4 presents the empirical findings and discussion, and the last section draws the conclusions.

2. Social Rental Housing toward Sustainability

2.1. Relevant Work

Although the types and definitions of SH vary in different countries, the European Liaison Committee for Social Housing (CECODHAS) highlights that SH in the European Union should assist families upon difficulty accessing decent housing and finding suitable housing in corresponding urban structures [42]. Hansson and Lundgren [43] stated that SH needs to meet two conditions: (1) The target families of SH should be those with limited financial resources. To ensure that long-term housing instead of temporary housing is provided for the target population, a distribution system must be appropriately designed. (2) The rents or prices of SH must be below the market value; hence, it is not economically self-sustaining and requires some forms of public or private financial contributions (subsidies). In this study, we use government-led social rental housing (SRH) projects as the revealing cases.

Recent international agendas have highlighted the importance of sustainable housing for the realization of sustainability. The United Nation’s Goal 11 in the 2030 Agenda for Sustainable Development has emphasized the target of ensuring ‘access for all to adequate, safe and affordable housing and basic services and upgrade slums’ by 2030. The UN Geneva Charter on Sustainable Housing, proposed by the United Nations Economic Commission for Europe in 2015, indicated that sustainable housing is related to environmental protection, economic benefits, social inclusion and participation, and cultural adequacy [44]. Sustainable SH can be defined as housing provided by the government or nonprofit organizations through various housing assistance programs, under which housing projects are constructed with environmentally friendly and sustainable materials that have long-term economic, environmental and social benefits, without increasing the life cycle costs while meeting the present and future housing needs in terms of overall social value [17]. Ecological compatibility, social acceptability and economic feasibility are the core issues of SH [14,45]. However, common assessment systems in practice tend to focus more on environmental sustainability, such as BREEAM in the United Kingdom, LEED in the United States, CASBEE in Japan, DGNB in Germany and GBTool in Canada. Limited attention has been paid to economic and social sustainability [15,22]. Ross et al. [46] proposed several principles for the sustainable development of low- and middle-income housing, suggesting that, in addition to considering minimizing resource consumption, it should also promote social and economic sustainability.

Several studies (see

Table 1. Summary of studies on sustainable social housing/public housing evaluation and decision making.

Author(s)	Research Topic/Area	Method	Brief Conclusion
Carter and Fortune [11]	Sustainable social housing procurement program/UK	Interviews and Online Questionnaires	Sustainability is not adequately addressed in the procurement of social housing projects.
Huang and Du [47]	Public housing satisfaction/Hangzhou, China	Questionnaire	Neighborhood environments, public facilities and housing characteristics are the main factors affecting residents’ satisfaction.
Li et al. [32]	Sustainable assessment model for public rental housing/Nanjing, China	Expert Questionnaire and ANP	Three subsystems covering society, economy and ecology were constructed to evaluate the Nanjing case and to determmine the need for further improvement in ecological sustainability.
Gan et al. [9]	Key Sustainability Performance Indicators (KSPI) for affordable housing/Chongqing, China	Expert Questionnaire	The most critical KSPI is financial feasibility, and the reduction in life cycle cost is the least important indicator.
Tupenaite et al. [6]	Assessment of sustainable housing development/Baltic Sea	Expert Questionnaire and ANP	Environmental sustainability is seen as more important than social or economic sustainability.
Tupenaite et al. [22]	Assessment of sustainable housing development/Baltic Sea	Expert Questionnaire and Simple Additive Weighting (SAW)	Energy and atmospheric factors, as well as the choice of environmentally friendly materials, affordable housing, public transport and the use of the most important public facilities (schools, kindergartens and medical institutions) are more important.
Oyebanji et al. [13]	Key factors for achieving sustainable social housing/England	Expert Questionnaire	Economics is the most important key factor, especially affordability, adequate funding and supply, and good management.
Wu et al. [15]	Assessment system of sustainability for public rental housing/China	Expert Questionnaire	Consideration of environmental, institutional and cultural sustainability remains insufficient.
Giannetti et al. [12]	Evaluation of social housing promotion/Brazil	Emergy Accounting	Suggestions for selecting development projects based on economic considerations alone may not be complete by quantifying the Environmental Sustainability Index and the Emergy Index for Construction Productivity.
Chan and Adabre [23]	Critical Success Criteria (CSC)/Countries of the World for Sustainable Affordable Housing Projects	Expert Questionnaire and Principal Component Analysis (PCA)	Housing prices relative to income, rent relative to income, the maintainability of housing facilities, end-user satisfaction with housing facilities and housing facilities as CSCs.
Li et al. [48]	Sustainable housing drivers/New Zealand	Expert Interview	Three case studies of New Zealand were evaluated, showing different goals in achieving environmental, economic, social and cultural sustainability.
Adabre et al. [18]	Barriers to affordable housing push/World Countries	Expert Questionnaire	The potential among incentive-related and housing-market-related barriers is associated with insufficient sustainable affordable housing in countries around the world.
Adabre and Chan [14]	Green retrofit for sustainable affordable housing/Ghana	Expert Questionnaire	Indicators related to the environment (e.g., energy efficiency and eco-friendliness of housing facilities) are important, and indicators of social sustainability (i.e., end-user satisfaction with housing facilities, the functionality of housing facilities, safety and housing quality) and indicators of affordability are rated high in terms of economy and sustainability indicators (i.e., prices/rents of housing facilities).
Saidu and Yeom [8]	Sustainable affordable housing success criteria/Nigeria	Expert Questionnaire	The highest-scoring success criterion is security, followed by accessibility.
Heffernan et al. [49]	Environmentally sustainable rental housing retrofit rivers and barriers/Australia	Expert Questionnaire	Four enabling forces were identified: communication, facilitation, motivation and regulation
Sharghi et al. [50]	Optimal location of housing for low-income group/Babolasr, Iran	GIS and TOPSIS	“Affordable criteria” is considered the key criteria in policy making.
Cardona-Trujillo et al. [51]	Life conditions of residents in social housing/Medellin, Colombia	Fuzzy AHP	Commune 16 (Belen) and commune 60 (San Cristobal) have the best and worst life conditions for inhabitants of social housing, respectively.

) have attempted to incorporate all three pillars of sustainability into a common assessment framework. Tupenaite et al. [6,22] proposed a housing sustainability assessment system for the Baltic Sea region that covers the three pillars of economy, environment and society and their related assessment indicators. The research exploring the sustainability assessment of social housing also adopts at least one or more various multi-attribute decision-making models to evaluate the application of at least one actual case and highlights the importance of social housing in achieving social and economic sustainability. Li et al. [32] used traditional ANP to explore the relationship between the social, economic and ecological subsystems of social rental housing in Nanjing, China. They found that social and economic sustainability is more important. In an indicator study exploring key sustainability indicators for social housing, Gan et al. [2] stated that aspects such as financial viability, cost recovery, reliability and durability, security of tenure and fairness are more important. Oyebanji et al. [13], through a survey of housing authorities in England and private non-profit social housing organizations, stated that economic sustainability involves the most important aspects, such as affordability, adequate funding and supply and good management, and social sustainability is not as important. Studies such as those by Chan and Adabre [23] and Adabre and Chan [14] have also stated through questionnaire surveys and statistical analyses that respondents believe that economic and social sustainability indicators are more important for the sustainable development of social housing. Wu et al. [15], based on an AHP survey of public housing projects in Guangzhou, stated the importance of accessible medical care, housing quality and a sense of security. Therefore, only by exploring the sustainability of social housing in terms of environment, society and economy can we examine its sustainable performance in all dimensions.

Questionnaire surveys are often adopted to collect people’s opinions on different indicators of sustainability of SH [8,9,13,14,18,23,24,25]. To obtain the weights of different factors, a large body of studies have adopted the classic AHP method [6,15,26,27,28]. However, the unrealistic assumption of independent relationships has been criticized because it conflicts with the causal relationship in a complex real-world decision-making environment [31]. The sustainable assessment of SH needs to consider different priorities [6,52]. However, the existing literature hardly considers the nonlinear interactions between dimensions and criteria for assessment. As a typical example, Li et al. [32] constructed a framework for China’s social rental housing based on the ANP proposed by Satty [53]. Although an ANP approach is more methodologically advanced than AHP due to its consideration of relationships between dimensions and criteria [54], the interactive relationships have not been demonstrated through a systematic approach [55]. This further discounts the credibility of weighting [37,38].

In short, the evaluation system often used in practice pays too much attention to the environmental dimension and not enough to the comprehensive evaluation of the sustainability of social housing. As Carter and Fortune [11] stated, the current principles and tools related to the sustainability of social housing packages, definitions and agendas range widely, but most carry equal weight on economic, social and environmental dimensions. In most current academic research fields, the lack of mutual influence in constructing evaluation decision-making models also strongly conflicts with the phenomenon of mutual influence in representing sustainable evaluation issues. Krishna et al. [36] adopted a more advanced DEMATEL to explore the housing situation in India. However, the sustainability assessment of low-cost housing only focuses on green parameters and lacks consideration of social and environmental dimensions, and the impact relationship has not been well incorporated into actual case assessments, which need further optimization. The construction of an evaluation system for the sustainable development of social housing through a more convincing and realistic systematic approach, especially to clarify the mutual influence of various dimensions/criteria and to apply it to actual case evaluations, can help with further compensation and optimization.

2.2. An Evaluation Framework for Sustainable Social Rental Housing

Existing research on affordable housing toward sustainability involves many criteria and factors, covering the social, economic and environmental pillars of sustainability [8]. For economic sustainability, Attia [56] emphasized the necessity of reducing construction and operating costs. It is also necessary, from a social sustainability perspective, to provide future security to improve people’s quality of life, support individual and collective well-being, strengthen local communities and maintain local social and cultural traditions. With regard to environmental sustainability, there is a need to integrate the project site and the surrounding environment; to use ecological, recyclable or reusable materials during construction; and to promote energy saving. Accordingly, this study proposes an assessment evaluation framework covering three dimensions—economic sustainability (D₁), social sustainability (D₂) and environmental sustainability (D₃)—related to 12 criteria for the development of SH toward sustainability (see

Table 2. The proposed evaluation framework for SH toward sustainability.

Criteria	Description	Reference
Economic sustainability (D1)
Guaranteed rent and lease (C1)	Affordable rent, such as below-market rent and guaranteed lease terms.	[2,6,13,14,18,45,57,58,59]
Reasonable development model (C2)	Through reasonable development models, such as self-construction by the government, the joint construction of sub-houses or setting superficies, sufficient funds are allocated to support its operation and maintenance to make its overall financial viability.	[2,15,32]
Space planning and design (C3)	Location conditions coupled with appropriate space planning and design provide the required diversified room types, a barrier-free connection of different activity spaces and a large area of open space and green space to promote efficiency and avoid idleness.	[2,8,13,15,17,32,57,58,60]
Operation management mechanism (C4)	Adopting an effective management mechanism at the construction and operation stage to minimize management, maintenance, and subsequent expansion costs during the entire life cycle.	[13,17,18,32,57,58,59,61]
Social sustainability (D2)
Provision of living facilities and services needed (C5)	In addition to providing appropriate residential infrastructure, such as roads, drainage facilities and power facilities, it is also related to residents’ commuting to the outside and to living facilities such as health care and education to ensure their welfare and quality of life.	[7,8,13,14,15,32,45,47,57,58,59,61,62,63,64]
Acquisition of working skills and employment opportunities (C6)	Providing community residents with skills or employment opportunities.	[9,13,15,32,57,61,63,64]
Promotion of social cohesion and inclusion (C7)	Promoting the participation of households in management affairs and various social activities between residents; enhancing cohesion among residents with different socio-economic and cultural backgrounds; and strengthening communication and interactions with neighboring residents to minimize social isolation.	[7,8,9,13,15,17,57,58,63,64]
Creation of a comfortable and safe environment (C8)	Creating a safe living environment for residents and ensuring the safety of residents’ lives and properties.	[8,9,13,15,17,32,38,45,57,59,63,64]
Cultural identity (C9)	Maintaining existing local cultural characteristics and encouraging residents to shape their cultural identity together. For example, participating in public art or painting activities together, creating unique cultural images and spirits and promoting a sense of belonging.	[2,13,55,63,64]
Environmental sustainability (D3)
Adoption of environmentally friendly technology and equipment (C10)	Using sustainable or green building materials and various environmentally friendly technical measures.	[13,32,45,55,62]
Maximizing environmental greening (C11)	Creating greening for open spaces such as roofs and open spaces, amd using local plantings to reduce biodiversity loss and mitigate the heat island effect.	[9,13,32,47,55]
Concordance of the visual landscape (C12)	Focusing on the concordance of the visual landscape to the surrounding environment.	[7,45,55,59]

).

2.2.1. Economic Sustainability (D₁)

Housing affordability can ensure the economic sustainability of an SH project [6,14]. With a lower rent rate, low-income groups and people with special needs can access SH [18]. Therefore, affordability, as a key goal of an affordable housing plan [2] can be used to measure the sustainability of SH [23]. In addition, lease tenure protection must effectively protect against improper evictions, improve the ability to work and ensure the positive development of vulnerable families as much as possible [57]. With an extended period of residence, satisfaction with social relationships can be improved [59]. From the perspective of SH providers, financial feasibility and cost recovery are key determinants in economic sustainability to avoid the termination of projects [2]. Accordingly, guaranteed rent and lease (C₁) and a reasonable development model (C₂) are included in the economic dimension.

House interior design, quality and safety, as well as exterior building design, have also been identified as critical factors of residential satisfaction in Chinese SH projects [59]. Sufficient living space has also been proven to be essential for improving resident satisfaction [57,58,59,60]. The quality of housing structures, such as window sizes and structural components, cross-ventilation in living areas, ceilings, walls and floor renovations also play an important role in low-income families’ health [8]. These all contribute to whether people are willing to live in these social houses. Poor designs tend to produce a higher vacancy rate [9], which can lead to problems of economic sustainability. Therefore, space planning and design (C₃) is included as one indicator under this dimension. On the other hand, effective maintenance and management mechanisms are also considered vital to the success of SH [9]. Reducing the operating costs of the residence through introducing energy-saving measures, for instance, can improve energy efficiency, thereby providing households with basic needs in other areas, such as healthcare [23]. Better lease management and property services have higher tenant satisfaction [58] and lower SH exit willingness [61]. Operation management mechanisms (C₄) are thus included in this dimension.

2.2.2. Social Sustainability (D₂)

Principles such as fairness, democratic participation, social integration, people’s livelihood, local awareness, safety and quality of life are essential elements for achieving social sustainability [63,64]. Social sustainability in general involves both physical and nonphysical factors [65]. The physical factors include actual housing, environmental quality, a barrier-free environment and convenience, whereas nonphysical factors are reflected in participation and local democracy, quality of life and well-being, social tolerance, social capital and security. Access to public services, the provision of various social facilities and the promotion of stakeholder participation in community decision making are all essential aspects for SH toward social sustainability [13]. For the elderly, some special needs such as community care services for the elderly also need to be considered, such as the provision of on-duty care and doctor visits, medical lectures, regular physical examinations and sports and fitness [62], and skill acquisition and employment opportunities are important for young low-income groups [12]. Besides these factors, security or residential safety has also been recorded as a crucial determinant of social sustainability [8,13,28,57]. Given the importance of the factors mentioned above, several criteria are selected under the social dimension: the provision of living facilities and services needed (C₅), the acquisition of working skills and employment opportunities (C₆) and the creation of a comfortable and safe environment (C₈).

The participation of tenants in the decision making regarding their houses and neighborhoods is essential for improving housing management services and overall service levels, generating more community ownership, and jointly developing measures to improve their quality of life [66]. Social integration should be encouraged in the organization of public areas [16]. The acceptability of social housing also depends on whether people’s culture and lifestyle are considered [8]. Therefore, the promotion of social cohesion and inclusion (C₇) and cultural identity (C₉) are another two important criteria.

2.2.3. Environmental Sustainability (D₃)

Environmental sustainability is closely related to the current climate agendas, which highlights reductions in greenhouse gas emissions. From a macro perspective, the adoption of various green technologies, sustainable materials and renewable energy and resources can contribute to long-term energy efficiency, water saving and effective waste management [2]. At the household level, reduced household energy costs through improved efficiency or renewable energy technologies can address the fuel shortage issue and help homeowners afford house energy use [67]. Notwithstanding the higher initial capital cost of applying green technology into water and energy infrastructure, the use of green technology should be promoted from the perspective of a building’s life cycle, considering the long-term energy and water-saving benefits and reduced utility costs [68]. Hence, we also include the adoption of environmentally friendly technology and equipment (C₁₀) as one factor.

Green infrastructure has also been recognized as having multiple benefits for realizing biodiversity and promoting environmental protection [38]. It delivers many benefits on health and well-being, but it is often overlooked in SH development [9]. Additionally, green space can also offer a place for social activities to strengthen social connections between residents [16]. Thus, maximizing environmental greening (C₁₁) is considered an indicator. Existing empirical studies have confirmed the linkage between poor landscape vision and SH residents’ complaints [7]. As an important issue affecting resident satisfaction [59], concordance of the visual landscape (C₁₂) is included under the environmental dimension.

3. Development of an N-HMADM Approach

3.1. Study Case: First Phase of Ankang SRH in Taichung City

In 1975, the government of Taiwan issued the “Public Housing Act” to solve Taiwan’s housing problems. However, due to a range of difficulties associated with loans and low-quality SH projects, the policy failed to reach its goals. Since, the government has revisited the policy and stimulated short-term demand in the real estate market through more mortgage interest rate subsidies, which further resulted in a sharp rise in housing prices and many homeless people. Under civic pressure after the 2012 presidential election, the government quickly passed the “Housing Act” to promote SH as a vital policy goal [69]. Taiwan’s Executive Yuan officially launched the “Social Housing Development Plan” in March 2017, proposing eight policy plans that expect to provide SH for a total of 200,000 households. The funds required during the implementation period were provided by the housing fund [70]. To promote SH implementation and management, the National Housing and Urban Regeneration Center (HURC) was established in August 2018 to support the government in implementing the SH program through a professional and credibly administrative legal body. As of September 2018, 13,955 households of SH had been completed, representing only 0.16% of the total housing stock of 8,694,889 in 2018 Q1 [71].

In Taichung City, one of Taiwan’s six capitals and the country’s second-most populous city, the government proposed the “Good Housing Plan” in 2018, which not only accelerated the supply of SH in terms of quantity but, more importantly, tried to enhance the quality of SH via a set of initiatives such as expanding care services, promoting green space, creating community shared spaces, and encouraging public participation. The Ankang SRH was the first SRH built by the government and a landmark project of the “Good Housing Plan”. The authors collected relevant information through relevant websites and policy reports [72,73,74,75]. Fieldwork was conducted in mid-June 2021 to collect grounding information regarding different indicators under three dimensions.

Table 3. Criteria information in study case.

Dimension	Criteria	Information
Economic sustainability (D1)	Guaranteed rent and lease (C1)	Rent is lower than the market rent: (1) The first year’s rent was at 50% of the market price (rent for one room type with 25 m2 was approximately NTD 3800–4300 per month including management fees); (2) The second year’s rent was at 40% of the market price; (3) The third year’s rent was at 30% of the market price. Moreover, for low-income, middle- and high low-income households, the rent was at 35% of the market price. Lease term: Three years, and the maximum renewal period shall not exceed six years.
	Reasonable development model (C2)	Self-built by the government and dedicated housing fund for operations: SH is planned and budgeted by the Taichung City Government and is then outsourced to the private sector for construction. Moreover, a housing fund to maintain operations related to SH was established in 2017.
	Space planning and design (C3)	Planning and Design: This SH is a reinforced concrete building designed based on a cluster-type style, which comprises two floors of underground parking space and 15 floors of living space. Living configuration: A total of 200 units are configured, including 120 units (25 m2) for one room, 60 units (50 m2) for two rooms and 20 units (75 m2) for three rooms.
	Operation management mechanism (C4)	Private property company to operate the SH: The Weixin Baoquan Co., Ltd., is responsible for managing the lease, including coordinating with the settlement of tenants. Dedicated “Gonghao Social Housing APP System”: The “Gonghao Social Housing APP System” provides a series of smart services, including building announcements and mail notifications to provide the residents with a convenient smart living choice. Smart room card: Rooms are associated with smart cards as door keys. In addition, when a tenant quits renting, simply, resetting the card saves the cost of replacing the traditional door lock and further protects the living safety of the new tenant.
Social sustainability (D2)	Provision of living facilities and services needed (C5)	Health Care Service—“Local Health Room”: A Local Health Room is established and supported by “China Medical University Hospital” to provide health care services, including medical consultations, adult preventative health care, cancer screening, health lectures, and health promotion services. Social service station—“Good Neighborhood Ankang Store”: “The Good Neighborhood Ankang Store” is operated and managed by the “Eden Social Welfare Foundation” to provide a series of social-related activities and services such as welfare referrals, assistive equipment rentals and meals for the elderly. Rooftop vegetable garden: The rooftop vegetable garden provides gardening experience and increases the opportunities for residents to meet and communicate with each other.
	Acquisition of working skills and employment opportunities (C6)	Assisting youth entrepreneurship: Providing the “Employment Counseling Program” and the “Gonghao Training Center” via cooperation with local organizations assists youth entrepreneurship.
	Promotion of social cohesion and inclusion (C7)	Seed households participating in community management: Some tenants, acting as seed households, are required to participate in community management activities for at least 2 h per month. Public practice base—“Ankang Good Living Room”: The public living room serves as a place where people can rest, chat and make things to enhance the connections and interactions between each other. It also has other functions for community activities, public art creation and a parent–child interaction space.
	Creation of a comfortable and safe environment (C8)	Concept of an organic building design: Each unit has a house with a unique open balcony, and each staircase is equipped with skylights. Provision of basic furniture: Each unit is equipped with basic furniture, such as an air-conditioner, kitchenware, bathroom equipment, single or double bed boxes, wardrobes, curtains and lamps. Some businesses such as Youqingmen Co., Ltd., and B&Q Tellus House Co., Ltd., also provide samples of home furnishings of various room types for purchase at favorable prices.
	Cultural identity (C9)	Public art: Residents are encouraged to participate in public art activities, which bring closer relationships between residents and art. The “Island of Objects” is a representative example.
Environmental Sustainability (D3)	Adoption of environmentally friendly technology and equipment (C10)	Green building silver label and the qualified smart building candidate label: This SH project has obtained the green building silver label and the qualified smart building certificate. Solar energy generation: Solar panels above the vegetable garden can generate 18.72 kW to meet the electricity needs of the building itself.
	Maximizing environmental greening (C11)	Open space and greening: Of the area, including the rooftop vegetable garden, 75% is used as a green space and open design plant area, consisting of 129 arbors and 20,000 shrubs.
	Harmony with the surrounding visual landscape (C12)	“Y”-shaped building landscape: “Y”-shaped building structures with three colorful corner balconies (yellow, blue-green and orange) are used to distinguish between different apartment types and improve the quality of life.

illustrates the evaluation information of the case project on different aspects.

The Ankang SRH is located at No. 2100, Yongkang Road, Fengyuan District, with a site area of 5552 m². It is close to the Fengyuan District Office, Fengnan Middle School, Fengyuan Hospital, Nanyang Market and Nanyang Park (see Figure 1). This SRH project offers housing units for 200 households, of which 120 are one-room units, 60 are two-room units and 20 are three-room houses. The government itself fully developed the SRH, and a private property company was introduced to manage it in conjunction with the “Gonghao community house APP system”. The rent was at least 30% lower than the market rent in June 2021. A range of facilities were developed with this project, including social service stations, health care service stations, shared living rooms, and roof vegetable gardens (see Table 3 and Figure 1).

3.2. Development of an N-HMADM Approach

The hybrid MADM approach proposed in this study integrates three different decision-making methods: Fuzzy DEMATEL, DEMATEL-based Analysis Network Process (DANP) and modified VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR). The development of this approach includes four main stages (see Figure 2).

3.2.1. Questionnaire Survey to Collect Expert Opinions

We designed an exclusive expert decision-making questionnaire in Chinese, mainly inviting experts to comment on two main parts: (1) interactions among the 12 proposed criteria and (2) the assessment of the Ankang case.

The questionnaire survey was conducted from July to the end of August 2020. An understanding of the background of Taiwan’s social housing laws and regulations was the standard for selecting experts. First, sixteen scientific researchers from universities or organizations relating to land management, urban planning, construction or property services were initially invited to the survey via email. Some experts did not provide feedback, and seven experts’ opinions were finally received (recovery rate of approximately 44%) (see

Table 4. Information on the 7 experts interviewed.

No.	Education	Working Years	Affiliation	Job Title	Area
					Land Management	Urban Planning	Architecture	Property Management
Exp. 1	Ph.D.	25	International Forum on Urbanism (IFoU)	Member of board of supervisors		․	․
Exp. 2	Ph.D.	18	University	Associate Professor	․
Exp. 3	Ph.D.	24	University	Assistant professor	․	․
Exp. 4	Ph.D. candidate	15	Property management company	Management	․			․
Exp. 5	Ph.D. candidate	10	Government sector	Section Chief	․		․
Exp. 6	Ph.D.	4	University	Associate Professor	․	․
Exp. 7	Ph.D.	3.5	University	Associate Professor		․		․

). Most of these experts came from universities or scientific research organizations with expertise in land management or urban planning. When conducting the survey, five experts had a doctoral degree, and others were Ph.D. candidates. Among them, five experts had more than ten years of work experience in relevant fields. To confirm whether the opinions of these experts were consistent, a consistency test was conducted with a consensus value of 95.53%, representing an average consensus gap of 4.70%, which was in line with the requirement of less than 5% in the literature [31,37,38]. This shows that the expert opinions in this study were consistent and met the requirements from a statistical perspective.

Although the sample size was small, it was acceptable, as the MADM is an expert decision-making method [31]. MADM methods, such as traditional AHP or ANP, are subjective methods for resolving specific problems [76]. The widespread popularity of MADM methods can be attributed to their capability to handle small sample sizes (of approximately four to nine people), and large sample sizes may affect the consistency of judgment because experts provide arbitrary answers. Previous studies on urban planning and urban renewal toward sustainability, based on the MADM approach, have had small sample sizes of seven to ten experts [20,29,30,33,77]. The seven experts selected with subject-related professional knowledge and relatively rich work experience in this study can ensure the passing of the consistency test; hence, their expert feedback opinions are representative and meaningful to support this research.

3.2.2. Fuzzy DEMATEL to Explore Relationships between Dimensions/Criteria

DEMATEL was first developed in 1972 [78,79], drawing upon the concept of system dynamics. It is considered an important decision-making method for exploring complex decision-making issues and identifying causal relationships [55,80]. Herein, fuzzy semantics were introduced into the original DEMATEL to resolve uncertainty in decision making. Then, an Influential Network Relationship Map (INRM) developed through Fuzzy DEMATEL could effectively identify the causal relationships between different indicator dimensions or criteria.

The main several steps for Fuzzy DEMATEL are as follows:

(1)

Setting the fuzzy scale (see

Table 5. Fuzzy scale.

Code	Linguistic Terms	L	M	U
1	No influence	0	0	0.25
2	Very low influence	0	0.25	0.5
3	Low influence	0.25	0.5	0.75
4	High influence	0.5	0.75	1
5	Very high influence	0.75	1	1

) used in the model for constructing the relation matrix, as follows:

(2)

Constructing the original fuzzy direct-relation matrix $\mathit{A}$ based on expert opinions, as follows:

$$\mathit{A}={[{\mathit{a}}_{\mathit{i}\mathit{j}}]}_{\mathit{n}\times \mathit{n}}$$

(1)

where ${\mathit{a}}_{\mathit{i}\mathit{j}}$ denotes the average comparisons from experts’ respondents on the effect of $\mathit{i}$ on $\mathit{j}$ criteria.

(3)

Normalizing $\mathit{A}$ obtains the initial influential relationship matrix $\mathit{X}$, as follows:

$$\mathit{X}=\mathit{s}\times \mathit{A}.\mathit{s}>0$$

(2)

where $\mathit{s}=\underset{\mathit{i},\mathit{j}}{\min }\left\{\frac{1}{\underset{1\le i\le \mathit{n}}{\max }{\displaystyle \sum _{\mathit{j}=1}^{\mathit{n}}{\mathit{a}}_{\mathit{i}\mathit{j}}}},\frac{1}{\underset{1\le \mathit{j}\le \mathit{n}}{\max }{\displaystyle \sum _{\mathit{j}=1}^{\mathit{n}}{\mathit{a}}_{\mathit{i}\mathit{j}}}}\right\},\hspace{1em}\mathit{i},\mathit{j}=1,2,3,\dots ,\mathit{n}$

(4)

Obtaining the fuzzy total influential relationship matrix for criteria ${\mathit{T}}_{\mathit{c}}$ is as follows:

$${\mathit{T}}_{\mathit{c}}=\mathit{X}{(\mathit{I}-\mathit{X})}^{-1}={\left[\begin{array}{ccccc}{\mathit{t}}_{\mathit{c}}^{11}& \cdots & {\mathit{t}}_{\mathit{c}}^{1\mathit{j}}& \cdots & {\mathit{t}}_{\mathit{c}}^{1\mathit{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{t}}_{\mathit{c}}^{\mathit{i}1}& \cdots & {\mathit{t}}_{\mathit{c}}^{\mathit{i}\mathit{j}}& \cdots & {\mathit{t}}_{\mathit{c}}^{\mathit{i}\mathit{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{t}}_{\mathit{c}}^{\mathit{m}1}& \cdots & {\mathit{t}}_{\mathit{c}}^{\mathit{m}\mathit{j}}& \cdots & {\mathit{t}}_{\mathit{c}}^{\mathit{m}\mathit{m}}\end{array}\right]}_{\mathit{n}\times \mathit{n}|\mathit{m}<\mathit{n},\hspace{0.33em}{\displaystyle {\sum }_{\mathit{j}=1}^{\mathit{m}}{\mathit{m}}_{\mathit{j}}=\mathit{n}}}$$

(3)

where ${\underset{\mathit{k}\to \infty }{\lim \mathit{X}}}^{\mathit{k}}={[0]}_{\mathit{n}\times \mathit{n}}$.

(5)

Defuzzifying into crisp values.

Based on the work of Opricovic and Tzeng [81], Converting Fuzzy data into Crisp Scores (CFCS) is used to obtain a crisp value of the total-relation matrix.

(6)

Then, the total influential relationship matrix for dimension ${\mathit{T}}_{\mathit{D}}$ is obtained as follows:

$${\mathit{T}}_D^{}={\left[\begin{array}{ccccc}{\mathit{t}}_{{}_D}^{11}& \cdots & {\mathit{t}}_{{}_D}^{1j}& \cdots & {\mathit{t}}_{{}_D}^{1m}\\ ⋮& & ⋮& & ⋮\\ {\mathit{t}}_{{}_D}^{i1}& \cdots & {\mathit{t}}_{{}_D}^{ij}& \cdots & {\mathit{t}}_{{}_D}^{im}\\ ⋮& & ⋮& & ⋮\\ {\mathit{t}}_{{}_D}^{m1}& \cdots & {\mathit{t}}_{{}_D}^{mj}& \cdots & {\mathit{t}}_{{}_D}^{mm}\end{array}\right]}_{n\times n|m<n,\hspace{0.33em}{\displaystyle {\sum }_{j=1}^m{m}_j=n}}$$

(4)

(7)

Summing up each row and column in $T_c$ is undertaken to obtain the sum vector of row $r_i$ and the sum vector of column $c_j$, as follows:

$$r_i={\left[{\displaystyle \sum _{i=1}^n{t}_{ij}}\right]}_{n\times 1}$$

(5)

$$c_j={\left[{\displaystyle \sum _{i=1}^n{t}_{ij}}\right]}_{n\times 1}^{\text{'}}$$

(6)

where $i=j=1,2,\dots ,n$. r_i represents the degree to which a certain criterion $i$ directly or indirectly impact the other criteria, and c_i represents the degree to which a certain criterion $i$ is directly or indirectly affected by other criteria.

3.2.3. DANP to Obtain the Weights for Evaluation

The ANP was proposed by Satty [53] to improve the unrealistic assumption of the classic AHP regarding the assumption of independent relationships between criteria [54]. However, the calculation of the traditional ANP assumes that the diagonal matrix is an identity matrix. Hence, the influence relationship it generates is still doubtful. The integration of DEMATEL and ANP is a powerful approach that can model causality [55]. The introduction of the interaction relationships derived from DEMATEL into the traditional ANP method can provide a stronger foundation for forming network relationships, which is also regarded as an advantageous approach to obtaining weights to evaluate the plan [31].

The main several steps for DANP are as follows:

(1)

The fuzzy total influential relationship matrix ${\mathit{T}}_{\mathit{c}}$ is normalized to form the normalized total influential relationship matrix ${\mathit{T}}_{\mathit{c}}^{\mathit{N}\mathit{o}\mathit{r}}$, as follows:

$${\mathit{T}}_{\mathit{c}}^{\mathit{N}\mathit{o}\mathit{r}}=\begin{array}{ll}& \begin{array}{ccccc}\stackrel{{\mathit{D}}_1}{{\mathit{c}}_{11\cdots }{\mathit{c}}_{1{\mathit{m}}_1}}& \cdots & \stackrel{{\mathit{D}}_{\mathit{j}}}{{\mathit{c}}_{\mathit{j}1\cdots }{\mathit{c}}_{\mathit{j}{\mathit{m}}_{{}_{\mathit{j}}}}}& \cdots & \stackrel{{\mathit{D}}_{\mathit{m}}}{{\mathit{c}}_{\mathit{m}1\cdots }{\mathit{c}}_{\mathit{m}{\mathit{m}}_{\mathit{m}}}}\end{array}\\ \begin{array}{}\begin{array}{c}{\mathit{D}}_1\\ ⋮\end{array}\begin{array}{c}{\mathit{c}}_{11}\\ {\mathit{c}}_{12}\\ ⋮\\ {\mathit{c}}_{1{\mathit{m}}_1}\\ ⋮\end{array}\\ \begin{array}{c}{\mathit{D}}_{\mathit{i}}\\ ⋮\end{array}\begin{array}{c}{\mathit{c}}_{\mathit{i}1}\\ {\mathit{c}}_{\mathit{i}2}\\ ⋮\\ {\mathit{c}}_{\mathit{i}{\mathit{m}}_{\mathit{i}}}\\ ⋮\end{array}\\ \begin{array}{c}{\mathit{D}}_{\mathit{m}}\\ ⋮\end{array}\begin{array}{c}{\mathit{c}}_{\mathit{m}1}\\ {\mathit{c}}_{\mathit{m}2}\\ ⋮\\ {\mathit{c}}_{\mathit{m}{\mathit{m}}_{\mathit{m}}}\end{array}\end{array}& {\left[\begin{array}{ccccc}{\mathit{t}}_{\mathit{c}}^{\mathit{N}\mathit{o}{\mathit{r}}_{11}}& \cdots & {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{1\mathit{j}}}& \cdots & {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{1\mathit{m}}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{\mathit{i}1}}& \cdots & {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{\mathit{i}\mathit{j}}}& \cdots & {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{\mathit{i}\mathit{m}}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{\mathit{m}1}}& \cdots & {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{\mathit{m}\mathit{j}}}& \cdots & {\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{\mathit{m}\mathit{m}}}\end{array}\right]}_{\mathit{n}\times \mathit{n}|\mathit{m}<\mathit{n},\hspace{0.33em}{\displaystyle {\sum }_{\mathit{j}=1}^{\mathit{m}}{\mathit{m}}_{\mathit{j}}=\mathit{n}}}\end{array}$$

(7)

where ${\mathit{D}}_{\mathit{m}}$ is the ${\mathit{m}}^{\mathit{t}\mathit{h}}$ cluster, ${\mathit{c}}_{\mathit{m}\mathit{m}}$ indicates the ${\mathit{n}}^{\mathit{t}\mathit{h}}$ criterion of the ${\mathit{m}}^{\mathit{t}\mathit{h}}$ cluster, and ${\mathit{t}}_c^{\mathit{N}\mathit{o}{\mathit{r}}_{\mathit{i}\mathit{j}}}$ denotes the eigenvector of the criterion’s influence when comparing the ${\mathit{j}}^{\mathit{t}\mathit{h}}$ cluster and the ${\mathit{i}}^{\mathit{t}\mathit{h}}$ cluster.

(2)

${\mathit{T}}_{\mathit{c}}^{\mathit{N}\mathit{o}\mathit{r}}$ is transposed to obtain the un-weighted super-matrix ${\mathit{W}}_{\mathit{c}}$, as follows:

$${\mathit{W}}_{\mathit{c}}={({\mathit{T}}_{\mathit{c}}^{\mathit{N}\mathit{o}\mathit{r}})}^{\prime }=\begin{array}{ll}& \begin{array}{ccccc}\stackrel{{\mathit{D}}_1}{{\mathit{c}}_{11\cdots }{\mathit{c}}_{1{\mathit{m}}_1}}& \cdots & \stackrel{{\mathit{D}}_{\mathit{j}}}{{\mathit{c}}_{\mathit{j}1\cdots }{\mathit{c}}_{\mathit{j}{\mathit{m}}_{{}_{\mathit{j}}}}}& \cdots & \stackrel{{\mathit{D}}_{\mathit{m}}}{{\mathit{c}}_{\mathit{m}1\cdots }{\mathit{c}}_{\mathit{m}{\mathit{m}}_{\mathit{m}}}}\end{array}\\ \begin{array}{}\begin{array}{c}{\mathit{D}}_1\\ ⋮\end{array}\begin{array}{c}{\mathit{c}}_{11}\\ {\mathit{c}}_{12}\\ ⋮\\ {\mathit{c}}_{1{\mathit{m}}_1}\\ ⋮\end{array}\\ \begin{array}{c}{\mathit{D}}_{\mathit{i}}\\ ⋮\end{array}\begin{array}{c}{\mathit{c}}_{\mathit{i}1}\\ {\mathit{c}}_{\mathit{i}2}\\ ⋮\\ {\mathit{c}}_{\mathit{i}{\mathit{m}}_{\mathit{i}}}\\ ⋮\end{array}\\ \begin{array}{c}{\mathit{D}}_{\mathit{m}}\\ ⋮\end{array}\begin{array}{c}{\mathit{c}}_{\mathit{m}1}\\ {\mathit{c}}_{\mathit{m}2}\\ ⋮\\ {\mathit{c}}_{\mathit{m}{\mathit{m}}_{\mathit{m}}}\end{array}\end{array}& {\left[\begin{array}{ccccc}{\mathit{W}}_{\mathit{c}}^{11}& \cdots & {\mathit{W}}_c^{i1}& \cdots & {\mathit{W}}_{\mathit{c}}^{\mathit{m}1}\\ ⋮& & ⋮& & ⋮\\ {\mathit{W}}_{\mathit{c}}^{1\mathit{j}}& \cdots & {\mathit{W}}_{\mathit{c}}^{\mathit{i}\mathit{j}}& \cdots & {\mathit{W}}_{\mathit{c}}^{\mathit{m}\mathit{j}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{W}}_{\mathit{c}}^{1\mathit{m}}& \cdots & {\mathit{W}}_{\mathit{c}}^{\mathit{i}\mathit{m}}& \cdots & {\mathit{W}}_{\mathit{c}}^{\mathit{m}\mathit{m}}\end{array}\right]}_{\mathit{n}\times \mathit{n}|\mathit{m}<\mathit{n},\hspace{0.33em}{\displaystyle {\sum }_{\mathit{j}=1}^{\mathit{m}}{\mathit{m}}_{\mathit{j}}=\mathit{n}}}\end{array}$$

(8)

(3)

The normalized total influence relationship matrix for dimension ${\mathit{T}}_D^{Nor}$ is introduced into ${\mathit{W}}_{\mathit{c}}$ to obtain the weighted super-matrix ${\mathit{W}}_c^{\alpha }$, as follows:

$${\mathit{W}}_c^{\alpha }={\mathit{T}}_D^{Nor}\times {\mathit{W}}_c^{}={\left[\begin{array}{ccccc}(\frac{t_D^{11}}{d_1})\times {\mathit{W}}_c^{11}& \cdots & (\frac{t_D^{1j}}{d_1})\times {\mathit{W}}_c^{i1}& \cdots & (\frac{t_D^{1m}}{d_1})\times {\mathit{W}}_c^{m1}\\ ⋮& & ⋮& & ⋮\\ (\frac{t_D^{i1}}{d_i})\times {\mathit{W}}_c^{1j}& \cdots & (\frac{t_D^{ij}}{d_i})\times {\mathit{W}}_c^{ij}& \cdots & (\frac{t_D^{im}}{d_i})\times {\mathit{W}}_c^{mj}\\ ⋮& & ⋮& & ⋮\\ (\frac{t_D^{m1}}{d_m})\times {\mathit{W}}_c^{1m}& \cdots & (\frac{t_D^{mj}}{d_m})\times {\mathit{W}}_c^{im}& \cdots & (\frac{t_D^{mm}}{d_m})\times {\mathit{W}}_c^{mm}\end{array}\right]}_{n\times n|m<n,\hspace{0.33em}{\displaystyle {\sum }_{j=1}^m{m}_j=n}}$$

(9)

(4)

Then, the weighted super-matrix is multiplied 100 times to converge into a stable super-matrix. Finally, the DANP global weight for criteria and dimensions are obtained.

$$\mathit{w}=Li{m}_{\phi \to \infty }{({\mathit{W}}_C^{\alpha })}^{\phi }$$

(10)

3.2.4. Modified VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) as a Method for Evaluating and Presenting Improvement Strategies

In the last step, the DANP weight is applied to the modified VIKOR to evaluate the case performance and propose improvement strategies. This method was improved by Opricovic and Tzeng [82,83], based upon the expected level proposed by Simon [84]. The traditional VIKOR only evaluates 1 and 0 as positive ideal solutions and negative ideal solutions, respectively, and this method cannot evaluate a single solution and is not able to inform decision makers about which countermeasures and methods can be adopted [31]. Modified VIKOR allows decision makers to evaluate any value from 0 to 10, calculate the gap between the value and the expected level and simultaneously combine the interaction relationship obtained by DEMATEL and its INRM to finally identify improvement measures and methods.

The main several steps for modified VIKOR are as follows:

(1)

The first step is to construct the average performance matrix collected from expert opinions, as follows:

$$p={[f_{kj}]}_{k\times n}$$

(11)

where $p$ represent the alternative’s total performance score, and $k$ denotes the number of alternatives.

(2)

Then, Sk, representing the average gap of certain alternatives (i.e., the average gap with the aspiration level) is obtained, as follows:

$$S_k={\displaystyle \sum _{j=1}^n{w}_j|f_j^{*}-f_{kj}^{}|/|f_j^{*}-f_j^{-}}|$$

(12)

where $w$ denotes the DANP weights; $f_j^{*}$ as the aspiration level; and $f_j^{-}$ is the worst level.

(3)

Qk, representing the maximum gap (i.e., the largest gap with the aspiration level), is obtained, as follows:

$$Q_k=\underset{j}{\max }\{|f_j^{*}-f_{kj}^{}|/|f_j^{*}-f_j^{-}|,j=1,2,\cdots ,n\}$$

(13)

(4)

To obtain the optimized compromise solution, they are sorted by setting the parameters v to obtain the integration value R_k:

$$R_k=\frac{v(S_k-S^{*})}{(S^{-}-S^{*})}+(1-v)\frac{(Q_k-Q^{*})}{(Q^{-}-Q^{*})} Q_k=ma{x}_j\left\{\frac{\left|f_j^{*}-f_{kj}\right|}{\left|f_j^{*}-f_j^{-}\right|}\left|j=1,2,\dots ,n\right.\right\}$$

(14)

Herein, the principles of min $S_k$ and min $Q_k$ are adopted. The former sets the S* = min $S_k$ (i.e., S* = 0) and S⁻ = max S_k (i.e., S⁻ = 1), and the latter sets the Q* = min $Q_k$ (i.e., Q* = 0) and Q⁻ = max $Q_k$ (i.e., Q⁻ = 1).

(5)

$1-R_k$ is used to build a “sustainable development index” for the evaluation with regard to the extent to which its decision making brings it closer to sustainable development.

4. Empirical Results and Discussion

4.1. Empirical Analysis of Fuzzy-DEMATEL and DANP

The calculated values related to DEMATEL and DANP are presented in Appendix A. First, we explore the influences and positions for dimensions (see

Table 6. Empirical results of Fuzzy DEMATEL and DANP.

	Fuzzy DEMATEL				DANP
Dimension/Criteria	ri	ci	ri + ci	ri − ci	Local Weight (Ranking)	Global Weight
Economic sustainability (D1)	12.716	11.792	24.508	0.924	0.343 (2)
Guaranteed rent and lease (C1)	2.848	2.952	5.8	0.104	0.082 (6)	0.240
Reasonable development model (C2)	2.337	3.296	5.633	0.958	0.063 (12)	0.183
Space planning and design (C3)	3.273	3.305	6.578	0.032	0.098 (2)	0.285
Operation management mechanism (C4)	3.333	3.164	6.498	−0.169	0.100 (1)	0.291
Social sustainability (D2)	13.686	14.402	28.088	−0.716	0.413 (1)
Provision of living facilities and services needed (C5)	3.143	3.229	6.372	0.087	0.089 (4)	0.216
Acquisition of working skills and employment opportunities (C6)	2.331	2.459	4.791	0.128	0.064 (11)	0.155
Promotion of social cohesion and inclusion (C7)	3.064	2.36	5.425	−0.704	0.088 (5)	0.213
Creation of a comfortable and safe environment (C8)	3.236	3.096	6.331	−0.14	0.098 (2)	0.237
Cultural identity (C9)	2.627	2.542	5.169	−0.086	0.074 (10)	0.179
Environmental sustainability (D3)	8.391	8.599	16.990	−0.208	0.243 (3)
Adoption of environmentally friendly technology and equipment (C10)	2.848	2.977	5.825	0.129	0.082 (6)	0.337
Maximizing environmental greening (C11)	2.909	2.803	5.712	−0.107	0.082 (6)	0.337
Harmony with the surrounding visual landscape (C12)	2.845	2.611	5.456	−0.233	0.079 (9)	0.325

Notes: r_i + c_i of threshold value for dimension and criteria are 23.195 and 5.799, respectively. r_i − c_i of threshold value is 0.

and the INRM shown in Figure 3). From the given vector r_i + c_i, the total influence degree is in the following order: social sustainability (D₂), followed by economic sustainability (D₁) and finally environmental sustainability (D₃). In this study, social and economic sustainability were greater than the threshold. In terms of r_i − c_i, showing how the total ability is affected by other dimensions, economic sustainability (D₁) has the largest value with 0.924, followed by environmental sustainability (D₃) with −0.208, and social sustainability (D₂) with −0.716. This result that economic sustainability (D₁) has a “cause” position and has a greater influence on other dimensions. Despite social sustainability (D₂) and environmental sustainability (D₃) having an “effect” position, environmental sustainability (D₃) with a smaller negative r_i − c_i can influence social sustainability (D₂). In other words, social sustainability (D₂) is influenced by economic sustainability (D₁) and environmental sustainability (D₃).

After analyzing the dimensions, the influences and causal positions among the criteria were observed. The threshold value of r_i + c_i, calculated by averaging the number of all criteria, is 5.799. Among the 12 criteria, 5 criteria are higher than the threshold. In order, these are space planning and design (C₃) (6.578), the operation management mechanism (C₄) (6.498), the provision of living facilities and services needed (C₅) (6.372), the creation of a comfortable and safe environment (C₈) (6.331) and the adoption of environmentally friendly technology and equipment (C₁₀) (5.825). The lowest three criteria are the acquisition of working skills and employment opportunities (C₆) (4.791), the promotion of social cohesion and inclusion (C₇) (5.425) and the concordance of the visual landscape (C₁₂) (5.456). Based on r_i − c_i, six criteria are greater than the threshold value of 0, indicating the cause position; these include the adoption of environmentally friendly technology and equipment (C₁₀) (0.129), the acquisition of working skills and employment opportunities (C₆) (0.128), guaranteed rent and lease (C₁) (0.104), a reasonable development model (C₂) (0.958), the provision of living facilities and services needed (C₅) (0.087) and space planning and design (C₃) (0.032). The rest of the criteria imply an effect position (i.e., the r_i − c_i value is below zero); these are the promotion of social cohesion and inclusion (C₇) (−0.704), the concordance of the visual landscape (C₁₂) (−0.233) and the operation management mechanism (C₄) (−0.169). The ones with the smallest values are the most affected by other criteria.

Next, we observed the Local Weight of DANP for the dimensions and criteria. First, the relative importance of the three dimensions was obtained based on the local weight, in the following order: social sustainability (D₂) (0.413), economic sustainability (D₁) (0.343) and environmental sustainability (D₃) (0.243). For all the criteria, the more weighted criteria in order are as follows: operation management mechanism (C₄) (0.100), the creation of a comfortable and safe environment (C₈) (0.098), space planning and design (C₃) (0.098), the provision of living facilities and services needed (C₅) (0.089) and the promotion of social cohesion and inclusion (C₇) (0.088). The smallest weight is reflected in the reasonable development model (C₂) (0.063) and the acquisition of working skills and employment opportunities (C₆) (0.064).

4.2. Empirical Analysis of Modified VIKOR

The DANP weight combined with the modified VIKOR was utilized to evaluate the performance and gap for Taiwan’s case (see

Table 7. Results of modified VIKOR.

Dimensions/Criteria	Performance	Gap	Ranking of Improvement
Economic sustainability (D1)	7.429	0.257	2
Guaranteed rent and lease (C1)	7.286	0.271	6
Reasonable development model (C2)	7.143	0.286	3
Space planning and design (C3)	7.143	0.286	3
Operation management mechanism (C4)	8.143	0.186	11
Social sustainability (D2)	7.457	0.254	3
Provision of living facilities and services needed (C5)	8.143	0.186	11
Acquisition of working skills and employment opportunities (C6)	7.143	0.286	3
Promotion of social cohesion and inclusion (C7)	7.429	0.257	7
Creation of a comfortable and safe environment (C8)	7.571	0.243	9
Cultural identity (C9)	7.000	0.300	2
Environmental sustainability (D3)	7.286	0.271	1
Adoption of environmentally friendly technology and equipment (C10)	7.429	0.257	7
Maximizing environmental greening (C11)	7.714	0.229	10
Harmony with the surrounding visual landscape (C12)	6.714	0.329	1
Total performance	7.403
Average gap		0.260
Maximum gap		0.329

). Among the three dimensions, the performance of social sustainability’s (D₂) value of 7.457 is better, followed by economic sustainability (D₁) with 7.429, and the last performance of environmental sustainability (D₃) with 7.286, reflecting that the gap of the aspiration level of environmental sustainability (D₃) of 0.271 is the largest. In terms of criteria (see Table 7 and Figure 4), six criteria reveal better performance (i.e., higher than the total performance) in the following order: operation management mechanism (C₄) and the provision of living facilities and services needed (C₅) with 8.143, maximizing environmental greening (C₁₁) with 7.714, the creation of a comfortable and safe environment (C₈) with 7.571, the promotion of social cohesion and inclusion (C₇), and the adoption of environmentally friendly technology and equipment (C₁₀) with 7.429. Conversely, the poor performers are as follows: the concordance of the visual landscape (C₁₂) with 6.714, cultural identity (C₉) with 7.000, a reasonable development model (C₂), space planning and design (C₃), the acquisition of working skills and employment opportunities (C₆) with 7.143 and guaranteed rent and lease (C₁) with 7.286.

Overall, we identified that the total performance is 7.403, and the average and maximum gaps are 0.260 and 0.329, respectively. The current performance is based on the group’s maximum utility strategy (i.e., the decision-making parameter equals 1) (see

Table 8. Intergraded value and sustainable development index under different decision-making parameters.

Decision-Making Parameter	Intergraded Value	Sustainable Development Index
0	0.329	0.671
0.1	0.322	0.678
0.2	0.315	0.685
0.3	0.308	0.692
0.4	0.301	0.699
0.5	0.294	0.706
0.6	0.287	0.713
0.7	0.280	0.720
0.8	0.273	0.727
0.9	0.267	0.733
1	0.260	0.740

). The sustainable development index is 0.740. Simulating different decision-making parameters also reveals different integrated values under different decision-making perspectives. For example, when the decision-making parameter is equal to 0, the mining personal regret strategy is considered, the integrated value of which is 0.329, and the sustainable development index is 0.671. When the decision-making parameter is increased to 0.5, the integrated value drops slightly to 0.294, and the sustainable development value increases to 0.706.

4.3. Discussion

This study uses N-HMADM to construct an evaluation framework for government-led SHR toward sustainability. This model has three primary purposes: (1) the DEMATEL method based on system dynamics deconstructs the influence relationship between evaluation dimensions and criteria, (2) the influence relationship based on DEMATEL is introduced into the traditional ANP framework to provide a solid basis on which to evaluate the cases, and (3) modified VIKOR with DANP weights can achieve sustainable development performance and gaps in all evaluation cases based on the perspectives of the different interests of groups or individuals to be better used for ranking evaluations and to form improvement strategies and paths to achieve the “aspiration level.” This method can evaluate not only multiple cases but also the advantages of a single plan and propose improvement strategies, which significantly improves the limitations and deficiencies of the traditional VIKOR method. Overall, the proposed N-HMADM in this study has more advantages than those of previous studies, which have failed to consider differences in weights among dimensions and criteria [8,13,18,23,39], AHP [6,15] or ANP [32].

The influence relationship based on DEMATEL, INRM and DANP allows critical identification for the development of SRH toward sustainability. It is suggested that policy makers promote SH sustainability by first considering economic sustainability (D₁). Although environmental sustainability (D₃) has the lowest DANP weight, its r_i − c_i is higher than that of social sustainability (D₂), which should be the second key dimension. This result was expected because limited public financial resources that hinder economic sustainability are the key impetus [14]. In terms of criteria, although creating a comfortable and safe environment (C₈) and operation management mechanism (C₄) have the largest DANP weights, their r_i − c_i is negative, which means that they are more susceptible to other criteria. Thus, decision makers need to pay attention to the criteria that have the “cause” position (i.e., r_i − c_i is a positive value); these include the reasonable development model (C₂), the provision of living facilities and services needed (C₅), the adoption of environmentally friendly technology and equipment (C₁₀), guaranteed rent and lease (C₁), the acquisition of working skills and employment opportunities (C₆) and space planning and design (C₃). Among these, attention should also be paid to space planning and design (C₃) (ranking third), the provision of living facilities and services needed (C₅) (ranking fifth), guaranteed rent and lease (C₁) (ranking sixth), and the adoption of environmentally friendly technology and equipment (C₁₀) (ranking eighth).

However, based on the results produced by a few Taiwanese experts, these findings still echo the results of the current literature. Even though several studies have asserted that policy makers have been paying too much attention to the economic dimension (D₁), which may be detrimental to the sustainable development of SH [16], the economic dimension and associated cause position highlight its importance in evaluations. This confirms the findings of Gan et al. [2] and Adabre et al. [14], who suggested that the economic dimension is key for sustainability. Exploration of the influence relationship in this study supports this argument and reveals that it affects the other two aspects. Additionally, the six core proposed criteria are largely rent affordability, economical design and effective use of resources, infrastructure service provision, the provision of skill acquisition, and employment opportunities, which require more attention identical to the work of Oyebanji et al. [13]. Among them, criteria such as space planning and design (C₃), the provision of living facilities and services needed (C₅) and guaranteed rent and lease (C₁) with higher DANP weights should be among the first for consideration. Additionally, other studies have confirmed that providing a sufficient living area is a vital factor in improving the satisfaction of SH residents [8,57,58,59]. The importance of providing various types of facilities and services [17,18,23,57], rent and lease guarantees [6,9,14,59] and environmentally friendly technologies and equipment (C₁₀) [62,68] is also consistent with the findings of most studies. The importance of other reasonable development models also reveals the positive role of the government in promoting SH because its hindrance is usually its financial infeasibility [2]. The key role of C₆—acquiring working skills and employment opportunities—suggests that SH projects should not only pay attention to the provision of built facilities but also provide employment skills to residents to enhance their economic capacity and reduce their dependence on affordable housing. Li et al. [61] stated that solving employment problems among young tenants in China can help them pull out of public housing.

4.4. Strategy Implications for the Case

Combining the revised VIKOR results and DEMATEL and its INRM provides an improvement strategy for this case study. First, decision makers should pay attention to dimensions and criteria with poor performance and have a cause position to drive sustainable development. In this case, the decision maker should first pay attention to improving economic sustainability (D₁) because it is ranked second; DEMATEL and DANP also highlight its significance. This improvement simultaneously promotes both environmental sustainability (D₃) and social sustainability (D₂). Second, the next best strategy is to invest in improving environmental sustainability (D₃), which further improves the performance of social sustainability (D₂). From the perspective of improvement strategies, a reasonable development model (C₂) (improvement ranking third), space planning and design (C₃) (improvement ranking third), acquisition of working skills and employment opportunities (C₆) (improvement ranking third), and guaranteed rent and lease (C₁) (improvement ranking sixth) can be regarded as the critical core improvement directions.

The improvement direction proposed in this study suggests that decision makers can adopt a cooperative development model with private developers, such as when planning the second phase of Ankang SH to reduce the government’s financial burden. Second, space planning and design can further optimize residential space features to improve the lack of low walls on balconies, safety ladders, and fences. Fenced iron nets are not safe enough, and improper drainage hole positions result in upstairs sewage affecting downstairs residents [85]. Furthermore, although this case cooperated with non-profit organizations to guide youth entrepreneurship to encourage entrepreneurship in SH tenants, the author identified that the focus of the organization’s activities has gradually shifted to other newly developed SH. Therefore, the continuous promotion of the entrepreneurial capacity of SH residents, in this case, must be considered. Finally, although the rent is based on 50% of the market price in the first year, approximately 25 m² requires a monthly rent of between NTD 3800 and NTD 4300. However, as the lease period increases, the rent approaches the market rent, posing a potential risk.

5. Conclusions and Policy Implications

This research proposes an evaluation framework with a hybrid N-HMADM model covering 3 pillars and 12 criteria and conducts a performance evaluation through an actual case in Taiwan to propose the simultaneous improvement of other criteria to promote sustainable development. Based on the opinions of experts, DEMATEL and INRM discovered that economic sustainability (D₁) is the core dimension that affects both environmental sustainability (D₃) and social sustainability (D₂), and environmental sustainability (D₃) affects social sustainability (D₂). Subsequently, economic sustainability (D₁) is the core of sustainable SH, followed by environmental sustainability (D₃) and, finally, social sustainability (D₂). Specifically, policy makers should pay more attention to the reasonable development model (C₂), the provision of living facilities and services needed (C₅), the adoption of environmentally friendly technology and equipment (C₁₀), guaranteed rent and lease (C₁), the acquisition of working skills and employment opportunities (C₆) and space planning and design (C₃). All of these have higher DANP weights, including space planning and design (C₃) and the provision of living facilities and services needed (C₅), as well as guaranteed rent and lease (C₁), which is core among them. The case evaluation of this research also indicates that economic sustainability (D₁) needs improvement. Based on these criteria, a reasonable development model (C₂), space planning and design (C₃), the acquisition of working skills and employment opportunities (C₆), guaranteed rent and lease (C₁) and the adoption of environmentally friendly technology and equipment (C₁₀) have poor performance but crucial influence. This study also recommends that the core be improved first.

The management strategies for the extension of the research results are as follows: (1) First, although social housing should be able to further promote the goal of social sustainability, its fundamentals still need to be solved in terms of economic sustainability and environmental sustainability to further enhance social sustainability and persistent goals. Therefore, when promoting social rental housing, the government also needs to think about how to promote a reasonable development model that can be financially self-supporting on the premise of affordable rent and lease term guarantees to promote the economic sustainability of social housing improvement strategies. Under this thinking, public-private partnership (PPP) or introducing a market-like mechanism for the operation and management of social housing can be promoted. (2) Secondly, adopting some environmentally friendly technologies and equipment to promote social housing projects can also further promote sustainability. In addition to achieving energy conservation and environmentally friendly development, a good environment can also create a good and safe space for realizing inclusion among residents of social housing and for the integration of social housing and the surrounding environment, further promoting social sustainability. (3) Special attention must also be paid to some positive initiatives in social sustainability. Building hardware facilities and media services that meet the needs of residents and provide appropriate counselling mechanisms to improve residents’ employment skill acquisition is also key for strengthening the social dimension, which has a positive effect on promoting social inclusion and overall sustainability. Overall, the findings of this study provide new insights into assessing the sustainability of social rental housing, thereby filling a knowledge gap in current research. Government policy makers, private real estate development, international organizations, etc., can rely on these CSCs for resource allocation to provide sustainable social rental housing.

The established evaluation system can provide a novel and comprehensive perspective on how to realize the sustainability of social rental housing. Because public rental SH is still a new phenomenon in Taiwan, exploring its sustainability evaluation system is necessary. The proposed evaluation framework in this study is more favorable than directly adopting an existing construction project evaluation system that focuses only on environmental sustainability. However, more consideration may be needed to balance the integrity, adaptability and operability of sustainability coverage in applying this proposed framework to the evaluation and comparison of SH projects in different countries or regions. Hence, the results and their interpretation should be carefully applied to other countries or regions in the future because they are only based on feedback from a small number of experts in Taiwan, and investigations and comparisons of similar issues in other regions need to consider factors such as the unique geographical environment and expert selection. In addition, because only the opinions of academic experts are considered, householders’ opinions are excluded. Overcoming this limitation in a future study by including evaluations from various stakeholders’ trade-off perspectives would be significant.