1 Introduction

The United Nations World Tourism Organization (UNWTO) [1] launched sustainable tourism as an effective tool for eliminating poverty (ST-EP). The sustainable development goals (SDGs) of tourism state that “tourism growth” benefits the poor. Tourism is assigned as a tool for alleviating poverty in all its forms [2,3,4]. Therefore, bed and breakfast (B&B) tourism is considered to be an efficient practice for elevating rural tourism [5, 6] and alleviating poverty in remote areas [3]. However, widespread poverty has remained in some remote areas with high B&B tourism growth [6]. Taitung area in Taiwan is such a region (Fig. 1).

Fig. 1
figure 1

Map of B&B tourism properties in Taitung

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Taitung, a popular tourism destination located in the southeastern Taiwan Island, has remained impoverished for decades. In the past 20 years, the development of tourism has increased the establishment of B&Bs island-wide. The Taitung region is placed third among the 23 counties of Taiwan [7]. However, despite the growth of B&Bs, Taitung has remained the poorest region in Taiwan because of its deteriorating socio–economic status and population loss [8]. Therefore, the dynamic factors that contribute to B&B tourism in Taitung need to be investigated. Furthermore, strategies that can help this destination alleviate its poverty, reduce outward population migration, and benefit from B&B tourism need to be developed.

The literature has generally favored economic indicators for analyzing the dynamic factors responsible for the positive effect of tourism [9, 10]. However, the lack of non-economic measures typically results in contradictory phenomena: less-favored localities experience tourism booms [11]. Therefore, studies should focus on interactions between human activities and land. Such interactions mainly center on “cultural landscapes” [12], the “locality” [13] and “regional revitalization” [6, 14] and manifest in dynamic land–man relationships. It is suggested that the ST-EP and SDG objectives can be achieved by investigating these interactions [1, 4].

Poverty and tourism are multidimensional and complex phenomena [9]. Decision-making trial and evaluation laboratory (DEMATEL) is a widely recognized automated solution for modeling intrinsically complex and interrelated phenomena [15, 16, 18]. DEMATEL based on multiple-criteria decision-making theory is a simple and efficient tool that uses an expert decision system to analyze and make deductions from real-world cases [15, 19,20,21,22].

However, the decision-making evaluation process relies on subjective judgments of experts for analysis and evaluation. The uncertainty and ambiguity of the natural semantic expression of the experts may result in incomplete information [23]. This problem has been addressed using fuzzy theory. For example, Hosseini et al. [24] proposed the use of fuzzy theory for developing recovery solutions for ecotourism centers, Farooque et al. [25] proposed using fuzzy theory for analyzing barriers to blockchain-based life cycle, and Xu et al. [26] identified critical barriers to the development of hydrogen energy using fuzzy theory. Subsequent studies have expanded the use of Zadeh’s [27] Z-numbers to simultaneously assess real-valued uncertain variables and their reliability (certainty) in our natural language. This method has proven useful in interdisciplinary fields such as the risk evaluation of green supplier selection [28], aircraft landing systems [29], and the selection of travel plans [30] and hotels [31]. Moreover, combined with DEMATEL, Z-numbers has strength of dealing interrelations of criteria in a comparatively simple process. However, few studies have applied the technique on tourism, and even fewer on B&B concerns. This motivates the current research to use this renovated Z-DEMATEL.

Therefore, to the best of our knowledge, this study is the first in which Z-numbers and DEMATEL are used to examine B&B tourism. The purpose of the study is to: (1) identify the determinants of B&B tourism in Taitung, (2) overcome the uncertainty of expert expression using information integration, (3) apply Z-DEMATEL to precisely identify the interrelations between the determinants, and (4) prepare improved strategies for poverty alleviation and population return. Therefore, this method can contribute to: (1) the use of Z-numbers for identifying the determinants of B&B tourism; and (2) the application of the Z-DEMATEL model for improving policies for poverty alleviation through B&B tourism.

The remainder of this paper is as follows. Section 2 reviews the relevant literature on the methods used to assess B&B tourism performance. Section 3 describes the research methodology and procedure of this study. Section 4 presents the results and discusses the findings and examines their implications. Section 5 concludes the article.

2 Literature Review

The B&B tourism in Taitung region and the dominant factors, cultural landscape, locality, and regional revitalization, were reviewed as the theoretical framework throughout the research. In addition, the strength and appropriateness of Z-DEMATEL was verified for the current study.

2.1 B&B Tourism and Taitung Region

B&B tourism has rapidly grown in the Taitung region since the weekends-off plan was implemented in 2001 to elevate domestic tourism. Because the region is isolated in the southeastern part of Taiwan Island, the infrastructure of Taitung—particularly its traffic system—remains underdeveloped [7]. This may have hindered its development, and the region remains pristine [32]. As a travel hot-spot, Taitung was listed as one of Asia’s best destinations in 2016 [33] and one of the world’s best emerging destinations [34]. Before the outbreak of the COVID-19 pandemic, the number of B&Bs properties in Taitung had increased to 1,330, and the region occupied third place among 23 counties of Taiwan [7].

Despite the booming of B&B industry, the population of Taitung has decreased from 289,451 to 216,781, which contrasts starkly with the 32.5% increase of the Taiwanese population from 1974 to 2019 [35]. Furthermore, according to the [36], Taitung has the largest number of low-income households in the state. This renowned B&B tourism destination has experienced lingering poverty and population loss [37].

The literature states that B&B tourism is an efficient method of alleviating poverty and population loss [38]. Land-based B&B tourism can generate job opportunities and benefit local communities [14, 39]. This addresses the positive effect of tourism development, particularly according to economic indicators (e.g., income and consumption). However, because of the complexity of poverty and population loss, noneconomic factors (e.g., social exclusion, community cohesion, personal dignity, and empowerment) may influence the interactions between land, human beings, and locality, and thereby influence individual perceptions of the locality [9, 10]. The local perception may reflect the cohesion between the people and the land within the context of B&B tourism environment. The positive effect may extend to reduce poverty and outward migration.

In the current case, the determinants of local perception and methods of generating the positive network effect between them need to be identified. Improvement strategies need to be developed to alleviate poverty and population loss in the region.

2.2 Cultural Landscape, Locality, and Regional Revitalization

From the land–man perspective, the positive effects of B&B tourism, the cultural landscape, locality, regional revitalization, have been identified and conceptualized as the theoretical framework of this study.

2.2.1 Cultural Landscape

The cultural landscape represents a tangible meeting point between nature and mind [40]. Therefore, it represents the interaction between human beings and nature [1]. Cultural geologists first proposed that the cultural landscape represents the formative process of human activity, in which culture is the agent, the natural area is the medium, and the cultural landscape is the result. This represents the evolution of human society and settlement [41]. Environmental determinism argues that under the limits set by nature, humans adapt to numerous possibilities [42]. However, other theories argue that human perceptions are correlated to the cultural landscape; in particular, the cultural landscape represents a sense of place beyond vision but related to mental perception [41, 43]. In both views, the cultural landscape changes because of alteration in landscape ushered by human activity under the influence of opportunities and/or the physical constraints of the natural environment, and the resulting social, economic and cultural forces that arise from both external and internal factors [1]. Consequently, cultural landscape conveys the way of life, identity, and sense of place of the inhabitants, which ensures that people live in the region [1, 42, 44].

In practice, cultural landscapes comprising natural environment and human features function as the primary attraction, marketing icon, and core tourism experience [45, 46]. Therefore, landscapes have been altered substantially by man-made creations, such as: (1) intentionally designed and created landscapes, (2) organically evolved landscapes, and (3) associative cultural landscapes. Therefore, sustaining land–use by combining natural values and culture through modern techniques has become the objective (The Bureau of Cultural Heritage, Ministry of Culture [44]. A few approaches have been proposed to achieve this objective: (1) phenomenology: focusing on the sense of place, considering the perceptions of people [47]; (2) politics: emphasizing the political–economic forces on the cultural landscape [48]; and (3) culture: focusing on the influence of culture on community cohesion, ideology, and identity [49]. These perspectives have influenced numerous cultural landscape theories.

Sauer (1925) [42] first proposed a cultural landscape process model and illustrated that the culture is the generating factor that functions via the natural landscape (the medium) over time, forming the variations in ways of living, such as population density, mobility, housing plans, structure, production, and communication, and finally producing the cultural landscape (the result) [5]. Subsequently, Zube (1982) [50] proposed the interactive cultural landscape model and emphasized the interactions between humans (expectation, experience, education, motivation, culture, social background, information, and characteristics), the landscape (physical elements, compositional constructs, location context, naturalism, man-made creatures, Gestalts, features, sounds, smells, and people), and outcomes (information, satisfaction, wellbeing, physical activities, stimuli, comforts, opportunities, values, prediction formulae, landmarks, behavioral patterns, and fears).

For the current study, the formation process and perception of physical components proposed by Sauer [41] and Zube [50] provide the implications to the perception of the locality in terms of the cultural landscape resulting from B&B tourism environment in the past 20 years in Taitung region.

2.2.2 Locality

The term “locality” originated from environmental psychology and refers to self-identity to land. This human–land connection is beyond emotional baggage [51], and is composed of conscious and subconscious aspects, such as belief, preference, feelings, values, goals, intentions, and environment [52]. Therefore, locality reflects the behavioral intention of an individual in a physical society or reveals their self-identity and perception in a place [53]. Theories related to locality are generally discussed from three perspectives: (1) essentialism, which considers that ancestry, language, customs, culture, and birth/growth places determine locality; (2) structuralism, which considers that locality is shaped by community teamwork through successive challenges, difficulties, and conquests; and (3) constructuralism, which considers that intrinsic man-made efforts and human mindsets influence locality [54]. These three perspectives may be exclusive or combined depending on the place and time.

In this context, the constituents of locality can vary [52]. Breakwell [50] proposed distinctiveness, continuity, self-esteem, and self-efficacy. Lalli [55] proposed external evaluation, general attachment, continuity of commitment with personal past, and perception of familiarity. Knez [56] identified distinctiveness, place referent continuity, place congruent continuity, self-esteem, and self-efficacy. Droseltis [57] included self-extension, environmental fit, place-self congruity, and emotional attachment. Most of these constructs are commonly addressed to emotional states and place attachment as essential components of locality [58].

Recently, Wang et al. [59] integrated the scales of Breakwell [50], Lalli [55], and Knez [56], and composed a leisure place attachment questionnaire, containing the variants of historical-cultural identity, place identity, distinctiveness, place-attachment, self-efficacy, and commitment. The overall Cronbach’s α they obtained was 0.869, which indicated a high reliance. If the B&B tourism in Taitung is considered as a factor that influences the locality, this value provides a useful measure to detect its influence.

2.2.3 Regional Revitalization

Regional revitalization originated from UNWTO’s initiative of SDGs, which includes 17 primary goals. Goal 1 is poverty reduction and job creation for the socio–economic sustainability of global destinations [14]. UNWTO [3] stated that tourism is well-positioned to foster economic growth and development at all levels and provide income. The sustainable development of tourism and its impact at the community level can be linked with national poverty reduction because with the development of tourism empowers entrepreneurs, small businesses, and empower less-favored groups.

The response to this initiative has been global. For example, the Japanese Regional Revitalization Law was implemented in 2014 to create jobs for youths through tourism entrepreneurship [60]. Numerous Chinese remote villages have alleviated extreme poverty via job creation through tourism entrepreneurships and small businesses [61]. In Taiwan, this concept is described in policy using three dimensions, namely, regions, products, and people, to revitalize the resource advantages of local communities [62].

Thus, regional revitalization can be a national policy, a positive tourism effect generator, and an action toward sustainability. Accordingly, life indices have been proposed to address this in the real-world. For example, [39] proposed the sustainable tourism livelihood approach (STLA), and Li et al. [6]

Extended STLA with socio-ecological system analysis. In Japan, the Plan, Do, Check and Act cycle has been proposed to encourage regional revitalization [63]. Though the measures may vary with regional distinctiveness, they share one commonality: the use of tourism to assess revitalization in social–economic networks energized/created by local commitment.

2.2.4 Cultural Landscape, Locality, and Regional Revitalization

Based on the above discussion, the dynamic factors determining positive B&B tourism development from the perspective of human–land interaction are presented in Table 1.

Table 1 Dimensions/ Criteria related to B&B tourism development
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Furthermore, cultural geographic literature has posited that the cultural landscape shapes the mental landscape, thereby integrating human beings, culture, and the land [12]; the locality provides the identity and enhances the cohesion of locals, and regional revitalization prompts tourism development with job opportunities and empowers community continuity [13]. These factors are inter-influencing, dynamic in formation process, and revive progress toward the SDGs [6, 14] based on human–land interaction, self-identity, and place commitment (Fig. 2).

Fig. 2
figure 2

Essences within the conceptualized framework of B&B tourism positive development

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2.3 Renovated Z-DEMATEL and B&B Tourism

Compared to current fuzzy methods, the emerging Z-DEMATEL is outstanding because it manages both the linguistic uncertainty and the interrelations between criteria in a simple process. This would more precisely detect the certainty of multivariate and group decisions and contribute to improving B&B tourism effects, particularly to the issue of poverty alleviation.

2.3.1 Renovated Z-DEMATEL

Zadeh [27] proposed that in the real-world, expression uncertainty is a universal phenomenon. However, he believes that humans have a remarkable ability of making rational decisions based on information that is uncertain, imprecise, and/or incomplete. Therefore, many techniques based on fuzzy set theory have been proposed, such as interval value fuzzy sets, hesitant fuzzy sets, intuitionistic fuzzy sets, interval value intuitionistic fuzzy sets (IVIFS), type-2 fuzzy sets (IFS2), picture fuzzy sets, spherical fuzzy sets, and neutrosophic sets [65, 66]. Among these, the neutrosophic sets are remarkable because they simultaneously consider a truth-membership, an indeterminacy-membership, and a falsity-membership, and efficiently resolve the ambiguity of natural semantic expression [65]. Therefore, they can overcome the challenges of incomplete, uncertain, and inconsistent information.

Recently, Z-numbers have attracted considerable research attention for enhancing the confidence of experts/decision-makers in addition to handling information ambiguity and assessment-environment uncertainty [27]. Based on fuzzy theory, Z-numbers simultaneously account for assessment scores and reliability [66]. These parameters are used to control the first component, A, which is a restriction (constraint) on the values which a real-valued uncertain variable may have; and to control the second component, B, which is a measure of the reliability (certainty) of A. Therefore, A and B exist in human natural language [27].

Z-DEMATEL additionally acquires the ability of DEMATEL to manage the inter-feedbacks between criteria through visual construction [19,20,21]. The model can precisely handle expressions via information integration, using both the exclusive semantic scale and the confidence level to detect expert data. Therefore, this method differs from previous techniques such as fuzzy DEMATEL [24,25,26] and grey DEMATEL [18, 67]. Specifically, Z-DEMATEL has superiorities compared with the current fuzzy methods. For instance, (1) triangular fuzzy number (TFN) method solves linguistic uncertainty only [27]; (2) Neutrosophic sets simply reflect the decision uncertainty [65]; (3) As to the Analytic Hierarchy Process (AHP) and the best–worst method (BWM), which have been widely used in evaluating systematic priority recently, both regard the criteria are independent to each other in the system and neglect the interaction between the criteria [15, 16, 18]; 4) It takes tedious time/effort to integrate such methods for a case study; and (5)Turning to Z-numbers, it is able to manage information integration in a simple processing (see Sect. 3) and efficiently overcome the mentioned shortages. Therefore, the Z-DEMATEL can be renovated as compared to these methods.

2.3.2 Appropriateness for Poverty Alleviation of B&B Tourism

Previous studies have considered these fuzzy conditions and used fuzzy DEMATEL to manage hospitality and tourism issues. For instance, Tseng [68] used the model to examine the cause-and-effect relations of hotel service quality. Nisa et al. [69] applied this model to propose the retrenchment strategies of five-star hotels, and Ocampo et al. [70] used it to clarify the causal relationships between job satisfaction and employee engagement of the hotel. Mehrdad [71] combined the model with the ANP to propose the customer satisfaction and the objectives of the organization. Erkal et al. [72] performed IVIF-DEMATEL to determine the importance degrees of the criteria in the Turkish tourism sector. In these studies, imprecise information in the field of tourism was handled using various fuzzy tools. However, few studies have investigated B&B tourism or poverty alleviation using Z-DEMATEL.

The issue of B&B tourism and poverty alleviation is intrinsic to multivariate and group decisions. The management of expert opinions is particularly critical to the present study. Therefore, Z-DEMATEL appears to be appropriate for simultaneously managing expression uncertainty and multiple-criteria. This study may be the first application of Z-DEMATEL for examining B&B tourism.

3 Methodology

In this study, the advanced Z-DEMATEL was used to manage the uncertainty and incompleteness of information collected from B&B tourism experts. The Z-DEMATEL model was constructed as follows.

3.1 Evaluation Construction of Z- DEMATEL

The construction of Z-DEMATEL can be divided into four stages as follows (Fig. 3):

  1. Stage 1

    Confirmation of the criteria and dimensions through in-depth interviews based on literature review (Table 1).

  2. Stage 2

    Determination of the Z-numbers addressing the consistency of information derived from expert opinions.

  3. Stage 3

    Integration of expert opinions via simple average weighting using reliability measurement.

  4. Stage 4

    Analysis of the interrelations using DEMATEL.

Fig. 3
figure 3

Process for investigating the poverty-alleviating characteristics of B&B tourism

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3.2 Process for Conducting Z-DEMATEL

The process for conducting Z-DEMATEL was as follows:

  1. 1.

    Establishing natural linguistic expression measurement: Three steps were included: First, the question was defined; thereafter, the natural linguistic expressions of the expert were clarified; and finally, the reliability of expert evaluation regarding the pair-comparison of criteria was assessed.

  2. 2.

    Coding the expression.

  3. 3.

    Coding the reliability degree with mutually influential weight: for the present study, in addition to using pair-comparison to collect influential relationships of Dimensions/ Criteria, reliability assessment was considered. Numerous criteria \(C_{i} = \left\{ {C_{i} ,\;C_{2} ,\; \ldots ,C_{n} } \right\}\) were considered to exist, and the degree of influence of Ci on Cj was established, whereupon each influential degree was assigned an \(\ell\), the reliability degree of Ci on Cj.

  4. 4.

    Calculating Z-numbers

If Z-numbers \(Z = \left( {F,\;\ell } \right)\). \(F = (f,\mu_{F} )\left| {x \in \left[ {0,1} \right]} \right.\) and \(r = (x,\mu_{\ell } )\left| {x \in \left[ {0,1} \right]} \right.\), sematic measure is trigonometric functions, and the reliability is probabilistic in nature.

$$\omega = \frac{{\int {^{x} \mu_{\ell } \;dx} }}{{\int {^{{\mu_{\ell } }} \;dx} }}$$
(1)

Using weight \(\omega\) of reliability, the evaluation score \(F\) and the weighted Z-numbers were calculated according to Eq. 2. That is, the radicand \(\omega\) can be included throughout the calculations as follows:

$$Z^{\omega } = \left\{ {\left( {x,\mu_{F\omega } } \right)\left| {\mu_{F\omega } \left( x \right) = \omega \mu_{F} (x),x \in \omega x} \right.} \right\}$$
(2)
  1. 5.

    Calculating the impact degree of the crisp score

The impact degrees of the crisp scores were obtained using fuzzy and de-fuzzy weighted Z-numbers as follows:

$${\varvec{A}} = \left[ {a_{ij} } \right] = \left[ {\begin{array}{*{20}c} {a_{11} } & \cdots & {a_{1j} } & \ldots & {a_{1n} } \\ \vdots & {} & \vdots & {} & \vdots \\ {a_{i1} } & \cdots & {a_{ij} } & \cdots & {a_{in} } \\ \vdots & {} & \vdots & {} & \vdots \\ {a_{n1} } & \cdots & {a_{nj} } & \cdots & {a_{nn} } \\ \end{array} } \right]_{n \times n}$$
(3)
  1. 6.

    Calculating the direct influential matrix: According to the influential degrees, the direct influential matrix was constructed and subsequently integrated with the weighted expert reliability using SAW.

  2. 7.

    Normalizing the direct influential matrix

Use the Eq. 4–5 to normalize the direct influential matrix.

$${\varvec{V}} = m{\varvec{V}} = \left[ {v_{ij} } \right] = \left[ {\begin{array}{*{20}c} {v_{11} } & \cdots & {v_{1j} } & \ldots & {v_{1n} } \\ \vdots & {} & \vdots & {} & \vdots \\ {v_{i1} } & \cdots & {v_{ij} } & \cdots & {v_{in} } \\ \vdots & {} & \vdots & {} & \vdots \\ {v_{n1} } & \cdots & {v_{nj} } & \cdots & {v_{nn} } \\ \end{array} } \right]_{n \times n}$$
(4)
$$m{\text{ = min}}\left\{ {1/\mathop {\max }\limits_{i} \sum\nolimits_{j = 1}^{n} {a_{ij} ,\;1/\mathop {\max }\limits_{j} \sum\nolimits_{i = 1}^{n} {a_{ij} \;\;} } } \right\},\;i,j \in \left\{ {1,2, \ldots ,n} \right\}$$
(5)
  1. 8.

    Obtaining the total influential matrix

Via unlimited inter-influencing calculations, the total matrix emerges. The equations used are Eqs. (6–11).

$$\begin{gathered} T = V + V^{2} + V^{3} + ... + V^{k} \hfill \\ \;\;\; = V(I + V + V^{2} + ... + V^{k - 1} )[(I - V)(I - V)^{ - 1} ] \hfill \\ \;\;\; = V(I - V^{k} )(I - V)^{ - 1} \hfill \\ \end{gathered}$$
(6)

Next, we have the following expression:

$${\varvec{T}} = {\varvec{V}}({\varvec{I}} - {\varvec{V}})^{ - 1} ,\;when\;k \to \infty ,\;{\varvec{V}}^{k} = \left[ 0 \right]_{n \times n}$$
(7)
  1. 9.

    Exploring the influential interrelations between criteria

    $${\varvec{r}} = (r_{1} ,...,r_{i} ,...,r_{n} )^{\prime} = \left[ {t_{{_{i} }} } \right]_{n \times 1} = \left[ {\sum\nolimits_{j = 1}^{n} {t_{ij} } } \right]_{n \times 1}$$
    (8)

Calculating the impact degree of criteria

$${\varvec{d}} = (d_{1} ,...,d_{i} ,...,d_{n} )^{\prime} = \left[ {t_{{_{j} }} } \right]_{n \times 1} = \left[ {\sum\nolimits_{i = 1}^{n} {t_{ij} } } \right]^{\prime }_{n \times 1}$$
(9)

Calculating the total influence degree: the larger the value, the more influential is the criterion.

$${\varvec{g}} = g_{i} = r_{i} + d_{i}$$
(10)

Calculating the net influence degree: positive values indicate causes, negative values indicate effects.

$${\varvec{u}} = u_{i} = r_{i} \,{ - }\,d_{i}$$
(11)
  1. 10.

    Constructing the inter-network relations map

By reflecting \({\varvec{g}}\) and \({\varvec{u}}\) onto the coordinate, the overall influential relations were obtained, which indicated the influencing directions for criteria A to B or B to A. Following the directions, the paths were depicted as a visional map, namely, an inter-network relations map (INRM).

3.3 Sampling and Data Collections

In this Z-DEMATEL study, the depth interview commenced with the query “considering the importance/influence of the following factors involving Taitung B&B tourism for poverty reduction, please give your rating in the blanks.” This study was conducted in two phases:

  1. (1)

    The initial interview: In this phase, we clarified the content validity of the initial questionnaire based upon the literature review (Table 1), including five experts: three B&B owners, one advocate, one scholar, and one regional official. The Cronbach’s α revealed a high reliability of 0.96, indicating that the tool was appropriate.

  2. (2)

    The formal interview: In this phase, we investigated the opinions of regional B&B tourism experts using the modified questionnaires. The experts were qualified with a minimum of 10 years of experience involving regional B&B tourism development. Because of the outbreak of COVID-19, individual on-line interviews were held. Each interview required approximately 60–90 min to complete (Table 2).

Table 2 Expert characteristics of the formal interview survey
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Subsequently, the consensus was examined, which indicated a high consensus rate of 0.95 (threshold value 5%) (Qu et al., 2019) (Table 3).

Table 3 Consensus test
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To manage the expert sematic expression, the Z-DEMATEL questionnaire first asked the expert to clarify semantic expressions using an exclusive semantic scale that accorded both maximum and minimum scores between 0 and 100 to each of five expressions, namely extreme, high, medium, low, and none. Thereafter, the expert undertook 36 pairwise comparisons of 11 criteria by ticking a preference blank that ranged from Very high influence (VHI) to No Influence (NI) (Table 4).

Table 4 Semantics of the experts
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L for low bound; M for medium bound; U for upper bound.

Simultaneously, the confidence level was detected. The expert was requested to provide a confidence score, ranging from 0 to 100, to each comparison; larger values of which indicated higher confidence levels (Table 5). In this way, the reliability of the information was confirmed.

Table 5 Semantics and reliabilities of the experts
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Finally, according to the values of the exclusive semantic scale and confidence level of each expert, the Z-numbers of the experts were obtained, as listed in Table 6. For instance, EXP1 evaluated that D1 to D2 has “Very High Influence” with 100% confidence level. The data were therefore coded as L, M, U, and R, with values correspondingly 0.800, 0.900, 1.000, and 1.000, respectively. This rule was applied throughout the coding process.

Table 6 Z-numbers of the experts
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4 Results and Discussions

Using the method of Z-DEMATEL, the results were gained and discussed. Furthermore, the useful improvement strategies were composed for decisions makers.

4.1 Analysis and Discussions

Based on the Z-numbers calculated in Sect. 3, the direct influence matrix A can be established. The total influence matrix T was obtained using Eq. (3–7) (Table 7).

Table 7 Transformation from questionnaire item data to the direct influence matrix A and total influence Matrix T
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Based on the above matrices, the inter-network relations between dimensions and criteria could be calculated (Table 8) and depicted in the INRMs for each dimension (Fig. 4).

Table 8 Interrelations and cause-effect relationships between Dimensions/Criteria
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Fig. 4
figure 4

Inter-network relations map (INRM) of the dimensions and criteria

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This result can be interpreted by inter-network relations, considering the interrelations or cause–effect relationships. According to Table 8, the influence of D2 (Locality) was outstanding, with the largest \({\varvec{r}}\), \({\varvec{d}}\), and \({\varvec{g}}\) values, which implied the critical role of the locality in producing interdimensional influence. According to the \({\varvec{r}}\) values, the impacting sequence can be ordered as \(D_{2} \succ D_{1} \succ D_{3}\), revealing that the locality was the most powerful influencing dimension. According to the \({\varvec{d}}\) values, \(D_{2} \succ D_{3} \succ D_{1}\), whereby the locality emerged as the most “influenced” dimension. According to the \({\varvec{g}}\) values, the order of influence was \(D_{2} \succ D_{1} \succ D_{3}\), demonstrating that the locality dominated the total influence by producing as well as receiving influence. This finding is consistent with the review in Sect. 2.2. Locality, as the essence of place attachment and self-identity can usher changes in the cultural landscape and revitalize engagement, and vice versa. The locality plays the role of nexus for interrelations among the dimensions.

In terms of the cause–effect relationship, \(D_{1}\) (Cultural landscape) emerged as the cause dimension with the largest u value of 0.45, followed by D2 (Locality) and D3 (Regional revitalization), which had u values of 0.39 and 0.313, respectively. Therefore, the cultural landscape impacts the regional revitalization and locality according to the cause–effect analysis. The order of influence was \(D_{1} \succ D_{3} \succ D_{2}\), suggesting that B&B tourism should holistically create a cultural landscape, empowering local revitalization and resulting in local recognition. This responds the argument that cultural landscapes function as the primary attraction, marketing icon, and core tourism experience [45, 46]. The cultural landscape is the starter pushing the cause-effect chain among the dimensions.

The above analysis can also be applied on the criteria in each dimension. In the \(D_{1}\) dimension (Cultural landscape), the \({\varvec{g}}\) values of the criteria revealed their order of influence to be \(C_{11} \succ C_{13} \succ C_{14} \succ C_{12}\), indicating that C11 (Humanity & culture) is the nexus of interrelations and dominates the total influence. C14 (Outcomes), which had a negative u value, was the effect of the three other criteria, which had positive u values. The cause–effect sequence was \(C_{11} \succ C_{13} \succ C_{14} \succ C_{12}\). This result reveals that all the efforts of humanity/culture, physical landscapes, and human-landscape contribute to outcomes shared by the locals [44, 50]. Therefore, these criteria are the starters generate cause-effect chain.

In the dimension of D2 (Locality), the order of influence of criteria by their \({\varvec{g}}\) values was \(C_{23} \succ C_{21} \succ C_{22}\), indicating that C23 (Commitment) has the largest influence and is a nexus in this dimension. This result suggests that the local commitment enforces the self-identity of inhabitants and subsequently produces place recognition. Moreover, the u value of C22 (Self-identity) was positive and functioned as the cause to the other two criteria, C21 (Place recognition) and C23 (Commitment). The cause–effect sequence was \(C_{22} \succ C_{21} \succ C_{23}\), which indicates that self-identity ushers place recognition and enhances the local commitment. This matches the discussion above that locality is self-identity to land beyond emotional baggage [51].

In the dimension of D3 (Regional revitalization), the order of influence according to g values was \(C_{33} \succ C_{32} \succ C_{34} \succ C_{31}\), indicating that C33 (Skill & entrepreneurship) has the largest influence and is a nexus of interrelations. Therefore, the skill and entrepreneurship value adds humanity/creativity and location distinctiveness, and can thereby alleviate poverty and population loss. This is consistent with previous findings of using the tool of upgrading skill and entrepreneurship to revitalize rural tourism [6]. Furthermore, the u value of C34 (Poverty reduction & population return) is positive, which indicates that it is the cause to the three other criteria, which have negative values. Because tourism can play a vital role in poverty reduction and population return as stated by UNWTO [1], this universal value may prompt all forms of revitalization efforts, such as C31 (Location distinctiveness), C32 (Humanity & creativity), and C33 (Skill & entrepreneurship). This supports the UNWTO’s initiative of SDGs, in which Goal 1 is poverty reduction and job creation for the socio–economic sustainability of global destinations [6, 14].

4.2 Implications

Some implications for efficient improvement strategies can be inferred from the interrelations and cause–effect relationships between the Dimensions/Criteria (Table 9). Holistically, P1 suggests that the influencing power of D2 (Locality) functions as a continuous nexus prompt for D1 (Cultural landscape) and D3 (Regional revitalization). The chain of effect may begin from the cause (D1) and subsequently approach D3 and fulfill D2, in that order.

Table 9 Improvement plans for B&B tourism and poverty alleviation using inter-network relations
Full size table

The same rule can be applied to each dimension. For example, P2 C11 (Humanity & culture) as a nexus can simultaneously influence C13 (Interaction), C12 (Physical landscapes) and C14 (Outcomes) through the influencing network. Via the cause–effect relationship, C14 (Outcomes) as the starter can create a chain effect for C13 (Interaction), C12 (Physical landscapes), and C11 (Humanity & culture). Such nexuses (e.g., D2, C11, C23, and C33) and starters (e.g., D1, C11, C23, and C33) can be traced from the perspective of dimensions or criteria by the INRM (Fig. 4), in terms of both interrelations and cause–effect chains. This synthesized index (Table 9) can yield two times the result with half the effort for policy makers, thereby improving the poverty-alleviating effect of B&B tourism.

5 Conclusion

This study investigated the novel Z-numbers model to examine the empirical case of the Taitung region for evaluating the role of B&B tourism in poverty alleviation. The results revealed that the model is appropriate and efficient (Table 9) and satisfies research requirements. Consequently, this model contributes to: (1) composing improvement strategies to alleviate the lingering poverty and population loss in the B&B tourism destinations using Z-DEMATEL; (2) managing the uncertainty of expert expression using the unique technique of information integration (e.g., exclusive somatic scale, confidence scale, and Z-numbers) and superior to the current fuzzy methods (ex. TFN, Fuzzy sets, Neutrosophic sets, AHP, BWM, and, etc.); (3) filling the gap in the literature by demonstrating the appropriateness between B&B tourism and poverty alleviation using Z-DEMATEL; (4) and providing an INRM of Z-DEMATEL model, which reveals the interrelation improvement compared to linear cause-effect findings (such as Structural Equation Modeling, SEM or Linear Structural Relations, LISERAL).

However, this study has some limitations. Firstly, the measurement scale developed in this study may not be generalizable for cross-industry application because it is tailored to the B&B tourism domain. Secondly, a comparison between the opinions of owners, officials, and locals would have deepened the discussion. Finally, further research is required to compare the performance of various fuzzy models (e.g., fuzzy DEMATEL, gray DEMATEL, and rough-DEMATEL) for methodological renovation.