A Fuzzy Method for Exploring Key Factors of Smart Healthcare to Long-Term Care Based on Z-Numbers

Abstract

As the proportion of the population comprising the elderly cohort increases, so too does the demand for medical care for long-term conditions among this demographic. The advent of information technology and artificial intelligence has prompted a crucial examination of the potential of smart medical technology and equipment to enhance the quality of long-term care and the operational efficiency of long-term care facilities. The introduction of smart healthcare into long-term care is influenced by a few factors, and expert opinions often exhibit ambiguity and subjectivity in the evaluation process. As Z-numbers are capable of adequately expressing the ambiguity of expert assessments and the degree of certainty associated with them, they are employed in this study to convey the opinions of the experts. Furthermore, the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is an effective approach to analyzing the relationships between factors. Consequently, this study integrates the Z-numbers and DEMATEL methods for empirical analysis. The present study focuses on two long-term care institutions with different natures as empirical subjects. The findings of the study indicate that Institution A identifies the “Internet of Things” as the most pivotal key factor, whereas Institution B deems “Smart clinics and urgent care centers” to be the most crucial key factor. The analysis demonstrates that three factors—global positioning systems, telemedicine, and electronic medical records—are all regarded as significant influencing factors for different long-term care institutions. Consequently, the analytical model of this study is not only theoretically sound but also effective in identifying the key factors and importance of introducing smart healthcare into long-term care institutions.

1. Introduction

In recent years, the proportion of the elderly population has continued to increase, resulting in a rapid increase in the demand for medical care for the elderly. In response to this, a new medical care model, designated as “long-term care”, has emerged. The term ‘long-term care’ encompasses a broad range of services provided to individuals with disabilities in various settings, including their own homes, nursing homes, and assisted living facilities [1]. Furthermore, shifts in family structure, changes in work patterns, and increased demand for labor have also contributed to an increase in the number of families requiring long-term care services. To meet the demand for long-term care services, long-term care institutions have emerged with the objective of assisting families who require these services and thereby alleviating the burden and pressure of care.

The enhancement of living conditions and the progression of medical technology have resulted in a sustained improvement in the standard of living and an accompanying increase in the average life expectancy of the global population. Furthermore, the decline in the birth rate of newborns has resulted in the gradual transition of many countries towards an aging population structure. Long-term care services can facilitate the elderly population’s engagement in daily activities, encourage social participation, and monitor their physical and mental well-being. Consequently, long-term care for the elderly has emerged as a significant concern [2].

In recent years, the advent of smart medicine has led to a reduction in the number of medical burdens through the utilization of smart medicine-related technologies and equipment. Additionally, Taiwan’s medical system is facilitating collaboration between the medical and electronic industries, thereby ushering in a new era of medical technology and healthcare. It is therefore imperative to introduce smart medical technology into the long-term care system with a view to improving the quality of care. The majority of long-term care units in Taiwan are deficient in both robust information systems and the operational capabilities required to effectively utilize them. This presents a significant challenge in the integration of smart medicine into long-term care settings. It is therefore imperative to identify the key factors of smart medical care for long-term care services and ascertain the psychological needs of long-term caregivers. Doing so will not only mitigate the impact of the shortage of medical professionals but also enhance the efficacy of integrating smart medical care into long-term care [3,4].

Indeed, numerous factors influence the integration of smart medical care into long-term care, with these factors often exhibiting a correlation [5]. Furthermore, the subjective assessment of experts when evaluating factors is typically vague and uncertain. Accordingly, the linguistic Z-number permits experts to articulate their subjective opinions in a comprehensive manner, thereby reducing the ambiguity and uncertainty inherent to the evaluation process [6]. The fuzzy Delphi method is an effective approach for incorporating and integrating the opinions of all experts [7,8]. Concurrently, the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is capable of effectively analyzing the degree of influence between factors, calculating the importance of key factors, and confirming the causal relationship of key factors [9,10,11]. Accordingly, this study employs a two-stage systematic analysis model that integrates the linguistic Z-number, the fuzzy Delphi method, and the DEMATEL method to effectively analyze the key factors and their importance in the introduction of smart medical care into long-term care. The initial phase of the study entailed the collation and examination of the pertinent literature, as well as the identification of pivotal factors through the linguistic Z-number and fuzzy Delphi methods. The second phase of the study entailed measuring the degree of relevance of the key factors and calculating the importance of the key influencing factors through the DEMATEL method. Moreover, a case study was conducted on two long-term care institutions with disparate characteristics and sizes.

2. Literature Review

2.1. Long-Term Care

In recent years, several factors have contributed to a significant growth in the social structure of the elderly population. These include the formation of an aging society, the expansion of medical technology, the increase in average life expectancy, and the decline in the birth rate. This has led to a rapid rise in the demand for medical care for the elderly. The term ‘long-term care’ encompasses a broad range of services provided to individuals with disabilities in various settings, including their own homes, nursing homes, and assisted living facilities [1]. Furthermore, shifts in family structure, alterations in work patterns, and an elevated demand for labor have contributed to an escalating number of families requiring long-term care services. It follows that long-term care institutions and care services are inextricably linked, rendering long-term care services a pivotal concern in the welfare policy for the elderly. Tchouaket et al. [12] posit that long-term care services encompass assistance with activities of daily living (ADL), including transfer and mobility, bathing, dressing, personal hygiene, toileting, meal preparation, and medication administration. The content of long-term care services varies from country to country due to differences in healthcare systems and funding mechanisms. However, there are common characteristics that are present in most long-term care services. These include the need for 24 h service, the provision of accommodation facilities, including professional medical services, and personal care services such as meals, laundry, and housekeeping services [13].

As the phenomenon of declining birthrate becomes increasingly serious, it has resulted in a shortage of care human resources and has also had an impact on the development of the long-term care industry. The interconnected reliability, preventive collaboration, and innovative features of the industry can serve to mitigate the impact of the shrinking human resource population. To illustrate, a robot with an appealing appearance and an anthropomorphic dialogue function could be employed to provide exercise classes and spiritual healing functions, thereby assisting caregivers in their daily care and rehabilitation guidance. The integration of intelligent medical care with care behavior not only preserves the user’s sense of self-worth but also curtails the expenditure incurred by long-term care institutions and long-term medical care on personnel.

2.2. Smart Medicine

The shift in population structure and the proliferation of information technology have precipitated the ascendance of smart healthcare as a pivotal aspect of global medical policy formulation in recent years. The concept of smart healthcare is not merely an advancement of medical technology; it also has a significant impact on the medical level [14]. This impact can be observed in several areas, including changes in the medical model (from disease-centered to patient-centered), changes in information construction (from clinical information to regional medical information), changes in medical management (from comprehensive management to personalized management), and changes in prevention and treatment concepts (from focusing on disease treatment to focusing on preventive healthcare). As defined by the World Health Organization [15], “smart health (e-health) is the utilization of information and communication technology in a cost-effective and secure manner to facilitate health and health-related domains, encompassing healthcare services, health monitoring, health literature, and health education, knowledge and research”. For hospitals, the implementation of smart health enables medical teams to dedicate a greater proportion of their time to direct patient care, while simultaneously reducing the expenditure associated with the acquisition and maintenance of information technology. From the perspective of medical staff, the utilization of smart health technologies can facilitate the selection of appropriate pharmaceuticals, provide information on potential adverse effects or interactions, and reduce instances of incorrect medication and medical errors, thus enhancing the overall safety of medical care [14]. The utilization of wearable devices facilitates the implementation of continuous monitoring and online medical consultations, thereby addressing patients’ specific medical care requirements and enhancing the efficiency of both medical professionals and patients [14].

In recent years, the development of technologies such as artificial intelligence, cloud computing, ICT, and the Internet of Things has facilitated the accelerated development of smart medical technologies and equipment, such as the application of telemedicine, AI surgical robots, and other related medical technologies [9,16]. At present, a considerable number of hospitals have commenced the implementation of the concept of smart wards. The proliferation of wireless networks, network-enabled medical instruments, wearable device sensors, and smartphone app applications has led to a significant expansion of the original medical environment beyond hospitals, encompassing individuals, families, institutions, communities, and even entire cities. The integration of information technology and communications allows for the development of smart medicine, which in turn facilitates the development of smart life and smart health.

In conclusion, the concept of smart healthcare can be defined as the integration of information technology, the Internet of Things, and multiple medical fields. The introduction of this concept into the long-term care industry has the potential to achieve several key objectives. Firstly, it has the capacity to save human resources, reduce the cost of chronic disease care, and obtain information needed for care without time and space restrictions. Secondly, it can facilitate the effective acceleration of long-term care development through the integration of smart healthcare and long-term care services. The term “smart healthcare” is used to describe the utilization of a range of information and communication technologies (ICTs) to deliver medical care and support services. This study presents a summary of the pertinent influencing factors associated with the introduction of smart healthcare into long-term care, as illustrated in Table 1.

Table 1. Factors influencing smart healthcare in long-term care.

	Source	A	B	C	D	E	F	G	H	I	J	K	L	M	N
Factors
3D printing technology													✓	✓	✓
Artificial intelligence (AI)		✓		✓									✓
Virtual reality (VR)							✓
Sensors		✓	✓	✓	✓		✓	✓	✓		✓	✓	✓	✓	✓
Global positioning system							✓					✓	✓		✓
Smart clinics and urgent care centers				✓			✓					✓
Telemedicine		✓	✓				✓	✓							✓
Internet of things		✓	✓		✓	✓	✓		✓		✓	✓	✓	✓	✓
Blockchain				✓			✓						✓	✓
Smart medical talent acquisition				✓	✓			✓	✓
Electronic medical records				✓			✓			✓					✓
Cloud technology				✓	✓	✓	✓		✓	✓	✓		✓	✓	✓
Personalized data analysis		✓		✓	✓	✓	✓		✓	✓			✓		✓
Smart medicine box							✓			✓
Wireless RF identification							✓		✓			✓			✓
Smart bed								✓					✓
Smart bidet system								✓						✓
Assistive smart wheelchair			✓					✓	✓						✓

A: Lukkien et al. [16], B: Legato et al. [17], C: Rubeis [18], D: Leu et al. [19], E: Wu et al. [20], F: Nguyen et al. [21], G: Wang et al. [22], H: Hussain et al. [23], I: Kruse et al. [24], J: Chou [25], K: Haddara and Staaby [26], L: Ganesh et al. [27]. M: Heo and Jeong [28], N: Ekanayaka et al. [29].

2.3. Fuzzy Set Theory

2.3.1. Triangular Fuzzy Numbers

A triangular fuzzy number is a frequently utilized representation of a fuzzy number in decision analysis models, with applications spanning numerous fields, including fuzzy control and fuzzy decision-making [30]. Since the operation of triangular fuzzy numbers is relatively simple and describes the ambiguity of experts’ opinions, this study uses triangular fuzzy numbers to express experts’ opinions and conduct operational analyses.

A triangular fuzzy number, represented by $\tilde{A}=\left(a,b,c\right)$, is a fuzzy set. Its membership function, ${\mu }_{\tilde{A}}\left(x\right)$, is as follows (see Figure 1) [31,32]:

$${\mathit{\mu }}_{\tilde{\mathit{A}}}\left(\mathit{x}\right)=\left\{\begin{array}{c}{\displaystyle \frac{\mathit{x}-\mathit{a}}{\mathit{b}-\mathit{a}}}, \mathit{a}\le \mathit{x}\le \mathit{b}\\ \mathbf{1}, \mathit{x}=\mathit{b} \\ {\displaystyle \frac{\mathit{x}-\mathit{c}}{\mathit{b}-\mathit{c}}}, \mathit{b}\le \mathit{x}\le \mathit{c}\\ \mathbf{0}, \mathit{x}<\mathit{a} \mathit{o}\mathit{r} \mathit{x}>\mathit{c}\end{array}\right.$$

(1)

Figure 1. Triangular fuzzy numbers.

2.3.2. Linguistic Variables

Linguistic variables are words or sentences in natural or human language that describe complex or ambiguous situations that cannot be expressed with crisp values [31]. In the context of decision-making, experts can readily employ linguistic variables to articulate their subjective perspectives in a comprehensive manner. To illustrate, the membership functions of five linguistic variables are presented in Figure 2. The triangular fuzzy number representing the linguistic variable “good” is expressed as (0.5, 0.75, 1.0).

Figure 2. Linguistic variable scale.

2.3.3. Fuzzy Operations

Let us assume that two positive triangular fuzzy numbers are given by $\tilde{A}=\left(a_1,b_1,c_1\right)$ and $\tilde{B}=(a_2,b_2,c_2)$. The fuzzy operation rules are as follows [33,34]:

$$({\mathit{a}}_{\mathbf{1}},{\mathit{b}}_{\mathbf{1}},{\mathit{c}}_{\mathbf{1}})\oplus ({\mathit{a}}_{\mathbf{2}},{\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{2}})=({\mathit{a}}_{\mathbf{1}}+{\mathit{a}}_{\mathbf{2}},{\mathit{b}}_{\mathbf{1}}+{\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{1}}+{\mathit{c}}_{\mathbf{2}})$$

(2)

$$({\mathit{a}}_{\mathbf{1}},{\mathit{b}}_{\mathbf{1}},{\mathit{c}}_{\mathbf{1}})\ominus ({\mathit{a}}_{\mathbf{2}},{\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{2}})=({\mathit{a}}_{\mathbf{1}}-{\mathit{c}}_{\mathbf{2}},{\mathit{b}}_{\mathbf{1}}-{\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{1}}-{\mathit{a}}_{\mathbf{2}})$$

(3)

$$({\mathit{a}}_{\mathbf{1}},{\mathit{b}}_{\mathbf{1}},{\mathit{c}}_{\mathbf{1}})\otimes ({\mathit{a}}_{\mathbf{2}},{\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{2}})\cong ({\mathit{a}}_{\mathbf{1}}\times {\mathit{a}}_{\mathbf{2}}, {\mathit{b}}_{\mathbf{1}}\times {\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{1}}\times {\mathit{c}}_{\mathbf{2}})$$

(4)

$$({\mathit{a}}_{\mathbf{1}},{\mathit{b}}_{\mathbf{1}},{\mathit{c}}_{\mathbf{1}})\oslash ({\mathit{a}}_{\mathbf{2}},{\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{2}})\cong ({\mathit{a}}_{\mathbf{1}}∕{\mathit{c}}_{\mathbf{2}}, {\mathit{b}}_{\mathbf{1}}∕{\mathit{b}}_{\mathbf{2}},{\mathit{c}}_{\mathbf{1}}∕{\mathit{a}}_{\mathbf{2}})$$

(5)

2.3.4. Defuzzification Methods

Defuzzification may be defined as the process of converting a fuzzy number into a crisp value. The centroid method is a frequently employed defuzzification technique. The calculation method is as follows [9,35]:

$$\mathit{S}\left(\tilde{\mathit{A}}\right)={\displaystyle \frac{\int \mathit{x}{\mathit{\mu }}_{\tilde{\mathit{A}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}{\int {\mathit{\mu }}_{\tilde{\mathit{A}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}}$$

(6)

where ${\mu }_{\tilde{A}}\left(x\right)$ is the membership function of the fuzzy set $\tilde{A}$, and $S\left(\tilde{A}\right)$ is the defuzzified value of $\tilde{A}$.

2.3.5. Z Number

Zadeh [36] expanded the concept of fuzzy numbers and proposed Z-numbers as a means of providing a basis for the calculation of incompletely reliable fuzzy sets. Z-numbers are represented by the formula Z = (A, R), where A is the fuzzy evaluation value and R is the reliability value of A [37]. Z-numbers provide a means of describing the situation of imperfect information pertaining to a random variable, through the use of an evaluation value and a credibility value [38,39]. Let us assume that a Z-number is represented by the equation Z = ($\tilde{\mathrm{A}}$,$\tilde{R}$), where $\tilde{\mathrm{A}}$ is a triangular fuzzy number, expressed as $\tilde{A}=(a,b,c)$. The reliability of the description, expressed as $\tilde{R}=(R_1,R_2,R_3)$, is represented by $\tilde{R}$.

The following is a description of the calculation process for converting a Z-number into a triangular fuzzy number ($\tilde{Z}$) and for defuzzification:

Step 1: Convert the fuzzy credibility ($\tilde{R}$) into a crisp value ($\alpha$) using the centroid method as follows [40]:

$$\mathit{\alpha }={\displaystyle \frac{\int \mathit{x}{\mathit{\mu }}_{\tilde{\mathit{R}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}{\int {\mathit{\mu }}_{\tilde{\mathit{R}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}}$$

(7)

where ${\mu }_{\tilde{R}}\left(x\right)$ is the membership function of $\tilde{R}$.

Step 2: The Z number should be converted into a triangular fuzzy number, designated as $\tilde{Z}$. The crisp value ($\alpha$) is multiplied by the fuzzy evaluation value $\tilde{\mathrm{A}}$ to obtain the triangular fuzzy number $\tilde{Z}$. The calculation formula is as follows:

$$\tilde{\mathit{Z}}=(\mathit{\alpha }\mathit{a},\mathit{\alpha }\mathit{b},\mathit{\alpha }\mathit{c})$$

(8)

Step 3: Use the centroid method to convert $\tilde{Z}$ into $S\left(\tilde{Z}\right)$, calculated as follows:

$$\mathit{S}\left(\tilde{\mathit{Z}}\right)={\displaystyle \frac{\int \mathit{x}{\mathit{\mu }}_{\tilde{\mathit{Z}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}{\int {\mathit{\mu }}_{\tilde{\mathit{Z}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}}$$

(9)

where ${\mu }_{\tilde{Z}}\left(x\right)$ is the membership function of triangular fuzzy number $\tilde{Z}$.

3. The Proposed Model

This study employs a combined approach, integrating the linguistic Z-number and the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method, to examine the pivotal influencing factors associated with the integration of smart medical care into long-term care. The proposed model comprises two stages. The initial stage employs the fuzzy Delphi method [7,8] in conjunction with the linguistic Z-number to identify the pivotal influencing factors associated with the integration of smart medical care into long-term care. This is achieved through a consensus among experts and the establishment of threshold values. The second stage employs the linguistic Z-number and the DEMATEL method [9,10,11] to analyze the mutual influence degree between key influencing factors and the importance of key factors. The research process of this study is shown in Figure 3.

Figure 3. The research process of this study.

3.1. Integrate Expert Opinions

This study employs the Fuzzy Delphi method and Linguistic Z-number to synthesize the opinions of experts and identify the pivotal factors for the integration of smart healthcare into long-term care. The following section outlines the steps in detail.

Step 1: Collect relevant literature and summarize the influencing factors $m(i=1,2,\dots ,m)$.

Step 2: The linguistic Z-number is employed by each expert to evaluate the importance of the influencing factors. The k-th expert (k = 1, 2, …, K) assesses the importance of the i-th factor as follows:

$${\mathit{Z}}_{\mathit{i}}^{\mathit{k}}=({\tilde{\mathit{A}}}_{\mathit{i}}^{\mathit{k}},{\tilde{\mathit{R}}}_{\mathit{i}}^{\mathit{k}})$$

(10)

where $Z_i^k$ is the linguistic Z-number evaluation value of the importance evaluation of the i-th factor by the k-th expert. ${\tilde{A}}_i^k$ is the linguistic evaluation value of the importance of the factor i by the expert $k$. ${\tilde{R}}_i^k$ is the degree of certainty of the importance of the factor i by the expert $k$.

Step 3: The objective is to transform the expert’s linguistic Z-number evaluation value into a triangular fuzzy number. The centroid method should be employed in order to defuzzify ${\tilde{R}}_i^k$into ${\alpha }_i^k$. Let us assume that ${\tilde{A}}_i^k$ is represented by the triplet $(a_{i1}^k,a_{i2}^k,a_{i3}^k)$. The $Z_i^k$ is then converted into a triangular fuzzy number, ${\tilde{Z}}_i^k=\left({\alpha }_i^k\times a_{i1}^k,{\alpha }_i^k\times a_{i2}^k,{\alpha }_i^k\times a_{i3}^k\right)$.

Step 4: A consensus is deemed to have been reached when the opinions of each expert align with those of at least one other expert. Once all experts have reached a consensus, the triangular fuzzy numbers ${\tilde{Z}}_i^k$, which represent the importance of the i-th factor according to all experts, are integrated as follows:

$${\tilde{\mathit{Z}}}_{\mathit{i}}=({\mathit{a}}_{\mathit{i}},{\mathit{b}}_{\mathit{i}},{\mathit{c}}_{\mathit{i}})$$

(11)

where ${\tilde{Z}}_i$is the triangular fuzzy number of the importance of the i-th influencing factor and $a_i=\underset{k}{\min }\left\{{\alpha }_i^k\times a_{i1}^k\right\}$, $b_i={\left(\prod _{k=1}^K{\alpha }_i^k\times a_{i2}^k\right)}^{{\displaystyle \frac{1}{K}}}$, $c_i=\underset{k}{\max }\left\{{\alpha }_i^k\times a_{i3}^k\right\}$.

Step 5: The integrated expert opinions should be defuzzied. The defuzzification of the triangular fuzzy number ${\tilde{Z}}_i=(a_i,b_i,c_i)$ associated with the i-th influencing factor is as follows:

$$\mathit{S}\left({\tilde{\mathit{Z}}}_{\mathit{i}}\right)={\displaystyle \frac{\int \mathit{x}{\mathit{\mu }}_{{\tilde{\mathit{Z}}}_{\mathit{i}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}{\int {\mathit{\mu }}_{{\tilde{\mathit{Z}}}_{\mathit{i}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}}$$

(12)

where $S\left({\tilde{Z}}_i\right)$ is the defuzzified value of the triangular fuzzy number ${\tilde{Z}}_i=(a_i,b_i,c_i)$.

Step 6: It is essential to identify and assess the key factors that contribute to the outcome of interest. If the threshold value of factor importance is assumed to be $\alpha$, then the influencing factor i is considered to be the key factor if the defuzzified value of ${\tilde{Z}}_i$is greater than or equal to the threshold value ($S\left({\tilde{Z}}_i\right)\ge \alpha$). In the event that $S\left({\tilde{Z}}_i\right)$ is less than the threshold value $\alpha$, the influencing factor i is removed.

3.2. Calculation of Key Factors Importance

The second stage is to analyze the causal relationship, influence intensity, and weight ranking between key factors through the use of linguistic Z-numbers and the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method. The following section outlines the relevant steps in detail.

Step 1: It is assumed that the initial stage finds the primary factors, indexed by n (with i = 1, 2, …, n).

Step 2: The role of the expert is to evaluate the degree of influence between any two factors. The linguistic Z-number is employed by each expert to assess the extent of influence exerted by the principal factors. The degree of influence exerted by the key factor i on the factor j, as evaluated by expert $k\left(k=1, 2, \dots ,K\right)$, is as follows:

$${\mathit{Z}}_{\mathit{i}\mathit{j}}^{\mathit{k}}=({\tilde{\mathit{F}}}_{\mathit{i}\mathit{j}}^{\mathit{k}},{\tilde{\mathit{R}}}_{\mathit{i}\mathit{j}}^{\mathit{k}})$$

(13)

where $Z_{ij}^k$represents the linguistic Z-number of the influence of the key factor i on the factor j by expert $k$. ${\tilde{F}}_{ij}^k$ represents the semantic evaluation value of the influence of factor i on factor j by expert $k$. ${\tilde{R}}_{ij}^k$ represents the degree of certainty of the degree of influence of factor i on factor j by expert $k$.

Step 3: Defuzzify ${\tilde{R}}_{ij}^k$ into ${\alpha }_{ij}^k$ using the centroid method. Assume that ${\tilde{F}}_{ij}^k=\left(f_{1ij}^k,f_{2ij}^k,f_{3ij}^k\right).$ The $Z_{ij}^k$ will be converted into triangular fuzzy numbers ${\tilde{Z}}_{ij}^k=({\alpha }_{ij}^k\times f_{1ij}^k,{\alpha }_{ij}^k\times f_{2ij}^k,{\alpha }_{ij}^k\times f_{3ij}^k)$.

Step 4: Once a consensus has been reached by the experts, the triangular fuzzy numbers provided by each expert are integrated in accordance with the following procedure:

$${\tilde{\mathit{Z}}}_{\mathit{i}\mathit{j}}=({\mathit{a}}_{\mathit{i}\mathit{j}},{\mathit{b}}_{\mathit{i}\mathit{j}},{\mathit{c}}_{\mathit{i}\mathit{j}})$$

(14)

where ${\tilde{Z}}_{ij}$ is the triangular fuzzy number of factor i influencing factor j, $a_{ij}=\underset{k}{\min }\left\{{\alpha }_{ij}^k\times f_{1ij}^k\right\}$, $b_{ij}={\left(\prod _{k=1}^K{\alpha }_{ij}^k\times f_{2ij}^k\right)}^{{\displaystyle \frac{1}{K}}}$, $c_{ij}=\underset{k}{\max }\left\{{\alpha }_{ij}^k\times f_{3ij}^k\right\}$.

Step 5: The ${\tilde{Z}}_{ij}$ should be defuzzified using the centroid method. The calculation is as follows:

$$\mathit{S}\left({\tilde{\mathit{Z}}}_{\mathit{i}\mathit{j}}\right)={\displaystyle \frac{\int \mathit{x}{\mathit{\mu }}_{{\tilde{\mathit{Z}}}_{\mathit{i}\mathit{j}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}{\int {\mathit{\mu }}_{{\tilde{\mathit{Z}}}_{\mathit{i}\mathit{j}}}\left(\mathit{x}\right)\mathit{d}\mathit{x}}}$$

(15)

Step 6: A direct relationship matrix (A) is established on the basis of the degree of influence exerted by key factors, as follows:

$$\mathit{A}={\left[\mathit{S}\left({\tilde{\mathit{Z}}}_{\mathit{i}\mathit{j}}\right)\right]}_{\mathit{n}\times \mathit{n}},(\mathit{i},\mathit{j}=\mathbf{1,2},\mathbf{3}\dots ,\mathit{n})$$

(16)

where $S\left({\tilde{Z}}_{ij}\right)$ is the degree value of the key factor i influencing factor j.

Step 7: In accordance with the direct relationship matrix A, a normalized direct relationship matrix D is to be established as follows:

$$\mathit{D}={\displaystyle \frac{\mathit{A}}{\mathbf{m}\mathbf{a}\mathbf{x}(\underset{\mathbf{1}\le \mathit{i}\le \mathit{n}}{\mathbf{max}}\sum _{\mathit{i}=\mathbf{1}}^{\mathit{n}}\mathit{S}\left({\tilde{\mathit{Z}}}_{\mathit{i}\mathit{j}}\right),\underset{\mathbf{1}\le \mathit{j}\le \mathit{n}}{\mathbf{max}}\sum _{\mathit{j}=\mathbf{1}}^{\mathit{n}}\mathit{S}\left({\tilde{\mathit{Z}}}_{\mathit{i}\mathit{j}}\right))}}$$

(17)

Step 8: In accordance with the principles set forth in the normalized direct relationship matrix D, the total influence relationship matrix T is to be constructed as follows:

$$\mathit{T}={\mathit{D}(\mathit{I}-\mathit{D})}^{-\mathbf{1}}$$

(18)

where $T={\left[t_{ij}\right]}_{n\times n},i,j=\mathrm{1,2},3\dots ,n$. The $t_{ij}$ represents that the total influence value of factor i influences factor j. The $I$ is the unit matrix.

Step 9: In accordance with the total influence relationship matrix, the centrality ($d_i$) and causality ($r_i$) of factor i are to be calculated as follows:

$${\mathit{d}}_{\mathit{i}}=\sum _{\mathit{j}=\mathbf{1}}^{\mathit{n}}{\mathit{t}}_{\mathit{i}\mathit{j}}$$

(19)

$${\mathit{r}}_{\mathit{i}}=\sum _{\mathit{j}=\mathbf{1}}^{\mathit{n}}{\mathit{t}}_{\mathit{j}\mathit{i}}$$

(20)

where $d_i$ represents the sum of the degree to which the i-th factor affects other factors, while $r_i$ denotes the sum of the degree to which the i-th factor is affected by other factors. The centrality of the i-th factor, represented by ($d_i+r_i$), indicates the total degree to which the i-th factor affects and is affected. It can therefore be used to demonstrate the core degree of the factor among all factors. ($d_i{-r}_i$) represents the causal degree of the i-th factor. A positive value for ($d_i{-r}_i$) indicates that the i-th factor exerts an influence on other factors. Should ($d_i{-r}_i$) be negative, this indicates that the i-th factor is affected by other factors.

The value of ($d_i$ + $r_i$) represents the total degree to which factor i affects and is affected by other factors. Consequently, the larger this value is, the more important factor i is considered to be. In this study, the normalization of this value is used to express the influential weight of factor i.

Step 10: Calculate the influential weight of each factor as follows:

$${\mathit{w}}_{\mathit{i}}={\displaystyle \frac{{\mathit{d}}_{\mathit{i}}+{\mathit{r}}_{\mathit{i}}}{\sum _{\mathit{i}=\mathbf{1}}^{\mathit{n}}({\mathit{d}}_{\mathit{i}}+{\mathit{r}}_{\mathit{i}})}}$$

(21)

where $w_i$ represents the importance of the i-th key factor.

Step 11: Construct factors causation

In accordance with the total influence relationship matrix (T), the threshold values (${\beta }_1$, ${\beta }_2$) for calculating the degree of influence are as follows:

$${\beta }_1={\displaystyle \frac{\sum _{i=1}^n\sum _{j=1}^n{t}_{ij}}{n\times n}}$$

(22)

$${\beta }_2={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\{\underset{i}{\max }{d}_i,\underset{i}{\max }{r}_i\}}{n}}$$

(23)

In order to construct the causal relationship matrix of the factors (C), it is first necessary to derive the total influence relationship matrix (T) and the threshold value ($\beta$) of the influenced degree. The causal relationship matrix of the factors (C) is as follows:

$$C={\left[c_{ij}\right]}_{n\times n},i=\mathrm{1,2},\dots ,n,j=\mathrm{1,2},\dots ,n$$

(24)

where

$$c_{ij}=\left\{\begin{array}{c}1, t_{ij}\ge {\beta }_t \\ 0, t_{ij}<{\beta }_t\end{array} \right.(t=1, 2)$$

A value of $c_{ij}=1$ indicates that factor i exerts an influence on factor j. Conversely, a value of $c_{ij}=0$ signifies that factor i does not exert any influence on factor j. The causal relationship matrix (C) can be employed to construct a causal relationship diagram encompassing all factors.

4. Empirical Analysis

4.1. Screening Key Influencing Factors

4.1.1. Summary of Influencing Factors

Based on the analysis of the existing literature and the subsequent discussion, this study presents a summary of the 18 key factors that have been identified as influencing the introduction of smart medical technology into long-term care, as illustrated in Table 2. The significance of each influencing factor is illustrated in Table 3.

Table 2. Influencing factors.

Code	Factor Name	Code	Factor Name
A	3D printing technology	J	Smart medical talent acquisition
B	Artificial intelligence	K	Electronic medical records
C	Virtual reality	L	Cloud technology
D	Sensors	M	Personalized data analysis
E	Global positioning system	N	Smart medicine box
F	Smart clinics and urgent care centers	O	Wireless RF identification
G	Telemedicine	P	Smart bed
H	Internet of things	Q	Smart bidet system
I	Blockchain	R	Assistive smart wheelchair

Table 3. The significance of each influencing factor.

Code	Name	Meanings
A	3D printing technology	A multi-layer stacking printing method that incorporates bespoke three-dimensional features. The three axes (X, Y, and Z) facilitate the materialization of objects in accordance with the requisite specifications.
B	Artificial intelligence	The term “artificial intelligence” (AI) is used to describe technology that presents or simulates human-like intelligence through programming and computational behavior.
C	Virtual reality	A simulated environment may be created through the utilization of the sensory experiences afforded by the computer, including those of vision and hearing.
D	Sensors	The deployment of sensors enables the real-time and continuous monitoring of health-related signals without the constraints of time or geography. This has the potential to address the challenges associated with inadequate staffing in long-term care settings and the difficulty in monitoring the outcomes of certain traditional medical treatments.
E	Global positioning system	The global positioning system enables the real-time detection of the caregiver’s location and position, thereby preventing the caregiver from becoming lost or wandering off.
F	Smart clinics and urgent care centers	In comparison to general clinics, emergency care centers offer a more extensive range of treatments and contribute to a reduction in overcrowding in emergency rooms. The introduction of cross-disciplinary long-term care professionals and the combination of medical resources are two key benefits of smart clinics.
G	Telemedicine	Medical personnel are able to provide remote care for patients, analyze electronic data with patients, and disseminate professional medical knowledge. This approach can reduce the frequency of patients entering and leaving the hospital, mitigate the impact of the shortage of medical professionals, and effectively utilize medical resources, thereby improving the efficiency of medical treatment for patients with limited mobility or in remote areas.
H	Internet of things	The Internet of Things encompasses a multitude of software technologies, cloud storage and computing, and information transmission and communication technologies. By means of analysis and effective health management, it is possible to grasp and monitor the progression of the disease, thus avoiding a deterioration in the patient’s condition and postponing the optimal period for treatment.
I	Blockchain	One of the defining characteristics of the blockchain is its immutable nature. To illustrate, long-term care institutions are able to record medical information via the utilization of blockchain accounts. With the informed consent of all relevant parties, including caregivers, patients, hospitals, insurance companies, and research institutions, the sharing of medical information can be facilitated, thereby reducing the time and cost associated with the current process of obtaining information from multiple sources.
J	Smart medical talent acquisition	In the field of smart healthcare, there is a persistent challenge in acquiring talent, particularly individuals who possess expertise in the intersection of information technology and medicine, as well as those who are adept at developing sophisticated medical capabilities.
K	Electronic medical records	Long-term caregivers utilize electronic medical records to document medication regimens, prescriptions, the frequency of illness, and other pertinent information. The utilization of electronic medical records enables healthcare professionals to make appropriate treatment decisions at any medical facility.
L	Cloud technology	The utilization of cloud technology in the construction of a drug evaluation system enables the comparison and detection of drug ingredients, thus facilitating the identification of potential conflicts.
M	Personalized data analysis	The application of data mining techniques may facilitate the quantitative modeling of the lifestyles of long-term caregivers, thereby enabling an understanding of their beliefs, values, and preferences. This, in turn, may facilitate the provision of personalized care.
N	Smart medicine box	A significant proportion of the elderly population is unable to adhere to medication instructions on a regular basis, which has an adverse impact on the efficacy of treatment. The implementation of smart medicine boxes has the potential to alleviate the burden on caregivers while simultaneously enhancing the regularity and efficacy of the elderly population’s medication regimens.
O	Wireless RF identification	The utilization of Wireless RF identification allows for the tracking of both caregivers and the movement of drugs, thereby reducing the probability of drug quantity and medication errors.
P	Smart bed	The utilization of advanced technology in smart beds, including infrared projectors, force-sensing resistors, and MAP systems, facilitates the care of patients with behavioral disorders. Additionally, these devices assist in the prevention of pressure sores and instances of patients rolling out of bed.
Q	Smart bidet system	The smart bidet system is capable of obtaining physiological data through the use of sensors and has the potential to prevent the onset of spinal diseases and to correct body posture.
R	Assistive smart wheelchair	The wheelchair is operated by a joystick, and through voice recognition and a human-computer interaction interface, the user’s mood can be identified via a camera, thus enabling the user to mitigate feelings of loneliness. In addition to its primary function of facilitating mobility, the wheelchair also serves as a companion for the caregiver.

4.1.2. Assessment of Factor Importance

In this study, the evaluation was conducted by a panel of 12 experts. As the evaluation data from three experts did not align with the responses of the other experts, the data from nine experts was ultimately adopted for analysis following the deletion of the data from the three experts. The nine experts were drawn from a range of industry categories, with a particular focus on the education and healthcare sectors. The experts held positions as either head of unit or professionals, and the majority of the companies they represented had more than 1000 employees. The relevant information pertaining to the experts is presented in Table 4.

Table 4. Background information of experts.

No.	Gender	Age	Type of Industry	Years of Working Experience	Position	No. of Employees.
1	Male	40–49	Education	11–20	Head of unit	1001 (above)
2	Male	50–59	Education	21–30	Professionals	501–1000
3	Female	40–49	Healthcare	11–20	Professionals	1001 (above)
4	Female	30–39	Healthcare	less than 10	Professionals	1001 (above)
5	Male	30–39	Public sector	less than 10	Professionals	1001 (above)
6	Male	40–49	Education	11–20	Head of unit	101–500
7	Female	40–49	Healthcare	11–20	Professionals	1001 (above)
8	Female	40–49	Public sector	21–30	Professionals	1001 (above)
9	Male	60+	Healthcare	31–40	Head of unit	100 or less

Each expert employed the linguistic Z-number to assign an evaluation value for the importance of the 18 factors in question. The triangular fuzzy number that corresponds to the linguistic Z-number is presented in Table 5. The linguistic Z-number evaluation values assigned by all experts are presented in Table 6, Table 7 and Table 8.

Table 5. Linguistic variables of importance and certainty.

Importance Rating			Certainty Assessment
Code	Linguistic Variables	Triangular Fuzzy Numbers	Code	Linguistic Variables	Triangular Fuzzy Numbers
${\tilde{A}}_0$	Absolutely unimportant	(0, 0, 0)	${\tilde{R}}_0$	Absolutely uncertain	(0, 0, 0)
${\tilde{A}}_1$	Very unimportant	(0, 0.2, 0.4)	${\tilde{R}}_1$	Very uncertain	(0, 0, 0.4)
${\tilde{A}}_2$	unimportant	(0.2, 0.4, 0.6)	${\tilde{R}}_2$	Not sure	(0.2, 0.4, 0.6)
${\tilde{A}}_3$	Fair	(0.4, 0.6, 0.8)	${\tilde{R}}_3$	ordinary	(0.4, 0.6, 0.8)
${\tilde{A}}_4$	important	(0.6, 0.8, 1)	${\tilde{R}}_4$	determine	(0.6, 0.8, 0.9)
${\tilde{A}}_5$	Very important	(0.8, 1, 1)	${\tilde{R}}_5$	Very sure	(0.8, 1, 1)
${\tilde{A}}_6$	Absolutely important	(1, 1, 1)	${\tilde{R}}_6$	Absolutely sure	(1, 1, 1)

Table 6. The linguistic Z-number evaluations of experts 1 to 3.

Code	Factor Name	Expert 1	Expert 2	Expert 3
A	3D printing technology	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.8,1,1)
B	Artificial intelligence	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
C	Virtual reality	(0.4,0.6,0.8), (0.4,0.6,0.8)	(0.4,0.6,0.8), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)
D	Sensors	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
E	Global positioning system	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
F	Smart clinics and urgent care centers	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
G	Telemedicine	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
H	Internet of things	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.4,0.6,0.8)	(0.6,0.8,1), (0.6,0.8,0.9)
I	Blockchain	(0.4,0.6,0.8), (0.4,0.6,0.8)	(0.6,0.8,1), (0.4,0.6,0.8)	(0.6,0.8,1), (0.6,0.8,0.9)
J	Smart medical talent acquisition	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.4,0.6,0.8)	(0.8,1,1), (0.8,1,1)
K	Electronic medical records	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
L	Cloud technology	(0.4,0.6,0.8), (0.4,0.6,0.8)	(0.8,1,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)
M	Personalized data analysis	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)
N	Smart medicine box	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.4,0.6,0.8)	(0.6,0.8,1), (0.6,0.8,0.9)
O	Wireless RF identification	(0.2,0.4,0.6), (0.4,0.6,0.8)	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
P	Smart bed	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)
Q	Smart bidet system	(0.6,0.8,1), (0.8,1,1)	(0.6,0.8,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
R	Assistive smart wheelchair	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)

Table 7. The linguistic Z-number evaluations of experts 4 to 6.

Code	Factor Name	Expert 4	Expert 5	Expert 6
A	3D printing technology	(0.6,0.8,1), (0.8,1,1)	(0.6,0.8,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
B	Artificial intelligence	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.4,0.6,0.8)	(0.8,1,1), (0.8,1,1)
C	Virtual reality	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.4,0.6,0.8)	(0.8,1,1), (0.8,1,1)
D	Sensors	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
E	Global positioning system	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
F	Smart clinics and urgent care centers	(0.8,1,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
G	Telemedicine	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
H	Internet of things	(0.6,0.8,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
I	Blockchain	(0.6,0.8,1), (0.6,0.8,0.9)	(0.4,0.6,0.8), (0.4,0.6,0.8)	(0.8,1,1), (0.8,1,1)
J	Smart medical talent acquisition	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
K	Electronic medical records	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
L	Cloud technology	(0.8,1,1), (0.8,1,1)	(0,0.2,0.4), (0.8,1,1)	(0,0.2,0.4), (0.8,1,1)
M	Personalized data analysis	(0.6,0.8,1), (0.4,0.6,0.8)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
N	Smart medicine box	(0.8,1,1), (0.8,1,1)	(0.4,0.6,0.8), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
O	Wireless RF identification	(0.6,0.8,1), (0.6,0.8,0.9)	(0.4,0.6,0.8), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
P	Smart bed	(0.8,1,1), (0.8,1,1)	(0.4,0.6,0.8), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
Q	Smart bidet system	(0.2,0.4,0.6), (0.6,0.8,0.9)	(0.2,0.4,0.6), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
R	Assistive smart wheelchair	(0.8,1,1), (0.8,1,1)	(0.4,0.6,0.8), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)

Table 8. The linguistic Z-number evaluations of experts 7 to 9.

Code	Factor Name	Expert 7	Expert 8	Expert 9
A	3D printing technology	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
B	Artificial intelligence	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
C	Virtual reality	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.6,0.8,0.9)
D	Sensors	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
E	Global positioning system	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
F	Smart clinics and urgent care centers	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)
G	Telemedicine	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.6,0.8,0.9)
H	Internet of things	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
I	Blockchain	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)
J	Smart medical talent acquisition	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
K	Electronic medical records	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.6,0.8,0.9)
L	Cloud technology	(0,0.2,0.4), (0.8,1,1)	(0,0.2,0.4), (0.8,1,1)	(0.4,0.6,0.8), (0.8,1,1)
M	Personalized data analysis	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.6,0.8,0.9)
N	Smart medicine box	(0.6,0.8,1), (0.6,0.8,0.9)	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)
O	Wireless RF identification	(0.8,1,1), (0.8,1,1)	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
P	Smart bed	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)
Q	Smart bidet system	(0.6,0.8,1), (0.8,1,1)	(0.4,0.6,0.8), (0.6,0.8,0.9)	(0.6,0.8,1), (0.8,1,1)
R	Assistive smart wheelchair	(0.8,1,1), (0.8,1,1)	(0.6,0.8,1), (0.6,0.8,0.9)	(0.6,0.8,1), (0.6,0.8,0.9)

4.1.3. Converting Linguistic Variables of Certainty to Crisp Values

The degree of certainty is calculated using the centroid method, which provides a crisp value. To illustrate, the linguistic variable “certainty” (${\tilde{R}}_4$) of the degree of certainty is represented by the following membership function:

$${\mu }_{{\tilde{R}}_4}\left(x\right)=\left\{\begin{array}{c}{\displaystyle \frac{x-0.6}{0.8-0.6}}, 0.6\le x\le 0.8\\ {\displaystyle \frac{0.9-x}{0.9-0.8}}, 0.8\le x\le 0.9\\ 0, x<0.6 or x>0.9\end{array}\right.$$

The calculation result using the centroid method is:

$$S\left({\tilde{R}}_4\right)={\displaystyle \frac{{\int }_{0.6}^{0.8}x{\mu }_{{\tilde{R}}_4}\left(x\right)dx+{\int }_{0.8}^{0.9}x{\mu }_{{\tilde{R}}_4}\left(x\right)dx}{{\int }_{0.6}^{0.8}{\mu }_{{\tilde{R}}_4}\left(x\right)dx+{\int }_{0.8}^{0.9}{\mu }_{{\tilde{R}}_4}\left(x\right)dx}}={\displaystyle \frac{0.073+0.042}{\left(0.9-0.6\right)\ast 1/2}}=0.767$$

4.1.4. Integration of All Expert Evaluations

The linguistic Z-number values of each factor, as determined by nine experts, were converted into triangular fuzzy numbers after consensus was reached among the experts. The fuzzy Delphi method was employed for the integration of the evaluation values provided by the nine experts. The integrated triangular fuzzy numbers for each influencing factor, along with their defuzzification results, are presented in Table 9.

Table 9. Integrated triangular fuzzy numbers and defuzzied values.

Code	Factor Name	Integrated Triangular Fuzzy Numbers	Crisp Value After Defuzzification
A	3D printing technology	(0.46,0.687,0.934)	0.694
B	Artificial intelligence	(0.36,0.719,0.934)	0.671
C	Virtual reality	(0.24,0.659,0.934)	0.611
D	Sensors	(0.46,0.869,0.934)	0.754
E	Global positioning system	(0.46,0.869,0.934)	0.754
F	Smart clinics and urgent care centers	(0.46,0.832,0.934)	0.742
G	Telemedicine	(0.46,0.832,0.934)	0.742
H	Internet of things	(0.36,0.771,0.934)	0.689
I	Blockchain	(0.24,0.585,0.934)	0.587
J	Smart medical talent acquisition	(0.46,0.81,0.934)	0.735
K	Electronic medical records	(0.46,0.872,0.934)	0.755
L	Cloud technology	(0,0.4587,0.934)	0.464
M	Personalized data analysis	(0.36,0.722,0.934)	0.672
N	Smart medicine box	(0.307,0.73,0.934)	0.657
O	Wireless RF identification	(0.12,0.644,0.934)	0.566
P	Smart bed	(0.307,0.667,0.934)	0.636
Q	Smart bidet system	(0.153,0.585,0.934)	0.557
R	Assistive smart wheelchair	(0.46,0.715,0.934)	0.703

4.1.5. Screening Evaluation Factors

When filtering factors, it is essential to set an appropriate threshold range. If the threshold is set too high, the number of factors to be filtered will be insufficiently representative. Conversely, if the threshold is set too low, the number of factors to be filtered will be excessive, thereby preventing the identification of the most important factors. In this study, we propose that at least half of the number of factors should be retained, and therefore the importance threshold is set at 0.68, and subsequently identified nine factors as detailed in Table 10.

Table 10. Key influencing factors.

Code	New Code	Factor Name	Crisp Value After Defuzzification
A	C1	3D printing technology	0.694
D	C2	Sensors	0.754
E	C3	Global positioning system	0.754
F	C4	Smart clinics and urgent care centers	0.742
G	C5	Telemedicine	0.742
H	C6	Internet of things	0.688
J	C7	Smart medical talent acquisition	0.734
K	C8	Electronic medical records	0.755
R	C9	Assistive smart wheelchair	0.703

4.2. Case Analysis

In order to gain insight into the key influencing factors, this study conducted a case analysis of two long-term care institutions, with a view to comparing the differences between the two.

4.2.1. Institution A

Institution A is situated in a northern city in Taiwan. The institution was established in 1998 and currently employs approximately 500 individuals. The service is designed to meet the needs of children, individuals with physical and mental disabilities, and the elderly. It offers direct and professional social services to a range of target groups. The institution’s principal services encompass home-based care for the elderly and community integration initiatives. Long-term care services encompass both home services and community-integrated services. The following analysis of Institution A identifies the key factors:

(1)

Assessment of the degree of mutual influence between factors

In order to evaluate Institution A, this study invited three experts to utilize the linguistic Z-number, as demonstrated in Table 11. The results of the evaluation conducted by the three experts on the degree of influence between factors are presented in Table 12, Table 13 and Table 14.

(2)

The outcomes of the integration of the triangular fuzzy number assessments provided by the three experts are presented in Table 15.

(3)

The direct relationship matrix of Institution A is presented in Table 16.

(4)

The normalized direct relationship matrix of Institution A is presented in Table 17.

(5)

The total influence relationship matrix (T) of Institution A is presented in Table 18.

(6)

The factor weights and rankings of Institution A, as derived from the total influence relationship matrix, are presented in Table 19.

(7)

Causation of key factors for Institution A

Table 11. Linguistic variables of influence and certainty.

Influence Rating			Degree of Certainty
Code	Linguistic Variables	Triangular Fuzzy Numbers	Code	Linguistic Variables	Triangular Fuzzy Numbers
${\tilde{F}}_0$	Absolutely not	(0, 0, 0)	${\tilde{R}}_0$	Absolutely not	(0, 0, 0)
${\tilde{F}}_1$	No	(0, 0, 1)	${\tilde{R}}_1$	Very uncertain	(0, 0, 0.4)
${\tilde{F}}_2$	Low	(0, 1, 2)	${\tilde{R}}_2$	Not sure	(0.2, 0.4, 0.6)
${\tilde{F}}_3$	Moderate	(1, 2, 3)	${\tilde{R}}_3$	ordinary	(0.4, 0.6, 0.8)
${\tilde{F}}_4$	High	(2, 3, 4)	${\tilde{R}}_4$	determine	(0.6, 0.8, 0.9)
${\tilde{F}}_5$	Very high	(3, 4, 4)	${\tilde{R}}_5$	Very sure	(0.8, 1, 1)
${\tilde{F}}_6$	Absolutely high	(4, 4, 4)	${\tilde{R}}_6$	Absolutely sure	(1, 1, 1)

Table 12. Evaluations of linguistic Z-number by expert 1 for Institution A.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	(0,0,0), (1,1,1)	(2,3,4), (0.4,0.6,0.8)	(2,3,4), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.4,0.6,0.8)	(1,2,3), (0.4,0.6,0.8)	(0,1,2), (0.6,0.8,0.9)	(1,2,3), (0.4,0.6,0.8)
C2	(0,0,1), (0.2,0.4,0.6)	(0,0,0), (1,1,1	(2,3,4), (0.6,0.8,0.9)	(1,2,3), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,1,2), (0.4,0.6,0.8)	(2,3,4), (0.6,0.8,0.9)
C3	(0,0,1), (0.6,0.8,0.9)	(2,3,4), (0.4,0.6,0.8)	(0,0,0), (1,1,1	(2,3,4), (0.4,0.6,0.8)	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(0,1,2), (0.8,1,1)	(3,4,4), (0.8,1,1)
C4	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(0,0,0), (1,1,1	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)
C5	(0,0,1), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(3,4,4), (0.2,0.4,0.6)	(0,0,0), (1,1,1	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.8,1,1)	(3,4,4), (0.6,0.8,0.9)
C6	(0,0,1), (0.6,0.8,0.9)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(1,2,3), (0.4,0.6,0.8)	(3,4,4), (0.8,1,1)	(0,0,0), (1,1,1	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)
C7	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.8,1,1)	(0,1,2), (0.6,0.8,0.9)	(2,3,4), (0.8,1,1)	(2,3,4), (0.8,1,1)	(0,0,0), (1,1,1	(2,3,4), (0.8,1,1)	(2,3,4), (0.8,1,1)
C8	(0,0,1), (0.6,0.8,0.9)	(1,2,3), (0.4,0.6,0.8)	(1,2,3), (0.4,0.6,0.8)	(2,3,4), (0.4,0.6,0.8)	(3,4,4), (0.8,1,1)	(1,2,3), (0.8,1,1)	(1,2,3), (0.8,1,1)	(0,0,0), (1,1,1	(1,2,3), (0.8,1,1)
C9	(0,0,1), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,1,2), (0.4,0.6,0.8)	(0,1,2), (0.4,0.6,0.8)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,0,0), (1,1,1

Table 13. Evaluations of linguistic Z-number by expert 2 for Institution A.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	(0,0,0), (1,1,1)	(2,3,4), (0.4,0.6,0.8)	(2,3,4), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.4,0.6,0.8)	(1,2,3), (0.4,0.6,0.8)	(0,1,2), (0.6,0.8,0.9)	(1,2,3), (0.4,0.6,0.8)
C2	(1,2,3), (0.4,0.6,0.8)	(0,0,0), (1,1,1)	(2,3,4), (0.6,0.8,0.9)	(1,2,3), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,1,2), (0.4,0.6,0.8)	(2,3,4), (0.6,0.8,0.9)
C3	(1,2,3), (0.4,0.6,0.8)	(2,3,4), (0.4,0.6,0.8)	(0,0,0), (1,1,1)	(2,3,4), (0.4,0.6,0.8)	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(0,1,2), (0.8,1,1)	(3,4,4), (0.8,1,1)
C4	(1,2,3), (0.4,0.6,0.8)	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(0,0,0), (1,1,1)	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)
C5	(1,2,3), (0.4,0.6,0.8)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(3,4,4), (0.2,0.4,0.6)	(0,0,0), (1,1,1)	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.8,1,1)	(3,4,4), (0.6,0.8,0.9)
C6	(1,2,3), (0.4,0.6,0.8)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(1,2,3), (0.4,0.6,0.8)	(3,4,4), (0.8,1,1)	(0,0,0), (1,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)
C7	(2,3,4), (0.6,0.8,0.9)	(0,0,1), (0.6,0.8,0.9)	(0,0,1), (0.8,1,1)	(0,1,2), (0.6,0.8,0.9)	(2,3,4), (0.8,1,1)	(2,3,4), (0.8,1,1)	(0,0,0), (1,1,1)	(2,3,4), (0.8,1,1)	(2,3,4), (0.8,1,1)
C8	(1,2,3), (0.4,0.6,0.8)	(1,2,3), (0.4,0.6,0.8)	(1,2,3), (0.4,0.6,0.8)	(2,3,4), (0.4,0.6,0.8)	(3,4,4), (0.8,1,1)	(1,2,3), (0.8,1,1)	(1,2,3), (0.8,1,1)	(0,0,0), (1,1,1)	(1,2,3), (0.8,1,1)
C9	(3,4,4), (0.8,1,1)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,1,2), (0.4,0.6,0.8)	(0,1,2), (0.4,0.6,0.8)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,0,0), (1,1,1)

Table 14. Evaluations of linguistic Z-number by expert 3 for Institution A.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	(0,0,0), (1,1,1)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)
C2	(0,1,2), (0.6,0.8,0.9)	(0,0,0), (1,1,1)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)
C3	(0,1,2), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,0,0), (1,1,1)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)
C4	(0,1,2), (0.6,0.8,0.9)	(1,2,3)(0.6,0.8,0.9)	(1,2,3)(0.6,0.8,0.9)	(0,0,0), (1,1,1)	(2,3,4), (0.6,0.8,0.9)	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.6,0.8,0.9)	(3,4,4), (0.6,0.8,0.9)	(0,1,2), (0.6,0.8,0.9)
C5	(0,1,2), (0.6,0.8,0.9)	(1,2,3)(0.6,0.8,0.9)	(2,3,4), (0.8,1,1)	(2,3,4), (0.8,1,1)	(0,0,0), (1,1,1)	(2,3,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(2,3,4), (0.6,0.8,0.9)
C6	(0,1,2), (0.6,0.8,0.9)	(2,3,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(2,3,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(0,0,0), (1,1,1)	(2,3,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(1,2,3)(0.6,0.8,0.9)
C7	(0,1,2), (0.8,1,1)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(2,3,4), (0.6,0.8,0.9)	(0,0,0), (1,1,1)	(0,1,2), (0.8,1,1)	(0,1,2), (0.8,1,1)
C8	(0,1,2), (0.8,1,1)	(2,3,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(0,0,0), (1,1,1)	(0,1,2), (0.8,1,1)
C9	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(3,4,4), (0.8,1,1)	(0,1,2), (0.8,1,1)	(0,1,2), (0.8,1,1)	(0,1,2), (0.8,1,1)	(0,1,2), (0.8,1,1)	(0,1,2), (0.8,1,1)	(0,0,0), (1,1,1)

Table 15. The integrated evaluations by three experts of Institution A.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	(0,0,0)	(0,1.183,2.4)	(0,0.89,1.8)	(0,0.89,1.8)	(0,0.89,1.8)	(0,0.951,2.802)	(0,1.509,3.736)	(0,1.509,3.736)	(0,1.509,3.736)
C2	(0,0,1.8)	(0,0,0)	(0,1.3,3.736)	(0,1.638,3.736)	(0,1.3,3.736)	(0,0.767,1.534)	(0,0.767,1.534)	(0,0.767,1.534)	(0,0.767,1.534)
C3	(0,0.89,1.8)	(0,1.728,3.736)	(0,0,0)	(0,1.728,3.736)	(0,2.064,3.736)	(0,1.509,3.736)	(0,1.509,3.736)	(0,1.509,3.736)	(0,1.509,3.736)
C4	(0,0.89,1.8)	(0,1.638,3.736)	(0,1.638,3.736)	(0,0,0)	(0,1.3,3.736)	(0,1.218,3.068)	(0,1.218,3.068)	(0,1.218,3.068)	(0,1.218,3.068)
C5	(0,0.89,1.8)	(0,1.638,3.736)	(0,2.002,3.736)	(0.802,2.559,3.736)	(0,0,0)	(0,1.875,3.736)	(0,2.064,3.736)	(0,2.064,3.736)	(0,2.064,3.736)
C6	(0,0.89,1.8)	(0,3.394,3.736)	(0.802,3.736,3.736)	(0.6,2.325,3.736)	(0.802,3.736,3.736)	(0,0,0)	(0.802,3.394,3.736)	(0.802,3.394,3.736)	(0.802,3.394,3.736)
C7	(0,0.819,1.868)	(0,1.3,3.736)	(0,0,3.736)	(0,1.3,3.736)	(0,2.002,3.736)	(0,2.002,3.736)	(0,0,0)	(0.802,2.965,3.736)	(0.802,2.965,3.736)
C8	(0,0.951,1.868)	(0,2.325,3.736)	(0.6,2.559,3.736)	(0.802,2.929,3.736)	(0.802,3.736,3.736)	(0.802,2.965,3.736)	(0.802,2.965,3.736)	(0,0,0)	(0,0.819,1.868)
C9	(0,2.204,3.736)	(0,2.204,3.736)	(0,2.204,3.736)	(0,1.279,3.736)	(0,1.279,3.736)	(0,0.819,1.868)	(0,0.819,1.868)	(0,0.819,1.868)	(0,0,0)

Table 16. Direct relationship matrix of Institution A.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	0	1.194	0.897	0.897	0.897	1.251	1.748	1.748	1.748
C2	0.6	0	1.679	1.791	1.679	0.767	0.767	0.767	0.767
C3	0.897	1.821	0	1.821	1.933	1.748	1.748	1.748	1.748
C4	0.897	1.791	1.791	0	1.679	1.429	1.429	1.429	1.429
C5	0.897	1.791	1.913	2.366	0	1.87	1.933	1.933	1.933
C6	0.897	2.377	2.757	2.22	2.757	0	2.644	2.644	2.644
C7	0.896	1.679	1.245	1.679	1.913	1.913	0	2.501	2.501
C8	0.94	2.037	2.298	2.489	2.757	2.501	2.501	0	0.896
C9	2.047	2.047	2.047	1.672	1.672	0.896	0.896	0.896	0

Table 17. Normalized direct relationship matrix of Institution A.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	0.000	0.063	0.047	0.047	0.047	0.066	0.092	0.092	0.092
C2	0.032	0.000	0.089	0.095	0.089	0.040	0.040	0.040	0.040
C3	0.047	0.096	0.000	0.096	0.102	0.092	0.092	0.092	0.092
C4	0.047	0.095	0.095	0.000	0.089	0.075	0.075	0.075	0.075
C5	0.047	0.095	0.101	0.125	0.000	0.099	0.102	0.102	0.102
C6	0.047	0.126	0.146	0.117	0.146	0.000	0.140	0.140	0.140
C7	0.047	0.089	0.066	0.089	0.101	0.101	0.000	0.132	0.132
C8	0.050	0.108	0.121	0.131	0.146	0.132	0.132	0.000	0.047
C9	0.108	0.108	0.108	0.088	0.088	0.047	0.047	0.047	0.000

Table 18. Total influence relationship matrix of Institution A.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	0.099	0.234	0.220	0.224	0.228	0.210	0.245	0.245	0.245
C2	0.113	0.147	0.229	0.238	0.234	0.165	0.174	0.174	0.174
C3	0.170	0.311	0.223	0.317	0.325	0.273	0.288	0.288	0.288
C4	0.155	0.283	0.283	0.202	0.286	0.237	0.250	0.250	0.250
C5	0.180	0.328	0.333	0.359	0.251	0.294	0.312	0.312	0.312
C6	0.217	0.418	0.434	0.419	0.447	0.260	0.402	0.402	0.402
C7	0.180	0.321	0.302	0.326	0.341	0.294	0.218	0.335	0.335
C8	0.196	0.369	0.380	0.397	0.413	0.350	0.368	0.252	0.297
C9	0.207	0.289	0.288	0.276	0.277	0.207	0.220	0.220	0.175

Table 19. The influential weights and ranking of key factors of Institution A.

Factor	${\mathit{d}}_{\mathit{i}}$	${\mathit{r}}_{\mathit{i}}$	${\mathit{d}}_{\mathit{i}}+{\mathit{r}}_{\mathit{i}}$	${\mathit{d}}_{\mathit{i}}-{\mathit{r}}_{\mathit{i}}$	Weight	Ranking
C1	1.948	1.519	3.467	0.429	0.0781	9
C2	1.647	2.699	4.347	−1.052	0.0979	8
C3	2.483	2.692	5.174	−0.209	0.1166	4
C4	2.195	2.757	4.952	−0.562	0.1116	6
C5	2.681	2.800	5.481	−0.119	0.1235	3
C6	3.402	2.290	5.692	1.111	0.1283	1
C7	2.651	2.477	5.128	0.174	0.1156	5
C8	3.022	2.477	5.499	0.545	0.1239	2
C9	2.160	2.477	4.637	−0.318	0.1045	7

In accordance with Table 18 and Table 19, the threshold values (${\beta }_1$, ${\beta }_2$) are calculated as follows:

$${\beta }_1={\displaystyle \frac{1.948+1.647+2.483+2.195+2.681+3.402+2.651+3.022+2.160}{81}}=0.274$$

$${\beta }_2={\displaystyle \frac{3.402}{9}}=0.378$$

In accordance with the total impact relationship matrix and the threshold value ${\beta }_1$, the causal relationship matrix can be derived as illustrated in Table 20. The causal relationship matrix in Table 20 allows the identification of the causal relationships between key factors, as illustrated in Figure 4. As illustrated in Figure 4, the global positioning system (C3), smart clinics and urgent care centers (C4), telemedicine (C5), the Internet of Things (C6), smart medical talent acquisition (C7), and electronic medical records (C8) are of particular significance. The Internet of Things (C6), smart medical talent acquisition (C7), and electronic medical records (C8) are identified as “influencing factors”. Three-dimensional printing technology (C1), sensors (C2), global positioning systems (C3), smart clinics and urgent care centers (C4), telemedicine (C5), and assistive smart wheelchairs (C9) are classified as “influenced factors”.

Table 20. Causal matrix of Institution A with ${\beta }_1$.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	0	0	0	0	0	0	0	0	0
C2	0	0	0	0	0	0	0	0	0
C3	0	1	0	1	1	0	1	1	1
C4	0	1	1	0	1	0	0	0	0
C5	0	1	1	1	0	1	1	1	1
C6	0	1	1	1	1	0	1	1	1
C7	0	1	1	1	1	1	0	1	1
C8	0	1	1	1	1	1	1	0	1
C9	0	1	1	1	1	0	0	0	0

Figure 4. Causal relationship of key factors of Institution A with ${\beta }_1$.

In accordance with the total impact relationship matrix and the threshold value ${\beta }_2$, the causal relationship matrix can be derived as illustrated in Table 21. The causal relationship matrix in Table 21 allows the identification of the causal relationships between key factors, as illustrated in Figure 5. As illustrated in Figure 5, the Internet of Things (C6), smart medical talent acquisition (C7), and electronic medical records (C8) are identified as “influencing factors”. The sensors (C2), global positioning systems (C3), smart clinics and urgent care centers (C4), telemedicine (C5), smart medical talent acquisition (C7), and assistive smart wheelchairs (C9) are classified as “influenced factors”.

Table 21. Causal matrix of Institution A with ${\beta }_2$.

	C1	C2	C	C4	C5	C6	C7	C8	C9
C1	0	0	0	0	0	0	0	0	0
C2	0	0	0	0	0	0	0	0	0
C3	0	0	0	0	0	0	0	0	0
C4	0	0	0	0	0	0	0	0	0
C5	0	0	0	0	0	0	0	0	0
C6	0	1	1	1	1	0	1	1	1
C7	0	0	0	0	0	0	0	0	0
C8	0	0	1	1	1	0	0	0	0
C9	0	0	0	0	0	0	0	0	0

Figure 5. Causal relationship of key factors of Institution A with ${\beta }_2$.

4.2.2. Institution B

Institution B is situated in the central region of Taiwan. The institution was established in 2010 and has a workforce of fewer than 200 employees. The organization is closely aligned with the needs of the community, offering a diverse range of services. By providing comprehensive services within the community, the organization implements the community care concept of “local aging”. The service business encompasses respite care, dementia centers, daycare, case management, community support, welfare services, and long-term care, with the objective of alleviating family care pressure and promoting social welfare development. A similar calculation process was employed in the case analysis, which is presented below:

(1)

The total influence relationship matrix (T) of Institution B is presented in Table 22.

(2)

The relative importance of the key factors of Institution B is determined through the calculation of the total influence relationship matrix, as illustrated in Table 23.

Table 22. Total influence relationship matrix of Institution B.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	0.489	0.647	0.632	0.707	0.704	0.645	0.536	0.694	0.546
C2	0.642	0.657	0.747	0.836	0.838	0.693	0.582	0.777	0.673
C3	0.567	0.689	0.542	0.742	0.727	0.584	0.467	0.692	0.583
C4	0.650	0.787	0.712	0.717	0.820	0.704	0.566	0.800	0.646
C5	0.567	0.653	0.624	0.745	0.602	0.583	0.463	0.716	0.519
C6	0.509	0.549	0.524	0.649	0.577	0.442	0.414	0.633	0.456
C7	0.638	0.765	0.718	0.830	0.826	0.670	0.470	0.781	0.556
C8	0.533	0.625	0.591	0.712	0.710	0.571	0.467	0.562	0.471
C9	0.576	0.651	0.636	0.686	0.692	0.593	0.494	0.658	0.452

Table 23. The influential weights and ranking of key factors of Institution B.

	${\mathit{d}}_{\mathit{i}}$	${\mathit{r}}_{\mathit{i}}$	${\mathit{d}}_{\mathit{i}}+{\mathit{r}}_{\mathit{i}}$	${\mathit{d}}_{\mathit{i}}-{\mathit{r}}_{\mathit{i}}$	Weight	Ranking
C1	5.600	5.171	10.771	0.430	0.1052	6
C2	6.445	6.023	12.467	0.422	0.1218	2
C3	5.592	5.725	11.318	−0.133	0.1105	5
C4	6.402	6.624	13.026	−0.222	0.1272	1
C5	5.470	6.496	11.966	−1.026	0.1169	3
C6	4.754	5.484	10.237	−0.730	0.1000	9
C7	6.253	4.459	10.712	1.794	0.1046	7
C8	5.243	6.312	11.555	−1.069	0.1129	4
C9	5.438	4.904	10.343	0.534	0.1010	8

As indicated in Table 23, the “smart clinics and urgent care centers (C4)” represent the most significant key factor, whereas the “Internet of Things (C6)” is identified as the least crucial for Institution B.

(3)

In accordance with Table 22 and Table 23, the threshold values (${\beta }_1$, ${\beta }_2$) is calculated as follows:

$${\beta }_1={\displaystyle \frac{5.6+6.445+5.592+6.402+5.47+4.754+6.253+5.243+5.438}{81}}=0.632$$

$${\beta }_2={\displaystyle \frac{6.624}{9}}=0.736$$

The causal relationship matrix can be obtained based on the total influence relationship matrix and threshold value ${\beta }_1$, as illustrated in Table 24. Figure 6 illustrates the causal relationships between the key factors of Institution B. As illustrated in Figure 6, the six factors, namely sensors (C2), global positioning systems (C3), smart clinics and urgent care centers (C4), telemedicine (C5), the Internet of Things (C6), and electronic medical records (C8), are of particular significance. The four factors, namely 3D printing technology (C1), sensors (C2), smart medical talent acquisition (C7), and assistive smart wheelchairs (C9), can be classified as “influencing factors”. The five factors, namely global positioning systems (C3), smart clinics and urgent care centers (C4), telemedicine (C5), the Internet of Things (C6), and electronic medical records (C8), are classified as “affected factors”.

Table 24. Causal matrix of Institution B with ${\beta }_1$.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	0	1	1	1	1	1	0	1	0
C2	1	1	1	1	1	1	0	1	1
C3	0	1	0	1	1	0	0	1	0
C4	1	1	1	1	1	1	0	1	1
C5	0	1	0	1	0	0	0	1	0
C6	0	0	0	1	0	0	0	1	0
C7	1	1	1	1	1	1	0	1	0
C8	0	0	0	1	1	0	0	0	0
C9	0	1	1	1	1	0	0	1	0

Figure 6. Causal relationship of key factors of Institution B with ${\beta }_1$.

The causal relationship matrix can be obtained based on the total influence relationship matrix and threshold value ${\beta }_2$, as illustrated in Table 25. Figure 7 illustrates the causal relationships between the key factors of Institution B. As illustrated in Figure 7, smart medical talent acquisition (C7) can be classified as “influencing factors”. The five factors, namely sensors (C2), global positioning systems (C3), smart clinics and urgent care centers (C4), telemedicine (C5), and electronic medical records (C8), are classified as “affected factors”.

Table 25. Causal matrix of Institution B with ${\beta }_2$.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	0	0	0	0	0	0	0	0	0
C2	0	0	1	1	1	0	0	1	0
C3	0	0	0	1	0	0	0	0	0
C4	0	1	1	0	1	0	0	1	0
C5	0	0	0	1	0	0	0	0	0
C6	0	0	0	0	0	0	0	0	0
C7	0	1	0	1	1	0	0	1	0
C8	0	0	0	0	0	0	0	0	0
C9	0	0	0	0	0	0	0	0	0

Figure 7. Causal relationship of key factors of Institution B with ${\beta }_2$.

Table 19 and Table 23 illustrate that there is a discrepancy in the weighting of the influential factors for Institution A and Institution B. The weighting of the critical factors for Institution A and Institution B is presented in Table 26. Table 26 also depicts the rankings and contrasts in the weights of the principal factors for Institution A and Institution B.

Table 26. Ranking and difference in critical factor weights for two institutions.

Codes	Factors	Institution A Ranking	Institution B Ranking	Difference
C1	3D printing technology	9	6	3
C2	Sensors	8	2	6
C3	Global positioning system	4	5	1
C4	Smart clinics and urgent care centers	6	1	5
C5	Telemedicine	3	3	0
C6	Internet of things	1	9	8
C7	Smart medical talent acquisition	5	7	2
C8	Electronic medical records	2	4	2
C9	Assistive smart wheelchair	7	8	1

4.3. Management Implications

The results of the analysis indicate that Institution A considers the “Internet of Things (C6)” to be the most significant factor influencing the integration of smart medical care into long-term care, whereas Institution B deems the “smart clinics and urgent care centers (C4)” to be the most crucial element.

(1)

Institution A

The data indicates that when implementing smart healthcare in Institution A, it is essential to consider factors such as the integration of hardware with long-term care and the attitudes of the staff. The following recommendations are proposed for Institution A with regard to the implementation of smart healthcare in long-term care:

(i)

By facilitating collaborative endeavors and fostering inter-institutional partnerships with entities specializing in 3D printing technology, long-term caregivers and employees can gain a deeper comprehension of the underlying principles of 3D printing, thereby reducing their sense of rejection.

(ii)

It would be beneficial to arrange training courses for employees to gain hands-on experience with smart assistive devices, such as smart wheelchairs and smart medicine boxes. This would help them to understand the advantages and challenges of the hardware.

(iii)

It would be beneficial to collaborate with hospitals or universities to acquire the requisite smart medical talents and thereby improve the feasibility of introducing smart medical care.

(2)

Institution B

The data indicates that when implementing smart healthcare in Institution B, it is essential to consider factors such as the acceptance of information technology and the integration of hardware with long-term care. The following recommendations are proposed for Institution B about the implementation of smart healthcare in long-term care:

(1)

It would be beneficial to establish an information department and to recruit additional personnel with information capabilities, with the objective of enhancing the information capabilities of the institution.

(2)

It would be beneficial to pilot short-term smart care services, such as obtaining the vital signs and status of the caregiver through the use of wearable devices, in order to gain a deeper understanding of the level of acceptance among both staff and care recipients.

(3)

It is recommended that hospitals collaborate with one another in order to mitigate the adverse effects of inadequate resources through the utilization of AI-based diagnostic techniques and robotic assistance.

Given that Institution A is an institution with a superior organizational structure and a higher level of information, the technical factors are accorded greater importance. Institution B is situated in a less favorable geographical location and has access to fewer resources, which makes the importance of medical factors more significant. In light of the aforementioned analysis, it can be concluded that the key factors for both institutions are the “global positioning system (C3)”, “telemedicine (C5)”, and “electronic medical records (C8)”. It can thus be concluded that the organizational structure and scale of long-term care institutions are disparate, and that the medical treatment and protection measures for caregivers remain the pivotal factors recognized by both institutions.

5. Conclusions

In light of the accelerated advancement of information technology, the integration of “smart medicine” into the domain of “long-term care” to enhance the quality of care has emerged as a pivotal concern. A number of factors influence the successful implementation of smart medicine in long-term care, and the assessment of these factors by experts is inherently subjective and ambiguous. Accordingly, this study employs fuzzy set theory and the linguistic Z-number as a foundation for the analysis of the pivotal factors influencing the integration of smart healthcare into long-term care.

This study is based on fuzzy set theory and employs the fuzzy Delphi method in conjunction with the linguistic Z-number to identify nine pivotal factors. The DEMATEL method and the linguistic Z-number method are employed to calculate the weights of the key influencing factors, after which a systematic analysis model is proposed for exploring the importance of different institutions for the key influencing factors of the introduction of smart medical care in long-term care. This study makes the following main contributions: (1) The key influencing factors of the introduction of smart medicine into long-term care can be effectively identified through the fuzzy Delphi method, which can then be used to develop technical measurement items for the introduction of smart medicine into long-term care institutions. (2) The DEMATEL method allows the relevance and importance of the key factors affecting the introduction of smart medicine into long-term care to be effectively grasped. (3) In consideration of the inherent fuzziness of expert opinions, a two-stage systematic analysis model is proposed using linguistic variables, which can effectively assist long-term care institutions in analyzing the introduction of smart medical technologies and equipment.

The principal constraints of this study are the lack of straightforward access to expert assessment data, the considerable number of variables influencing the integration of smart healthcare into long-term care (LTC) institutions, and the high degree of diversity within LTC institutions. These limitations can be investigated in greater depth in future empirical studies, thus enhancing the practical value of the findings.