A r,s,t-spherical fuzzy decision-making model of university happiness: case study of University of Economics Ho Chi Minh City

Abstract

A seven-domain university well-being model was evaluated using r,s,t-Spherical Fuzzy DEMATEL to identify the most influential domains perceived as exerting upstream influence at the University of Economics Ho Chi Minh City (UEH). Judgments were obtained from a 20-member expert panel comprising academic staff, administrators, and senior lecturers, allowing domain interactions to be assessed under linguistic uncertainty. The analysis showed that physical health, mental–emotional balance, and especially financial security act as core drivers, while social relationships, environmental quality, career conditions, and self-fulfilment operate primarily as receivers. The most influential sub-criteria were income sufficiency, future financial security, growth mindset, balanced nutrition, and clear development pathways. These results suggest that financial support mechanisms, mindset-development initiatives, and foundational health programs may yield the broadest well-being gains. The study demonstrates the applicability of r,s,t-spherical fuzzy causal modelling within a Vietnamese higher-education context and highlights the need for longitudinal and multi-campus studies to confirm the causal hierarchy observed.

Introduction

Universities around the world have been moving steadily away from a narrow preoccupation with admissions, research counts, and graduate salaries toward a more holistic “happy campus” agenda. The OECD now reports student and staff well-being indicators in Education at a Glance and presents them as prerequisites for “learning environments that nurture physical, mental, social and economic health” (Education at a Glance 2023: OECD Indicators 2023). Parallel shifts can be seen across ranking and accreditation schemes, which increasingly weight well-being criteria alongside research impact and teaching quality. Across Southeast Asia, comparable developments have taken place as rapidly expanding higher-education systems confront rising academic pressure, demographic growth, and intensified competition. Universities in Thailand (Thanoi et al. 2023), Indonesia (Ekawati et al. 2025), and Malaysia (Shahira et al. 2018) have therefore begun adopting well-being metrics as part of broader quality-assurance and institutional-governance reforms, reflecting a regional recognition that psychological, social, and financial conditions significantly shape performance and sustainable development. University leaders often face the practical question of where to intervene first when resources are limited and well-being domains interact; however, existing empirical studies rarely provide guidance on the sequencing or relative leverage of such interventions.

At the institutional level, the University of Economics Ho Chi Minh City (UEH) exemplifies this transition. As one of Vietnam’s largest multidisciplinary public universities, UEH serves a diverse population of students, faculty, and administrative staff across multiple urban campuses and has undertaken various initiatives aimed at strengthening community well-being. Its scale, urban context, and institutional complexity make it a representative case for examining how well-being domains interact in large Southeast Asian universities.

A growing empirical literature demonstrates why happiness has become a strategic priority for universities. A meta-analysis of 6837 studies reports that one third of undergraduates present clinically relevant mental-health symptoms, with prevalence ranging from 2% to 75.2% (Kartikasari et al. 2025). Students receiving mental-health treatment are 4.3–8.3 percentage points more likely to withdraw from university (Zając et al. 2024), and academic staff with lower occupational well-being exhibit higher turnover intentions and weaker organisational commitment (Yousaf et al. 2024). By contrast, institutions that adopt structured positive-psychology programmes show semester-level improvements in life satisfaction and affect (Dorri Sedeh and Aghaei 2024) and enjoy reputational gains among applicants and donors (Wu et al. 2024). These findings position well-being as a determinant of learning outcomes, workforce stability, and institutional prestige.

Guidance is drawn from established frameworks such as PERMA and the OECD Student Well-Being model, which span emotional, social, physical, and resource-based dimensions (Kern et al. 2015; Seligman 2018). These models inform emerging discussions on educational quality in Vietnam and motivate the seven-domain structure used here: Physical, Mental & Emotional, Relational & Social, Self-Fulfilment, Career, Environmental, and Financial well-being. Each domain has documented links to academic or organisational performance—for example, physical activity correlates with higher GPA, and green, inclusive spaces reduce student stress (Kotera et al. 2024; Suavansri et al. 2022; Usmany et al. 2025). The structure is sufficiently flexible for cross-cultural comparison while reflecting conditions common to rapidly expanding Southeast Asian universities.

Traditional descriptive or correlational approaches are limited because well-being domains interact. Financial stress may heighten emotional strain, which then reduces physical activity or undermines social relationships. Such recursive pathways require a causal method capable of distinguishing drivers from outcomes. DEMATEL is therefore employed because it maps directional influences among interdependent factors rather than merely estimating correlations.

These modelling demands also require a fuzzy MCDM framework. Well-being evaluations rely on subjective, linguistically expressed judgments (“rarely,” “often,” “very high”), which involve uncertainty and hesitation. Fuzzy MCDM techniques allow experts to express such ambiguity without forcing premature numerical precision (Wang et al. 2024), treat each well-being facet as a decision criterion, and provide structured aggregation and trade-off mechanisms (Belton and Stewart 2012; Nhieu 2024; Triantaphyllou 2000). Fuzzy logic is introduced here simply as a means of representing nuanced expert assessments.

Among available fuzzy approaches, the r,s,t-spherical fuzzy extension offers the greatest expressive flexibility because membership, non-membership, and hesitation can vary independently. This is particularly relevant for well-being evaluation, where judgments frequently involve asymmetric or culturally influenced uncertainty. Unlike intuitionistic, Pythagorean, or classical spherical sets, r,s,t-spherical fuzzy sets allow richer representation and yield more stable causal inference when combined with DEMATEL (Gül 2020).

A synthesis of recent campus happiness studies confirms the gap. Most investigations rely on descriptive statistics, and only a small subset adopt advanced fuzzy MCDM techniques; even fewer attempt to trace causal relationships among interdependent well-being dimensions. Within the ASEAN region, the literature is especially thin: while recent policy reports discuss “people-centric smart cities” and macro-level happiness economics (Otsuka and Oikawa 2024), university-level analyses remain limited to single-domain surveys that do not integrate financial, environmental, or career factors. No published study has applied r,s,t-spherical fuzzy DEMATEL to model campus happiness in any ASEAN setting. The present work addresses this omission by offering the first uncertainty-aware causal map of well-being drivers for a large Vietnamese university.

Consequently, a threefold gap is identified: (i) the absence of a systemic, causal approach to university-level happiness; (ii) the lack of applications that leverage the full expressive capability of r,s,t-spherical fuzzy DEMATEL; and (iii) the scarcity of evidence from ASEAN, and particularly Vietnamese, contexts. To guide the analysis, three research questions were formulated to directly reflect the study’s objectives: RQ1 corresponds to validating the seven-domain framework by identifying influential components; RQ2 examines how causal pathways propagate across domains; and RQ3 prioritises drivers that can guide managerial intervention.

The overarching purpose is threefold: first, to validate a concise seven-domain, twenty-eight indicator instrument; second, to reveal the directional influence structure among domains; and third, to identify high-leverage drivers that can guide practical decision-making. The methodological choices introduced above also reinforce the “so what” element: by clarifying which domains exert the strongest perceived directional influence, the study provides actionable guidance for university leaders—especially within ASEAN—seeking to design evidence-based well-being strategies, allocate resources efficiently, and strengthen institutional resilience.

Accordingly, this study does not seek to estimate behavioural determinants of well-being outcomes, but rather to elicit and structure expert-perceived influence relationships among interdependent well-being domains, with the aim of supporting institutional diagnosis and policy prioritization under uncertainty.

Literature review

Happiness-university-related studies

A decisive policy shift toward holistic campus well-being has been documented during the past decade. The OECD now reports staff- and student-well-being indicators alongside attainment metrics, highlighting that sustainable excellence requires supportive learning environments (Education at a Glance 2023: OECD Indicators 2023). In ASEAN, higher-education conditions differ from Western systems in several structural and cultural dimensions. Financial pressure, urban congestion, parental expectations, and unequal access to academic support services exert stronger effects on student and staff well-being in Thailand (Thanoi et al. 2023), Indonesia (Ekawati et al. 2025), and Malaysia (Shahira et al. 2018) than in many OECD contexts. Comparative studies consistently show that Southeast Asian students experience greater economic and familial pressures, whereas Western findings emphasise autonomy, self-efficacy, and institutional belonging.

Empirical prevalence work has reinforced the urgency of this shift. A 952-study meta-analysis covering more than 2 million undergraduates reported mild depression at 35.4% and severe depression at 13.4% (Paiva et al. 2025). Randomised trials of digital mental-health interventions show pooled anxiety- and depression-reduction effects of 0.46 and 0.55, respectively (Madrid-Cagigal et al. 2025). Financial strain compounds these risks; a qualitative U.S. study found that financial stress was associated with sleep disturbance, diet degradation, and social withdrawal in 75% of participants (Moore et al. 2021).

To clarify the conceptual grounding of the seven-domain model, each domain was linked to its underlying theoretical foundation. The PERMA framework contributes Positive Emotion, Engagement, Relationships, Meaning, and Accomplishment, while the OECD Student Well-Being framework extends these constructs to physical health, environmental quality, and material conditions. Empirical higher-education studies further validate career development and financial stability as essential components of well-being. The corresponding summary table demonstrates how these frameworks collectively inform the final domain structure.

Evidence for individual well-being domains has accumulated across multiple strands. Physical well-being has been associated with academic performance, with a 23-study meta-analysis reporting an odds ratio of 3.04 for high versus low performers (Trott et al. 2024). Mental & Emotional well-being gains have been demonstrated in PERMA-based interventions, including life-satisfaction improvements following a 12-week programme (Dorri Sedeh and Aghaei 2024). Relational & Social well-being has been linked to academic persistence through belonging and intrinsic motivation (Mtshweni 2024). Self-fulfilment has been connected to growth mind-set processes; a Chinese survey of 560 students found that interpersonal distress mediated the association between growth mind-set and loneliness (Wang et al. 2024). Career well-being research emphasises employability; a business-simulation study improved life skills and career confidence among U.K. students (Scheuring and Thompson 2025), and a cross-national review highlighted integrated placements as critical to graduate outcomes (Xu et al. 2025). Environmental well-being effects are supported by landscape research, with 96% of 52 studies showing positive associations between blue-green spaces and stress reduction (Aghabozorgi et al. 2024), and additional evidence confirming perceived campus greenness as restorative (Liu et al. 2025). Financial well-being influences both mental health and performance, with debt anxiety identified as a significant predictor of lower GPA (Moore et al. 2021). Parallel staff studies show similar patterns; autonomy-supportive leadership improves vitality and reduces turnover intentions among Australian faculty (Collie 2023), while higher occupational well-being predicts lower quit intentions in Pakistan (Yousaf et al. 2024).

The seven domains operate as an interconnected system rather than independent components. Financial strain can affect emotional well-being, which subsequently influences physical health, relational engagement, and self-fulfilment. Environmental conditions shape academic satisfaction, stress, and sense of community. Such systemic interactions are documented widely in global research and are especially pronounced in emerging economies, where multiple stressors accumulate.

Instrument development research has advanced accordingly. A five-factor Student Well-Being Scale demonstrated composite reliabilities above 0.7 across four cohorts (Khatri et al. 2024), and the Multidimensional Student Well-Being (MSW) instrument confirmed similar factorial integrity alongside strong convergent validity with PERMA measures (Craven et al. 2024). However, most studies remain descriptive, reporting mean-level differences without modelling cross-domain dynamics.

These findings confirm the importance of each domain but reveal a persistent gap: well-being studies continue to examine domains individually, with limited attempts to trace causal pathways across the broader happiness system.

Fuzzy multiple criteria decision-making studies

Early decision studies in higher education were dominated by crisp MCDM tools. A review of 72 journal articles showed that the Analytic Hierarchy Process (AHP) remained the most widely used method for campus problems up to 2021, supporting programme evaluation and infrastructure decisions (Yüksel et al. 2023). Classical AHP ranked university-choice criteria for Turkish applicants, while TOPSIS produced comparable results with faster computation (Gülsün and Miç 2019). Crisp DEMATEL was also applied to course-selection, though linguistic uncertainty had to be forced into fixed numeric scales (Altınırmak et al. 2017).

Fuzzy methods were introduced to capture vagueness in stakeholder judgements (Wang et al. 2024). Fuzzy AHP supported emergency-grant allocation by integrating qualitative satisfaction indicators with income thresholds (Wei and Yang 2023). A fuzzy-poverty index summarised student dissatisfaction in the U.K. using trapezoidal membership functions to reflect nuanced perceptions (Cook et al. 2024).

Fuzzy DEMATEL variants then emerged for causal modelling (Le and Nhieu 2022). A Fuzzy Delphi–DEMATEL approach identified teacher–student relationships and financial hardship as key impediments to engagement (Aria et al. 2020). Intuitionistic-fuzzy DEMATEL mapped psychosocial risks among Turkish academics, with emotional demands identified as the strongest driver (Tepe et al. 2025). Pythagorean-fuzzy DEMATEL further improved hesitation capture in supplier-selection studies, though its use remained outside higher education (Giri et al. 2022).

Spherical-fuzzy DEMATEL (SF-DEMATEL) extended these methods by modelling membership, non-membership, and hesitation simultaneously (Gül 2020). Integrations with ANP (Analytic Network Process) and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) improved rank stability in smart-city evaluation (Büyüközkan et al. 2024). Educational applications of spherical sets have focused mainly on weighting, such as ranking classroom factors with WASPAS (Weighted Aggregated Sum Product Assessment) (Gao and Yu 2025) and evaluating augmented-reality providers with spherical-fuzzy TOPSIS (Nguyen 2024). SF-DEMATEL itself has been applied mostly outside campus contexts, including drone-risk assessment (Pandey et al. 2023) and wearable-app issue prioritization (Pandey et al. 2024). The r,s,t-spherical fuzzy set (r,s,t-SFS) introduces tunable parameters for richer hesitation (Ali and Naeem 2023), yet it has not been combined with DEMATEL in any higher-education study. q-Rung orthopair fuzzy DEMATEL shows further potential but remains non-academic [50].

Across these developments, persistent gaps remain: advanced fuzzy causal tools (especially SF-DEMATEL and r,s,t-SF DEMATEL) are seldom used; most studies emphasise ranking rather than cause–effect mapping; and ASEAN universities are almost absent from the literature. Prior fuzzy MCDM work in well-being contexts relies largely on intuitionistic or Pythagorean sets, which impose structural constraints on membership, non-membership, and hesitation. The r,s,t-spherical fuzzy extension removes these constraints by allowing independent variation across components, enabling more realistic modelling of culturally influenced expert uncertainty.

Methodology

Preliminaries

Definition 1. (Ali and Naeem 2023) A r,s,t-spherical fuzzy set (r,s,t-SFS) $\tilde{A}$ on the universe of discourse $X$ is defined as

$$\tilde{A}\,=\{(x,\alpha \left(x\right),\,\gamma \left(x\right),\beta \left(x\right)){|x}\in X\}$$

(1)

$${\rm{where}}\,\alpha ,\gamma ,\beta :\,X\to \left[0,1\right]\,{\rm{and}}\,0\le {\alpha }^{r}\left(x\right)+{\gamma }^{s}\left(x\right)+{\beta }^{t}\left(x\right)\le 1\,\forall t{\mathbb{\in }}{\mathbb{N}}{\mathbb{,}}x\in X$$

(2)

The notation $\alpha (x),\gamma (x),$ and $\beta (x)$ are the degree of membership, hesitancy, and non-membership of $x$ to $\tilde{A}$, respectively. The indeterminacy degree of $x$ in $\tilde{A}$ is defined as

$$r\left(x\right)={\left(1-\left({\alpha }^{r}\left(x\right)+{\gamma }^{s}\left(x\right)+{\beta }^{t}\left(x\right)\right)\right)}^{\frac{1}{l}}$$

(3)

Where $l$ is the least common multiple (LCM) of $r,\,s,\,{and}\,t$. The $\tilde{A}=(\alpha ,\gamma ,\beta )$ is known as a r,s,t-spherical fuzzy number (r,s,t-SFN).

Definition 2. (Ali and Naeem 2023) The score value $({SV})$ of the r,s,t-SFN $\tilde{A}=(\alpha ,\gamma ,\beta )$ is defined as

$${SV}\left(\tilde{A}\right)=\frac{1}{2}\left(1+\left({\alpha }^{r}-{\gamma }^{s}-{\beta }^{t}\right)\right)$$

(4)

and the accuracy value $({AV})$ of the r,s,t-SFN $\tilde{A}=(\alpha ,\gamma ,\beta )$ is defined as

$${AV}\left(\tilde{A}\right)=\frac{1}{2}\left(1+\left({\alpha }^{r}+{\gamma }^{s}+{\beta }^{t}\right)\right)$$

(5)

Definition 3. (Ali and Naeem 2023) Consider two r,s,t-SFN ${\tilde{A}}_{1}=({\alpha }_{1},{\gamma }_{1},{\beta }_{1})$ and ${\tilde{A}}_{2}=({\alpha }_{2},{\gamma }_{2},{\beta }_{2})$, the comparison is defined as

• i. If$\,{SV}\left({\tilde{A}}_{1}\right) < {SV}\left({\tilde{A}}_{2}\right),\,{then}{\,\tilde{A}}_{1} < {\tilde{A}}_{2};$

• ii. ${\rm{If}}{SV}\left({\tilde{A}}_{1}\right)={SV}\left({\tilde{A}}_{2}\right),{\rm{and}}$

• a. If ${AV}\left({\tilde{A}}_{1}\right) < {AV}\left({\tilde{A}}_{2}\right),\,{then}\,{\tilde{A}}_{1} < \,{\tilde{A}}_{2}$

• b. If ${AV}\left({\tilde{A}}_{1}\right) > {AV}\left({\tilde{A}}_{2}\right),\,{then}\,{\tilde{A}}_{1} > \,{\tilde{A}}_{2}$

• c. If ${AV}\left({\tilde{A}}_{1}\right)={AV}\left({\tilde{A}}_{2}\right),\,{then}\,{\tilde{A}}_{1}\simeq \,{\tilde{A}}_{2}$

Definition 4. (Ali and Naeem 2023) Consider two r,s,t-SFN$\,{\tilde{A}}_{1}=({\alpha }_{1},{\gamma }_{1},{\beta }_{1})$ and ${\tilde{A}}_{2}=({\alpha }_{2},{\gamma }_{2},{\beta }_{2})$ with two triple (${r}_{1},{s}_{1},{t}_{1}$) and (${r}_{2},{s}_{2},{t}_{2}$), the basic operations are defined as

$${\tilde{A}}_{1}\oplus \,{\tilde{A}}_{2}=\left({\left({\alpha }_{1}^{{r}^{* }}+{\alpha }_{2}^{{r}^{* }}-{\alpha }_{1}^{{r}^{* }}{\alpha }_{2}^{{r}^{* }}\right)}^{\frac{1}{{r}^{* }}},{\gamma }_{1}{\gamma }_{2},\,{\beta }_{1}{\beta }_{2}\right)$$

(6)

$${\tilde{A}}_{1}\otimes {\tilde{A}}_{2}=\left({\alpha }_{1}{\alpha }_{2},{\left({\gamma }_{1}^{{s}^{* }}+{\gamma }_{2}^{{s}^{* }}-{\gamma }_{1}^{{s}^{* }}{\gamma }_{2}^{{s}^{* }}\right)}^{\frac{1}{{s}^{* }}},\,{\left({\beta }_{1}^{{t}^{* }}+{\beta }_{2}^{{t}^{* }}-{\beta }_{1}^{{t}^{* }}{\beta }_{2}^{{t}^{* }}\right)}^{\frac{1}{{t}^{* }}}\right)$$

(7)

$$\omega {\tilde{A}}_{1}=\,\left({\left({1-\left(1-{\alpha }_{1}^{{r}^{* }}\right)}^{\omega }\right)}^{\frac{1}{{r}^{* }}},{\gamma }_{1}^{\omega },{\beta }_{1}^{\omega }\,\right)$$

(8)

$${({\tilde{A}}_{1})}^{\omega }=\left({\alpha }_{1}^{\omega },{\left({1-\left(1-{\gamma }_{1}^{{s}^{* }}\right)}^{\omega }\right)}^{\frac{1}{{s}^{* }}},{\left({1-\left(1-{\beta }_{1}^{{t}^{* }}\right)}^{\omega }\right)}^{\frac{1}{{t}^{* }}}\,\right)$$

(9)

where r* = max (r_1, r₂), s* = max (s₁, s₂), t* = max(t₁, t₂), ω >0 

Definition 5. (Ali and Naeem 2023) Consider r,s,t-SFNs$\,{\tilde{A}}_{i}=({\alpha }_{i},{\gamma }_{i},{\beta }_{i})$ with $i=1\ldots m$, the r,s,t-SF weighted aggregator (r,s,t-SFWA) with the weight vector $w=\left({w}_{1},{w}_{2},\ldots ,{w}_{m}\right)$ are defined as

$$\begin{array}{c}{\rm{r}},{\rm{s}},{\rm{t}}-{\rm{SFWA}}\left({\tilde{A}}_{1},{\tilde{A}}_{2},\ldots ,{\tilde{A}}_{m}\right)=\,{\oplus }_{i=1}^{m}{w}_{i}{\tilde{A}}_{i}\\ =\left({\left(1-\mathop{\prod }\limits_{i=1}^{m}{\left(1-{\alpha }_{i}^{r}\right)}^{{w}_{i}}\right)}^{\frac{1}{r}},\,\mathop{\prod }\limits_{i=1}^{m}{\alpha }_{i}^{{w}_{i}},\,\mathop{\prod }\limits_{i=1}^{m}{\beta }_{i}^{{w}_{i}}\right)\end{array}$$

(10)

where

$$0\le {w}_{i}\le 1,\,i=1\ldots m$$

(11)

and

$$\mathop{\sum }\limits_{i=1}^{m}{w}_{i}=1$$

(12)

The proposed r,s,t-SF DEMATEL approach

The methodological objective of this study is not predictive estimation or hypothesis testing, but structural diagnosis. r,s,t–spherical fuzzy DEMATEL is employed because it is specifically designed to elicit perceived influence relationships among interdependent criteria under linguistic uncertainty, a task for which econometric or SEM-based approaches are unsuitable in the absence of large-scale behavioural datasets.

The study is grounded in a pragmatic research paradigm, which prioritizes methodological flexibility and problem-solving utility, while drawing from critical realism to acknowledge that well-being constructs possess both observable and latent causal properties. An abductive reasoning approach was adopted because the seven-domain framework was iteratively refined through theory, institutional context, and expert judgment. The analysis follows a cross-sectional time horizon, as expert evaluations were collected at a single point in time; this design allows the identification of stable causal structures but does not capture temporal evolution.

The procedure of the r,s,t-SF DEMATEL approach includes 11 steps as illustration in Fig. 1. In general, the expert-provided linguistic terms were first converted into r,s,t-spherical fuzzy numbers. These fuzzy values were then aggregated across experts to form the fuzzy direct influence matrix, which was subsequently defuzzified to obtain the numerical matrix used for normalization and total-influence computation. This progression ensures a transparent link from qualitative expert judgments to the quantitative causal structure.

Fig. 1: The proposed r,s,t-SF DEMATEL approach.

Flowchart illustrating the eleven-step r,s,t–spherical fuzzy DEMATEL procedure used in this study. The diagram presents the sequential process from expert identification and linguistic evaluation to aggregation, normalization, total-influence computation, network relation mapping, and global weight derivation. Arrows indicate the analytical progression, and shaded blocks represent key computational stages.

Step 1

A group of experts$\left(k=1\ldots K\right)$ is identified, and their expertise is quantified using r,s,t-SFNs ${\tilde{Q}}^{k}=\left({\alpha }_{{\tilde{Q}}^{k}},{\gamma }_{{\tilde{Q}}^{k}},{\beta }_{{\tilde{Q}}^{k}}\right)$ as shown Table 1. Experts were selected purposively based on domain knowledge, institutional experience, and familiarity with student and staff well-being. To reduce bias, experts were drawn from academic, administrative, and student-support units. Each expert met predefined criteria: a minimum of five years of professional experience, direct involvement in student or staff development, and participation in well-being initiatives. Before rating began, experts received a short briefing document explaining the seven domains, the linguistic scale, and the meaning of influence relationships. Calibration was conducted through a guided example, after which experts provided independent judgments. No group discussion was permitted during scoring to avoid anchoring, conformity, or dominance biases. Each expert is assigned a normalized weight (${\varPsi }_{k}$) based on the linguistic evaluation of their competence as Eq. (13) with $l$ is the least common multiple (LCM) of $r,\,s,\,{and}\,t$.

$${\varPsi }_{k}=\frac{1-\root{{l}}\of{\left(\left(1-{\alpha }_{{\tilde{Q}}^{k}}^{r}\right)+{\gamma }_{{\tilde{Q}}^{k}}^{s}+{\beta }_{{\tilde{Q}}^{k}}^{t})/3\right)}}{\mathop{\sum }\limits_{l=1}^{K}\left(1-\root{{l}}\of{\left(\left(1-{\alpha }_{{\tilde{Q}}^{k}}^{r}\right)+{\gamma }_{{\tilde{Q}}^{k}}^{s}+{\beta }_{{\tilde{Q}}^{k}}^{t})/3\right)}\right)}$$

(13)

where $\mathop{\sum }\limits_{k=1}^{K}{\varPsi }_{k}=1$ and $0\le \,{\alpha }_{{\tilde{Q}}^{k}}^{r}+{\gamma }_{{\tilde{Q}}^{k}}^{s}+{\beta }_{{\tilde{Q}}^{k}}^{t}\le 1$

Table 1 Linguistic terms for expertise.

Step 2

The assessment criteria $\left(i=1\ldots I\right)$ and sub-criteria $(j=1\ldots J)$ are defined by experts and literature. Experts then perform pairwise comparisons of these criteria using linguistic terms, which are converted into r,s,t-SFNs as shown in Table 2. This coarse scale was adopted to minimize the cognitive load on experts and to reduce judgment variability when assessing a large number of relationships. Prior fuzzy MCDM studies note that excessively fine linguistic scales may introduce inconsistency, whereas coarser scales enhance reliability in pairwise assessments. Although simplified, the chosen scale was applied consistently across all evaluations, and the resulting causal rankings remained stable. As a result, the individual r,s,t-SFN direct influence matrices for criteria (${\tilde{D}}^{k})$ and the individual r,s,t-SFN direct influence matrices for sub-criteria (${\tilde{E}}^{k})$ established as Eqs. (14) and (15).

$$\begin{array}{cc}{\tilde{D}}^{k}={\left[{\tilde{d}}_{{ip}}^{k}\right]}_{i\times i}\,{with}\,{\tilde{d}}_{{ip}}^{k}=\left({\alpha }_{{\tilde{d}}_{{ip}}^{k}},{\gamma }_{{\tilde{d}}_{{ip}}^{k}},\,{\beta }_{{\tilde{d}}_{{ip}}^{k}}\right) & i=1\ldots I,p=1\ldots I\end{array}$$

(14)

$$\begin{array}{cc}{\tilde{E}}^{k}={\left[{\tilde{e}}_{{jp}}^{k}\right]}_{j\times j}\,{with}\,{\tilde{e}}_{{jp}}^{k}=\left({\alpha }_{{\tilde{e}}_{{jp}}^{k}},{\gamma }_{{\tilde{e}}_{{jp}}^{k}},\,{\beta }_{{\tilde{e}}_{{jp}}^{k}}\right) & j=1\ldots J,p=1\ldots J\end{array}$$

(15)

Table 2 Linguistic terms for criteria/sub-criteria influence.

Step 3

Individual direct influence matrices from each expert are aggregated into a single matrix as the r,s,t-SFN direct influence matrix for criteria $\left(\tilde{D}\right)$ and the r,s,t-SFN direct influence matrix for sub-criteria ($\tilde{E}$) using the r,s,t-SFWA, incorporating their respective weights $\left({\varPsi }_{k}\right)$.

$$\begin{array}{cc}\tilde{D}={\left[{\tilde{d}}_{{ip}}\right]}_{i\times i}\,{with}\,{\tilde{d}}_{{ip}}=\left({\alpha }_{{\tilde{d}}_{{ip}}},{\gamma }_{{\tilde{d}}_{{ip}}},\,{\beta }_{{\tilde{d}}_{{ip}}}\right) & i=1\ldots I,p=1\ldots I\end{array}$$

(16)

where

$$\begin{array}{cc}{\alpha }_{{\tilde{d}}_{{ip}}}=\,{\oplus }_{k=1}^{K}{\varPsi }_{k}{\alpha }_{{\tilde{d}}_{{ip}}^{k}} & i=1\ldots I,p=1\ldots I\end{array}$$

(17)

$$\begin{array}{cc}{\gamma }_{{\tilde{d}}_{{ip}}}=\,{\oplus }_{k=1}^{K}{\varPsi }_{k}{\gamma }_{{\tilde{d}}_{{ip}}^{k}} & i=1\ldots I,p=1\ldots I\end{array}$$

(18)

$$\begin{array}{cc}{\beta }_{{\tilde{d}}_{{ip}}}=\,{\oplus }_{k=1}^{K}{\varPsi }_{k}{\beta }_{{\tilde{d}}_{{ip}}^{k}} & i=1\ldots I,p=1\ldots I\end{array}$$

(19)

$$\begin{array}{cc}\tilde{E}={\left[{\tilde{e}}_{{jp}}\right]}_{j\times j}{with}\,{\tilde{e}}_{{jp}}=\left({\alpha }_{{\tilde{d}}_{{jp}}},{\gamma }_{{\tilde{d}}_{{jp}}},\,{\beta }_{{\tilde{d}}_{{jp}}}\right) & j=1\ldots J,p=1\ldots J\end{array}$$

(20)

where

$$\begin{array}{cc}{\alpha }_{{\tilde{e}}_{{ip}}}=\,{\oplus }_{k=1}^{K}{\varPsi }_{k}{\alpha }_{{\tilde{e}}_{{ip}}^{k}} & j=1\ldots J,p=1\ldots J\end{array}$$

(21)

$$\begin{array}{cc}{\gamma }_{{\tilde{e}}_{{ip}}}=\,{\oplus }_{k=1}^{K}{\varPsi }_{k}{\gamma }_{{\tilde{e}}_{{ip}}^{k}} & j=1\ldots J,p=1\ldots J\end{array}$$

(22)

$$\begin{array}{cc}{\beta }_{{\tilde{e}}_{{ip}}}=\,{\oplus }_{k=1}^{K}{\varPsi }_{k}{\beta }_{{\tilde{e}}_{{ip}}^{k}} & j=1\ldots J,p=1\ldots J\end{array}$$

(23)

Step 4

The aggregated r,s,t-SFNs in the direct influence matrix are defuzzified using the r,s,t-SFS score function to obtain crisp matrices suitable for linear algebraic operations.

$$D={\left[{d}_{{ip}}\right]}_{i\times i}$$

(24)

where

$${d}_{{ip}}={SV}\left({\tilde{d}}_{{ip}}\right)$$

(25)

$$E={\left[{e}_{{jp}}\right]}_{j\times j}$$

(26)

where

$${e}_{{ip}}={SV}\left({\tilde{e}}_{{jp}}\right)$$

(27)

Step 5

The initial direct influence matrices are normalized as Eqs. (28)–(31). Following the correction of the normalization procedure, the spectral radius of each normalized direct-influence matrix was computed to ensure the mathematical validity of the DEMATEL transformation. DEMATEL requires that the normalized matrix N satisfy the convergence condition $\rho (N) < 1$, where $\rho (N)$ denotes the spectral radius. This condition guarantees that the infinite series expansion used to derive the total-influence matrix converges and that the matrix inversion ${(I-N)}^{-1}$ is well defined.

$$N={\left[{n}_{{ip}}\right]}_{i\times i}$$

(28)

where

$$\begin{array}{cc}{n}_{{ip}}={d}_{{ip}}\times \min \left(\frac{1}{\mathop{\max }\limits_{1\le i\le I}{\sum }_{p=1}^{I}{d}_{{ip}}},\frac{1}{\mathop{\max }\limits_{p1\le p\le I}{\sum }_{i=1}^{I}{d}_{{ip}}}\right) & i=1\ldots I,p=1\ldots I\end{array}$$

(29)

$$M={\left[{m}_{{jp}}\right]}_{j\times j}$$

(30)

where

$$\begin{array}{cc}{m}_{{jp}}={m}_{{jp}}\times \min \left(\frac{1}{\mathop{\max }\limits_{1\le j\le J}{\sum }_{p=1}^{J}{e}_{{jp}}},\frac{1}{\mathop{\max }\limits_{p1\le p\le J}{\sum }_{j=1}^{J}{e}_{{jp}}}\right) & j=1\ldots J,p=1\ldots J\end{array}$$

(31)

Step 6

The total influence matrices are derived, capturing both direct and indirect relationships among criteria according to Eqs. (32) and (33).

$$H=N+{N}^{{\prime} }=N{\left(I-N\right)}^{-1}={\left[{h}_{{ip}}\right]}_{i\times i}$$

(32)

$$L=M+{M}^{{\prime} }=M{\left(I-M\right)}^{-1}={\left[{l}_{{jp}}\right]}_{j\times j}$$

(33)

Step 7

In this step, for criteria, the row sums $({x}_{i})$ and the column sum $({y}_{i})$ of the total influence matrix are computed according to Eqs. (34)–(37). The prominence $({x}_{i}\,+\,{y}_{i})$ and relation $({x}_{i}-\,{y}_{i})$ values for each criterion are calculated from the total influence matrix. The ${jth}$ criterion can be grouped into the cause group if $({x}_{i}-\,{y}_{i})$ is positive. Conversely, if $({x}_{i}-\,{y}_{i})$ is negative, the ${jth}$ criterion is influenced by the other criteria. Then, it can be grouped into the effect group. The prominence $({r}_{j}\,+\,{c}_{j})$ represents the strength of influence that is received or given by the criterion.

$${x}_{i}=\mathop{\sum }\limits_{p=1}^{I}{h}_{{ip}}\,\,\,\,\,\,\,\,\,i=1...I$$

(34)

$${y}_{p}=\mathop{\sum }\limits_{i=1}^{I}{h}_{{ip}}\,\,\,\,\,\,\,\,\,\,p=1...I$$

(35)

$${Criteria}\,{{prominence}}_{i}=\,{x}_{i}\,+\,{y}_{i}\,\,\,\,\,\,\,\,\,i=1...I$$

(36)

$${Criteria}\,{{relation}}_{i}=\,{x}_{i}-\,{y}_{i\,\,\,\,\,\,\,\,\,\,\,}i=1...I$$

(37)

Step 8

This procedure repeated for all sub-criteria according to Eqs. (38)–(41).

$$\begin{array}{cc}{{x}^{{\prime} }}_{j}=\mathop{\sum }\limits_{p=1}^{J}{l}_{{jp}} & j=1...J\end{array}$$

(38)

$$\begin{array}{cc}{{y}^{{\prime} }}_{j}=\mathop{\sum }\limits_{j=1}^{J}{l}_{{jp}} & p=1...J\end{array}$$

(39)

$$\begin{array}{cc}{{{prominence}}^{{{\prime} }}}_{i}=\,{{x}^{{{\prime} }}}_{j}\,+\,{{y}^{{\prime} }}_{j} & i=1...J\end{array}$$

(40)

$$\begin{array}{cc}{{{relation}}^{{{\prime} }}}_{i}=\,{{x}^{{\prime} }}_{j}-\,{{y}^{{\prime} }}_{j} & i=1...J\end{array}$$

(41)

Step 9

A four-quadrant Network Relation Map (NRM) is constructed based on prominence and relation values, helping visualize the causal structure of criteria. By calculating the mean of prominence $(x+y)$, the NRM can be divided into four quadrants as illustrated in Fig. 2. Based on the criteria’s position on four-quadrant NRM, decision-makers can visually detect the complex causal relationships among criteria and further spotlight valuable insights for decision making.

Fig. 2: The four-quadrant NRM.

Conceptual structure of the Network Relation Map (NRM). The horizontal axis represents prominence (total influence given and received), and the vertical axis represents relation (net influence direction). Quadrants distinguish driver domains (positive relation) from effect domains (negative relation), with higher prominence indicating stronger systemic leverage.

Step 10

The local weight of each criterion or sub-criterion is determined by normalizing the prominence value across all criteria/sub-criteria, forming the final importance vector.

$$\begin{array}{cc}{w}_{i}=\,\frac{{x}_{i}+{y}_{i}}{{\sum }_{i}^{I}({x}_{i}+{y}_{i})} & i=1...I\end{array}$$

(42)

$$\begin{array}{cc}{{w}^{{\prime} }}_{j}=\frac{{{x}^{{\prime} }}_{j}+{{y}^{{\prime} }}_{j}}{{\sum }_{j=1}^{J}({{x}^{{\prime} }}_{j}+{{y}^{{\prime} }}_{j})} & j=1...j\end{array}$$

(43)

Step 11

The global weight of each sub-criteria ${jth}$ is computed by multiple with its local weight with the local weight of corresponding criteria ${ith}$.

$$\begin{array}{cc}{W}_{j}={{w}^{{\prime} }}_{j}* {w}_{i} & i=1...I,\,j=1...j\end{array}$$

(44)

The r,s,t–spherical fuzzy DEMATEL approach provided analytical insights that traditional methods could not reveal. Its ability to model membership, non-membership, and hesitancy independently allowed experts to express uncertainty inherent in well-being assessments more accurately than with crisp or classical fuzzy DEMATEL. This richer uncertainty structure enabled clearer identification of asymmetric causal relationships and more stable driver–effect patterns across domains. As a result, the method offered a more faithful representation of the complex, culturally embedded interdependencies shaping happiness at UEH.

All research procedures were performed in accordance with the relevant guidelines and regulations approved by the University of Economics Ho Chi Minh City. As the study involved expert interviews only, no experiments on humans or animals were conducted.

Case study: the happiness assessment in University of Economics Ho Chi Minh City

In this study, the parameter set (r,s,t) = (2,1,2) was used to represent a low-hesitation judgment environment, consistent with experts’ confidence in evaluating relationships among the well-being domains. UEH was selected as a representative large Vietnamese university with an established commitment to well-being assessment. Cultural factors such as collectivism, respect for hierarchy, and strong emphasis on self-improvement shape how fulfilment, belonging, and supportive environments are perceived, while Vietnam’s socioeconomic conditions—rapid modernization, rising living costs, and financial pressure on students and early-career professionals—help explain the strong prominence of financial security and career development in the results. Although UEH regularly administers a campus-wide happiness survey, these responses were used only to contextualize the institutional setting and not in the causal modelling. All causal judgments were derived solely from the expert panel, encoded as r,s,t-spherical fuzzy numbers, and processed using the procedures outlined in Section 3, ensuring the causal map reflects expert-based interpretations of the seven-domain, twenty-eight-indicator framework.

Expert identification and weighting

A purposive sampling procedure was employed to convene a panel of 20 experts who possessed both teaching and managerial experience at the University of Economics Ho Chi Minh City. Candidates were screened for a minimum of five years’ instructional service and active involvement in well-being–related committees or initiatives. Diversity across academic ranks and functional units was ensured so that perspectives from undergraduate instruction, postgraduate supervision, human-resource management, and campus services could be represented. As shown in Supplementary Table A1 (Supplementary Material), the expertise level of experts is determined based on their highest degree, working experience, and management level. In the next step, the expertise level is converted to r,s,t-SFNs to calculate the weights of the experts according to Eq. (13) as shown in the Supplementary Table A2 and Fig. 3. Each expert’s competence level was evaluated using a predefined linguistic scale, which was then converted into r,s,t-spherical fuzzy values and subsequently defuzzified to produce numerical weights. These weights were applied during aggregation to ensure that judgments from more experienced or domain-relevant experts contributed proportionally more to the construction of the direct influence matrices. This weighting procedure was applied consistently throughout the analysis.

Fig. 3: The obtained expert weight.

Distribution of normalized expert weights derived from competence evaluation. Each bar represents the relative contribution (${\varPsi }_{k}$) of an individual expert to the aggregated direct-influence matrix, reflecting differences in expertise level.

Assessment criteria, sub-criteria identification and UEH’s happiness assessment model

This section explains how the assessment criteria and their twenty-eight sub-criteria were identified for UEH’s happiness model. A two-round modified Delphi process was conducted, during which the expert panel reviewed candidate indicators extracted from the contemporary well-being literature; suggestions were iteratively refined until full consensus was achieved. As a result, seven extensive domains—Physical, Mental & Emotional, Relational & Social, Self-Fulfilment, Career, Environmental, and Financial well-being—were retained, and four to five concise sub-criteria were specified for each domain to reflect both scholarly findings and context-specific considerations at UEH. Because the instrument was designed for expert-elicited causal assessment rather than statistical scale analysis, conventional reliability measures such as Cronbach’s alpha or factor analysis—which require respondent-level variance—were not applicable. Instrument coherence was therefore established through theoretical grounding in existing well-being frameworks and expert consensus during the Delphi review.

The UEH happiness assessment model is illustrated in Fig. 4 and detail described below.

Fig. 4: The UEH’s happiness assessment model.

Structure of the seven-domain, twenty-eight-indicator happiness framework used for the University of Economics Ho Chi Minh City (UEH). The diagram presents the hierarchical relationship between major well-being domains and their corresponding sub-criteria.

CC – Career Well-being concerns how work at UEH supports professional growth and economic security.

• CC1 Autonomy & Resources measures the degree of decision-making latitude and availability of tools needed to perform; job-autonomy studies and meta-analyses on perceived control consistently link higher autonomy to stronger engagement and job satisfaction (Aithal and Aithal 2019; Christensen 2011).

• CC2 Development & Progress assesses the presence of clear career pathways and training; evidence from higher-education samples shows that perceived career-development opportunities predict employability beliefs and psychological well-being (Petruzziello et al. 2023).

• CC3 Supportive & Innovative Environment captures collegial backing and an organizational climate that encourages experimentation—conditions shown to foster learning behaviour and job-crafting in knowledge-intensive settings (Gross 2015).

• CC4 Stability & Livelihood reflects job security and a wage level that affords a decent living; cross-national studies demonstrate a robust positive association between employment security and subjective well-being (Ray 2022).

CP – Physical Well-being refers to the day-to-day integrity of the body and the health habits maintained by UEH staff and students. It is captured through four inter-linked sub-criteria.

• CP1 Healthy & Rested gauges whether individuals awaken free of illness or fatigue, signalling adequate physiological recovery and the absence of chronic conditions that hinder study or work (Mohanavelu et al. 2017).

• CP2 Balanced Diet & Hydration assesses routine consumption of all five food groups together with a daily fluid intake of roughly 1.5 litres; research shows that varied, nutrient-dense diets and sufficient hydration jointly support metabolic efficiency and cognitive performance (Cena and Calder 2020; Mohanavelu et al. 2017).

• CP3 Active Lifestyle measures adherence to the World Health Organization recommendation of 150–300 min of moderate-intensity (or 75–150 min vigorous-intensity) physical activity per week, a level consistently associated with reduced non-communicable-disease risk and improved functional capacity (Bull et al. 2020).

• CP4 Proactive Health Care reflects behaviours such as self-monitoring bodily signals, maintaining good posture, seeking credible health information, and consulting professionals when needed—components of health literacy that facilitate early detection and effective management of emerging issues among university populations (Kühn et al. 2021).

  CF – Financial Well‑being captures perceived economic security, a key but often overlooked driver of happiness in academic settings.

• CF1 Shock Resilience measures confidence in covering an unexpected expense; population‑level analyses find that higher financial worries strongly predict psychological distress, whereas financial cushions buffer it (Bialowolski et al. 2021).

• CF2 Income Sufficiency asks whether current earnings comfortably meet day‑to‑day needs; studies of university personnel show that perceived income adequacy is associated with better off‑work recovery and self‑rated health (Black et al. 2025).

• CF3 Future Security taps saving behaviour and long‑term planning; longitudinal research confirms that feeling on track for future financial goals significantly boosts overall subjective well‑being (Jalal Ahamed 2024).

CE – Environmental Well‑being concerns how the campus itself—both its tangible setting and its work culture—supports health and happiness.

• CE1 Green, Sustainable Campus captures the availability of trees, gardens, and low‑impact infrastructure; studies consistently show that perceived “greenness” on university grounds reduces stress and improves mental‑health scores among students and staff (Aghabozorgi et al. 2024).

• CE2 Adequate Facilities refers to whether classrooms, laboratories, sports areas, and dining spaces are sufficient and well‑maintained; campus‑wide wellbeing reviews list high‑quality, readily accessible facilities as a prerequisite for academic success and holistic wellness (Scherer and Leshner 2021).

• CE3 Inclusive & Inspiring Spaces gauges how far learning and working areas are designed to be welcoming, diverse, and aesthetically stimulating—qualities linked to stronger belonging and retention in higher‑education populations (Scherer and Leshner 2021).

• CE4 Efficient Systems & Digitalization covers clear processes and digital tools that strip away bureaucratic “hassles”; evidence from university automation projects shows that reducing administrative burden frees staff time and lifts reported job satisfaction (Kalucza and Sievert 2024).

• CE5 Positive, Innovative Culture reflects a collaborative, humane atmosphere that encourages experimentation; empirical work demonstrates that such cultures lower stress and raise overall employee well‑being (Dóra et al. 2019).

CM – Mental & Emotional Well-being reflects the psychological climate under which UEH community members study and work.

• CM1 Life/Work Satisfaction gauges global contentment with life and campus experience; empirical work on the Satisfaction-With-Life Scale shows that such cognitive evaluations are a core facet of subjective well-being (Diener et al. 1985).

• CM2 Positive & Flexible Outlook taps optimism and adaptive re-planning, attributes repeatedly linked to lower morbidity and better overall well-being in meta-analytic evidence on dispositional optimism (Rasmussen et al. 2009).

• CM3 Emotion Regulation captures the capacity to monitor and modify emotional responses in ways that support goal attainment—an ability regarded as central to mental health across clinical and non-clinical populations (Aldao 2013).

• CM4 Vital Engagement denotes sustained energy, enthusiasm, and absorption in tasks, paralleling the “vigour” component of work-engagement models that predict reduced burnout and higher performance (Van Schalkwyk 2015).

• CM5 Self-esteem & Achievement assesses feelings of personal worth and accomplishment; longitudinal and meta-analytic studies show robust positive associations between self-esteem, academic success, and life satisfaction (Ferradás et al. 2019; Saadat et al. 2012).

CS – Self-Fulfilment represents the eudaimonic side of happiness: feeling that one’s life is purposeful, self-guided, and continuously expanding.

• CS1 Self-acceptance & Direction gauges the extent to which staff or students hold a positive view of themselves and have clear, intrinsic goals—core pillars of Ryff’s model of Psychological Well-Being, which links high self-acceptance and purpose in life to stronger overall well-being (Abdullahi et al. 2020; Ryff and Keyes 1995).

• CS2 Growth Mindset & Learning captures an orientation toward continuous improvement and intellectual curiosity; meta-analytic evidence shows that endorsing a growth mindset is reliably associated with higher motivation, persistence, and life satisfaction (Burnette et al. 2023).

• CS3 Meaning, Pride & Future Plans reflects seeing one’s work at UEH as meaningful, feeling proud of that affiliation, and actively shaping a hopeful future self—factors repeatedly tied to higher positive affect and greater resilience among university populations (Wong and Chiu 2019; Wu et al. 2024).

CR – Relational & Social Well-being addresses the breadth and depth of interpersonal connections within and beyond the university.

• CR1 Family & Close Support measures the degree of emotional and practical backing from family or intimate ties; systematic reviews of health-promotion models highlight family support as a key determinant of well-being across the lifespan (Ho et al. 2022).

• CR2 Social Satisfaction & Belonging captures adequate social activity and a felt sense of inclusion on campus, outcomes repeatedly shown to buffer stress and enhance academic persistence among university cohorts (Samadieh and Reshvanloo 2023).

• CR3 Trust & Reciprocity gauges mutual trust, warmth, and fair exchange within social networks; community-level studies link higher social trust and generalized reciprocity to better self-rated health and life satisfaction (Choi et al. 2020; Mellor et al. 2008).

• CR4 Contribution to Others’ Growth represents prosocial involvement—helping, mentoring, and fostering collective happiness—which experimental and longitudinal research associates with elevated positive affect and sustained happiness gains for givers as well as recipients (Weiss-Sidi and Riemer 2023).

The r,s,t-SF DEMATEL implementation

In this section, the consensus sub-criteria were converted into causal maps using the r,s,t-SF DEMATEL procedure. Each of the 20 experts evaluated the influence among criteria and among sub-criteria within each domain using a four-level linguistic scale. These linguistic terms were transformed into r,s,t-SFNs following Table 2, producing individual direct-relation matrices that were then aggregated through spherical-fuzzy averaging (Eqs. (10)–(12)). The resulting criteria-level matrix is presented in Table 3, while sub-criteria matrices appear in Supplementary Tables A163–A169 in the supplementary file.

Table 3 The aggregated r,s,t-SFNs direct influence matrix for criteria.

The aggregated r,s,t-SFNs were next defuzzified with the score function SV(·), yielding crisp direct-influence matrices D (criteria) and E (sub-criteria) suitable for linear-algebraic operations (Eqs. (24)–(27)). These matrices, shown in Table 4 and Supplementary Tables A170–A176, preserve relative influence strengths while removing fuzzy uncertainty. Normalisation was then applied so that no row or column sum exceeded one, producing matrices N and M (Eqs. 28)–(31)); the criteria-level normalised matrix is reported in Table 5.

Table 4 The direct influence matrix for criteria.

Table 5 The initial direct influence matrix for criteria.

Because the spectral radius of N and M fell below one, total-influence matrices H and L were computed using geometric-series inversion (Eqs. (32) and (33)), capturing both direct and indirect effects (see Table 6). Prominence and relation values were then calculated from row and column sums (Eqs. (34)–(41)), allowing criteria and sub-criteria to be classified into driver or receiver groups. Finally, local weights were obtained by normalising prominence values (Eqs. (42) and (43)), generating the weighting vectors wᵢ and w′ⱼ shown in Table 7.

Table 6 The total influence matrix for criteria.

Table 7 The global weight of sub-criteria.

The result reveal a balanced distribution of importance across the seven well-being domains, indicating that no single criterion overwhelmingly dominates the structure of happiness at UEH. Career Well-being (0.143), Physical Well-being (0.145), Financial Well-being (0.145), Mental & Emotional Well-being (0.145), Environmental Well-being (0.142), Self-Fulfilment (0.139), and Relational & Social Well-being (0.141) all fall within a narrow band. This pattern suggests that campus happiness is perceived as fundamentally multidimensional, where improvements in any domain are unlikely to compensate for deficiencies in others. Such weight proximity also implies that well-being at UEH is understood as a system of interdependent conditions that jointly support student and staff flourishing.

Within each domain, however, meaningful patterns emerge. In Career Well-being, the four sub-criteria receive nearly equal weights, with Autonomy & Resources (0.257) and Stability & Livelihood (0.247) slightly outranking Development & Progress (0.253) and Supportive & Innovative Environment (0.243). This distribution shows that both structural security and self-directed work conditions remain essential to perceived career satisfaction. The Physical Well-being sub-criteria follow a similarly balanced pattern, with Healthy & Rested (0.263) and Proactive Health Care (0.256) slightly more important than Balanced Diet & Hydration (0.243) and Active Lifestyle (0.238), suggesting that daily physical readiness and preventive care are seen as foundational to a productive academic or professional life.

More pronounced differentiation appears in Financial Well-being, where Income Sufficiency (0.335) and Future Security (0.335) share the highest weight, followed closely by Shock Resilience (0.330). This concentration around financial stability, future assurance, and economic resilience reflects a strong sensitivity to financial pressures among the UEH community, consistent with broader regional studies in Southeast Asia. In Environmental Well-being, weights are distributed evenly across all five indicators, with Inclusive & Inspiring Spaces (0.205) and Adequate Facilities (0.203) slightly higher than the others. This suggests that the physical and digital learning environment is valued holistically rather than being driven by a single factor.

In the Mental & Emotional Well-being cluster, the weights range from 0.191 to 0.211, with Self-esteem & Achievement (0.211) and Emotion Regulation (0.202) identified as the most influential components. These results highlight the psychological dimension of academic life, where emotional competence and a sense of personal capability are viewed as essential to resilient engagement. Meanwhile, in Self-Fulfilment, a clear structure emerges: Growth Mindset & Learning (0.342) and Meaning, Pride & Future Plans (0.341) strongly outweigh Self-acceptance & Direction (0.317). This suggests that aspirational and future-oriented dimensions of personal development are highly valued within UEH’s academic culture.

Finally, Relational & Social Well-being presents a moderately differentiated distribution. Trust & Reciprocity (0.264) and Social Satisfaction & Belonging (0.261) hold slightly higher importance than Contribution to Others’ Growth (0.238) and Family & Close Support (0.237). This indicates that campus-based social experiences and interpersonal exchanges carry slightly more weight than external family relationships, reflecting the centrality of peer and colleague interactions to daily university life.

Finally, global importance scores were obtained by multiplying each sub-criterion’s local weight (${w{\prime} }_{j})$ by the weight of its parent criterion (${w}_{i}$), as defined in Eq. (44). This scaling ensures that sub-criterion priorities reflect both their internal influence and the overall prominence of their domain. As a result, strongly weighted domains appropriately elevate their key sub-criteria, while items within weaker domains do not disproportionately dominate the ranking. The resulting global weights provide a coherent, system-wide priority order for all twenty-eight sub-criteria, as illustrated in Fig. 5.

Fig. 5: The global weight of sub-criteria in UEH happiness assessment model.

Ranking distribution of global importance weights across all twenty-eight sub-criteria. Bars represent normalized global weights derived from the multiplication of local sub-criterion weights and their parent-domain weights.

The global-weight distribution provides a clearer picture of which specific well-being elements exert the strongest overall influence on happiness at UEH. Three broad patterns emerge. First, the Financial Well-being sub-criteria remain the highest contributors in the entire model, with Future Security (4.859%), Income Sufficiency (4.850%), and Shock Resilience (4.789%) forming the top tier of global importance. This indicates that long-term financial assurance, stable income capacity, and protection from unexpected financial shocks are perceived as foundational determinants of happiness within the university community. The dominance of these three factors suggests that economic stability continues to shape emotional security, life satisfaction, and overall well-being in a higher-education environment where students and staff face rising living costs and performance demands.

The second notable cluster consists of Self-Fulfilment elements, where Growth Mindset & Learning (4.755%) and Meaning, Pride & Future Plans (4.739%) emerge as major drivers. Self-acceptance & Direction (4.404%) also receives a comparatively high weight. Together, these findings indicate that personal development, a sense of future purpose, and confidence in one’s trajectory are nearly as influential as financial security. This implies that individuals at UEH value not only external economic conditions but also internal psychological growth, identity coherence, and long-term aspiration. When viewed alongside the financial indicators, these results underscore that happiness at UEH is shaped jointly by structural stability and self-determined motivation, reflecting the dual importance of external resources and internal agency. A third set of influential sub-criteria arises from Physical Well-being and Relational & Social Well-being. Healthy & Rested (3.809%) and Proactive Health Care (3.700%) appear prominently within physical well-being, while Trust & Reciprocity (3.716%) and Social Satisfaction & Belonging (3.683%) lead in the social domain. These results reinforce the notion that everyday functioning—adequate rest, manageable workload, social connectedness, and mutual respect—plays a significant role in sustaining overall happiness. These sub-criteria directly influence the lived experience of students and staff and serve as key mechanisms linking institutional structures to personal well-being outcomes.

In contrast, the Environmental and Mental–Emotional domains show comparatively lower global weights, although differences remain modest. The environmental sub-criteria range narrowly from 2.761% to 2.926%, indicating that while campus facilities, sustainability, and culture are valued, they are not viewed as primary domains perceived as exerting upstream influence compared to financial, personal-growth, or physical factors. Similarly, the mental–emotional sub-criteria fall between 2.765% and 3.050%, suggesting that emotional stability and satisfaction play supportive—but not central—roles when considered in conjunction with more dominant structural and developmental factors.

The global weight distribution shown in Fig. 5 reflects the integrated influence of each sub-criterion within the causal network. In the DEMATEL–MCDM framework, higher global weights indicate sub-criteria that exert stronger system-level leverage because they are positioned at structurally influential points in the causal graph. In this model, CF2 (Income Sufficiency) and CF3 (Future Security) emerge as the most influential determinants of overall happiness, followed closely by fulfilment-related elements such as CS2 (Growth Mindset & Learning) and CS3 (Meaning, Pride & Future Plans). These results suggest that financial stability and clarity of personal purpose play foundational roles in shaping both emotional states and functional well-being across the university.

Network relation map analysis

The network relation maps (NRMs) were examined to visualise the causal architecture among criteria and sub-criteria, with prominence plotted on the horizontal axis and relation values on the vertical axis. This structure allows the simultaneous interpretation of influence strength and cause–effect orientation across all dimensions of the UEH happiness model. To assist interpretation, the horizontal axis in the DEMATEL network relation map represents prominence, indicating the total degree of influence (received + exerted) of each criterion, while the vertical axis represents the relation value, which distinguishes whether a criterion functions mainly as a cause (positive value) or an effect (negative value). Quadrant I contains high-prominence criteria that act as perceived causal drivers; Quadrant II contains lower-prominence but still causal domains; Quadrant III consists of low-prominence effect domains; and Quadrant VI (upper left of the map) contains high-prominence effect domains.

The NRM for the main criteria (Fig. 6) shows that Self-Fulfilment and Environmental Well-being occupy Quadrant II, reflecting low prominence but positive relation values, and therefore function as modest causal initiators within the system. In contrast, Financial, Career, Mental–Emotional, and Physical Well-being cluster in Quadrant VI, where high prominence is paired with negative relation scores, indicating that these domains represent central outcomes shaped by upstream drivers rather than exerting causal force themselves. Relational & Social Well-being lies near the horizontal axis with moderate prominence, suggesting a largely effect-oriented but balanced role. Together, these patterns imply that deeper psychological meaning and environmental conditions form the foundation of the happiness structure at UEH, while financial, academic, emotional, and physical experiences emerge as consequential reflections of these antecedent states.

Fig. 6: The network relation map of criteria in UEH happiness assessment model.

Network Relation Map illustrating perceived influence relationships among the seven well-being domains. The horizontal axis denotes prominence, and the vertical axis denotes relation. Points above the horizontal axis indicate upstream influence domains, while those below indicate predominantly effect-oriented domains.

The NRMs for the sub-criteria reveal consistent internal causal hierarchies within each domain. In Career Well-being (Fig. 7), Supportive & Innovative Environment and Development & Progress act as causal elements, while Autonomy & Resources and Stability & Livelihood operate as key outcomes. Similarly, in Physical Well-being (Fig. 8), proactive health behaviours (Balanced Diet & Hydration, Proactive Health Care) initiate influence, whereas Healthy & Rested and Active Lifestyle reflect downstream physical states. Financial Well-being (Fig. 9) demonstrates a clearer structure in which Future Security serves as the primary causal driver, while Shock Resilience emerges as a secondary, effect-oriented component. Environmental Well-being (Fig. 10) follows the same logic, with cultural and sustainability elements initiating influence and facilities, inspiring spaces, and digital systems responding to these broader conditions.

Fig. 7: The network relation map of Career Well-being sub-criteria.

NRM showing influence structure among Career Well-being sub-criteria. Each point represents one sub-criterion, positioned according to prominence (horizontal) and relation (vertical) values, distinguishing upstream and downstream elements within the domain.

Fig. 8: The network relation map of Physical Well-being sub-criteria.

NRM depicting the directional influence structure among Physical Well-being sub-criteria. Positive relation values indicate perceived initiating behaviours, while negative values represent outcome-oriented states.

Fig. 9: The network relation map of Financial Well-being sub-criteria.

NRM illustrating influence relationships within Financial Well-being. Sub-criteria positioned in the upper region function as perceived drivers, whereas those in the lower region reflect downstream financial outcomes.

Fig. 10: The network relation map of Environmental Well-being sub-criteria.

NRM presenting influence patterns among Environmental Well-being sub-criteria. The map highlights the relative prominence and directional influence of sustainability, facilities, cultural, and digital environment components.

A comparable pattern is observed across the emotional, fulfilment, and relational domains. In Mental & Emotional Well-being (Fig. 11), Positive & Flexible Outlook and Vital Engagement act as causal elements supporting downstream outcomes such as life satisfaction and emotional regulation. Self-Fulfilment (Fig. 12) is driven by Growth Mindset & Learning and Meaning–Pride–Future Plans, with Self-Acceptance positioned as an outcome shaped by these higher-level orientations. Relational & Social Well-being (Fig. 13) identifies Social Satisfaction & Belonging as the principal causal driver, while Trust & Reciprocity, Family Support, and Contribution to Others’ Growth function as effect-oriented components.

Scope clarification: All influence relationships reported in this study reflect expert-perceived structures rather than empirically observed behavioural causation. The results therefore support policy sequencing and diagnostic insight, not statistical causal inference.

Fig. 11: The network relation map of Mental & Emotional Well-being sub-criteria.

NRM showing perceived directional relationships among Mental & Emotional Well-being indicators. Sub-criteria with positive relation values operate as upstream psychological drivers within the domain.

Fig. 12: The network relation map of Self-Fulfilment well-being sub-criteria.

NRM depicting influence hierarchy within Self-Fulfilment. The map distinguishes growth- and meaning-oriented sub-criteria from downstream identity and satisfaction components.

Fig. 13: The network relation map of Relational & Social Well-being sub-criteria.

NRM illustrating perceived influence structures among relational and social indicators. Prominence reflects systemic importance, while relation distinguishes initiating from responsive social components.

Sensitivity analysis

A sensitivity analysis was conducted to examine the robustness of the causal structure obtained from the r,s,t–spherical fuzzy DEMATEL model. Because the expressive power of r,s,t–spherical fuzzy numbers depends on the choice of the $(r,s,t)$ parameter set, multiple configurations were tested to evaluate whether variations in hesitation allowance, uncertainty spread, or membership flexibility would alter the prominence and relation patterns across criteria and sub-criteria. By re-estimating the direct-influence matrices under alternative $(r,s,t)$ values, the stability of causal rankings and driver–effect orientations could be assessed, allowing the reliability of the UEH happiness model to be verified under different fuzzy environments. Sensitivity analysis across alternative $(r,s,t)$ parameterizations indicates that the identified influence hierarchy is not an artifact of a specific fuzzy configuration, supporting the methodological robustness of the r,s,t–spherical fuzzy extension relative to more restrictive fuzzy forms.

Three parameter scenarios were evaluated to test the stability of the r,s,t–spherical fuzzy DEMATEL results. The base scenario $(r,s,t)=(\mathrm{2,1,2})$ is shown in the previous sections. Scenario 1, defined as $(\mathrm{2,2,2})$, was introduced to increase the symmetry between membership and non-membership functions, thereby allowing a broader uncertainty spread and testing the behaviour of the model under higher hesitation awareness. Scenario 3, defined as $(\mathrm{3,3,3})$, was chosen to represent an even more permissive fuzzy environment, where the degrees of membership, non-membership, and hesitancy are allowed wider ranges; this scenario places the strongest emphasis on capturing ambiguous expert judgments. These scenarios were designed to evaluate whether the causal rankings and driver–effect structures remain consistent when the expressive capacity of the fuzzy numbers is systematically expanded.

The sensitivity analysis demonstrates that the global priority structure of the UEH happiness model remains highly stable across the three r,s,t parameter scenarios. Although slight numerical fluctuations are observed as the fuzzy environment becomes more permissive, no reversals in the ranking order emerge within any domain. As shown in Fig. 14, The Career and Physical Well-being sub-criteria show small downward drifts when moving from the base case to Scenarios 1 and 2, yet their internal ordering remains unchanged, indicating that their relative influence is resilient to increased uncertainty. The Financial Well-being sub-criteria display exceptionally high stability, with variations below 0.05%, confirming that perceptions of income sufficiency, future security, and shock resilience are consistently dominant regardless of the fuzzy parameterization.

Fig. 14: The sensitivity analysis results.

Comparison of global weight distributions across alternative (r,s,t) parameter configurations. The figure displays stability of ranking positions under increasing uncertainty tolerance, demonstrating robustness of the influence structure.

Environmental and Mental–Emotional sub-criteria exhibit similarly stable patterns, with only marginal adjustments in weights as hesitation tolerance increases. Interestingly, a slight upward movement is observed for items such as CE1 (Green, Sustainable Campus), CE5 (Positive, Innovative Culture), CM2 (Positive & Flexible Outlook), and CM4 (Vital Engagement), suggesting that these psychologically or environmentally grounded criteria become marginally more influential when experts are allowed greater expressive uncertainty. However, these shifts remain small and do not alter rank positions, reinforcing robustness in the causal architecture of these domains.

The most notable parameter sensitivity occurs within the Self-Fulfilment and Relational domains, where CS1, CS2, CS3 and CR1, CR4 show moderate increases across scenarios, reflecting their heightened salience when the fuzzy environment expands. Even so, their internal ordering remains preserved, and the broader pattern—that fulfilment-related meaning and relational belonging remain central contributors—does not change. Overall, the consistency of all sub-criteria across the three scenarios confirms that the r,s,t–spherical fuzzy DEMATEL model yields a structurally stable prioritization, and that the UEH happiness model is not materially affected by variations in fuzzy uncertainty specifications.

Discussion

The findings of this study provide a comprehensive view of the causal architecture underlying happiness at the UEH. At the criterion level, the network relation map indicated that Self-Fulfilment and Environmental Well-being operate as upstream drivers despite exhibiting lower prominence scores. These two domains appear to activate broader institutional and psychological processes that shape downstream experiences. By contrast, Financial, Career, Mental–Emotional, and Physical Well-being emerged as highly prominent but predominantly effect-oriented outcomes, suggesting that they reflect the consequences of deeper motivational and environmental conditions rather than serving as initial causal sources. Relational & Social Well-being held an intermediate position, functioning largely as an outcome shaped by fulfilment-related and environmental influences. When viewed together, these patterns suggest that the happiness architecture at UEH is shaped by internal meaning and environmental context before manifesting as financial confidence, academic motivation, emotional stability, or physical health.

The sub-criteria analyses provided a more granular picture of these causal pathways and reflected dynamics that align closely with Vietnam’s cultural and socioeconomic context. In the career domain, growth opportunities and an innovative environment rose as the primary causal elements—mirroring the importance placed on career progression and academic competitiveness in Vietnamese higher education culture. Financial well-being was anchored by Future Security, which held consistent perceived directional influence, a finding that resonates with Vietnam’s rising cost of living, high family expectations for upward mobility, and widespread financial precarity among young adults. Physical well-being was driven by behavioural practices such as diet and proactive care, while restfulness and activity levels emerged as effects. Emotional well-being was shaped by positive outlook and engagement—characteristics often reinforced in collectivist cultures where perseverance and adaptability are valued. In fulfilment-related well-being, the dominance of meaning, pride, and growth orientation reflected the central role of long-term aspiration in Vietnamese educational identity formation. In the relational domain, belonging emerged as the core causal driver, which is consistent with the strong collectivist norms and community-oriented values prevalent in Vietnam. These findings collectively show that perceived directional influence tends to be concentrated in deeper cultural, motivational, and structural elements, whereas day-to-day emotional or behavioural states tend to emerge as downstream expressions of these foundations.

The global weights further supported this interpretation by identifying Future Security, Income Sufficiency, Growth Mindset, Meaning, and Belonging as the highest-leverage factors across the entire system. These drivers combine financial assurance, aspiration, and relational embeddedness—elements that are particularly salient within Southeast Asian societies navigating rapid socioeconomic transition. In comparison with Western and higher-income university contexts, where autonomy, mental health resources, and work–life balance are often found to be primary drivers of well-being, the prominence of financial and fulfilment-oriented variables at UEH highlights contextual differences shaped by economic development level, cultural expectations, and educational pressures. This contrast suggests that well-being architectures may be culturally contingent rather than universally structured. Although similarities exist—such as the importance of purpose and belonging—Vietnamese respondents appear to prioritize financial stability and future orientation more strongly than reported in North American or European studies.

While the present study does not conduct cross-institutional estimation, the identified influence structure differs meaningfully from patterns commonly reported in Western university studies, where autonomy, work–life balance, and psychological services often emerge as primary drivers. The stronger upstream influence of financial security and future orientation observed here suggests that well-being architectures may be context-dependent, particularly in emerging-economy higher-education systems.

The robustness of the findings was confirmed through sensitivity analysis. All causal orders and ranking positions remained stable across multiple r,s,t parameter configurations, demonstrating that the results were not artifacts of any particular fuzzy assumption. Minor shifts were observed in Self-Fulfilment and Relational Well-being, yet these patterns did not alter the broader causal interpretations. The persistent influence of financial and career-related elements across scenarios further underscored their structural significance within the Vietnamese university context. Overall, the consistency of the results validates the applicability of the r,s,t-spherical fuzzy DEMATEL framework in modelling culturally embedded, multidimensional well-being systems in higher education.

Conclusion

The increasing prioritization of student and staff well-being in global higher education has reoriented institutional evaluation beyond traditional indicators such as enrolment, research productivity, and employability. International frameworks, including the OECD’s well-being metrics, have encouraged universities to adopt more holistic assessment tools capable of representing multidimensional and interdependent forms of well-being. This shift motivated the present study, particularly because causal modelling of happiness in ASEAN universities remains limited and methods capable of handling linguistic ambiguity have rarely been applied. The University of Economics Ho Chi Minh City (UEH) was selected as an illustrative case to address this methodological and regional gap.

A seven-domain well-being model—covering Physical, Mental & Emotional, Relational & Social, Self-Fulfilment, Career, Environmental, and Financial dimensions—was operationalised through twenty-eight sub-criteria synthesised from the literature and expert consultation. Pairwise influences were collected through a 20-member expert panel using r,s,t–spherical fuzzy representations to incorporate hesitancy and linguistic nuance. The r,s,t–SF DEMATEL method was then employed to extract prominence and relation structures under uncertainty. The results showed that Self-Fulfilment and Environmental well-being act as upstream causal domains, while Financial, Physical, Career, and Mental–Emotional dimensions emerge as downstream experiential outcomes. At the sub-criterion level, Future Security, Income Sufficiency, Growth Mindset & Learning, Meaning & Future Plans, and Social Belonging were identified as the highest-leverage drivers shaping overall happiness at UEH. These patterns reinforce global findings that purpose, meaning, and relational belonging strongly predict well-being, while also extending international evidence by revealing the amplified role of financial security within an emerging-economy context.

The study contributes to theory, method, and practice. Theoretically, it extends global literature by demonstrating how cultural and socioeconomic conditions in Vietnam elevate the influence of financial sufficiency and future security beyond levels typically observed in Western institutions, where autonomy, life satisfaction, and mental health resources often emerge as primary drivers. Methodologically, this study presents the first application of r,s,t–spherical fuzzy DEMATEL to higher-education well-being, showing how the framework effectively models asymmetric causal relations and linguistic hesitancy that conventional crisp or classical fuzzy methods would not fully capture. Practically, the results provide a sequenced roadmap for policy intervention at UEH and, more broadly, for universities in ASEAN and other emerging economies. Policies that strengthen purpose formation, developmental pathways, inclusiveness, and financial assurance appear most capable of producing system-wide improvements.

Several limitations should be acknowledged. The expert panel was staff-heavy, which may introduce bias by amplifying financial, career, and environmental perceptions more commonly prioritised by employees than by students. Linguistic bias may also be present because all judgments were expressed through linguistic terms that required conversion into r,s,t–spherical fuzzy numbers; although this method captures hesitancy, some semantic distortion is unavoidable. Furthermore, the cross-sectional nature of the expert elicitation prohibits conclusions about temporal causality beyond what is structurally inferred through DEMATEL. The expert-based design necessarily prioritizes institutional and managerial perspectives over lived individual experience. While this limits behavioural validation, it is appropriate for the study’s diagnostic purpose: experts possess integrative knowledge across student, staff, financial, and infrastructural systems that individual respondents cannot observe holistically. These limitations point to several future research opportunities: the use of stratified student–staff panels; longitudinal causal tracking to validate directional stability; multi-institutional comparisons across ASEAN contexts; and the development of hybrid DEMATEL–SEM or DEMATEL–Bayesian approaches to test causality over time.

Taken together, the study offers a transferable diagnostic framework for universities—particularly in ASEAN and emerging economies—to structure expert knowledge, prioritize interventions, and inform subsequent empirical validation, rather than a definitive model of behavioural causation.