Evaluating Perceived Resilience of Urban Parks Through Perception–Behavior Feedback Mechanisms: A Hybrid Multi-Criteria Decision-Making Approach

Abstract

Amid the increasing complexity of urban risks, urban parks not only serve ecological and recreational functions but are increasingly becoming a critical spatial foundation supporting public psychological resilience and social recovery. This study aims to systematically evaluate the daily adaptability of urban parks in the context of micro-risks. The research integrates the theories of “restorative environments,” environmental safety perception, urban resilience, and social ecology to construct a five-dimensional framework for perceived resilience, encompassing resilience, safety, sociability, controllability, and adaptability. Additionally, a dynamic feedback mechanism of perception–behavior–reperception is introduced. Methodologically, the study utilizes the Fuzzy Delphi Method (FDM) to identify 17 core indicators, constructs a causal structure and weighting system using DEMATEL-based ANP (DANP), and further employs the VIKOR model to simulate public preferences in a multi-criteria decision-making process. Taking three representative urban parks in Guangzhou as empirical case studies, the research identifies resilience and adaptability as key driving dimensions of the system. Factors such as environmental psychological resilience, functional diversity, and visual permeability show a significant path influence and priority intervention value. The empirical results further reveal significant spatial heterogeneity and group differences in the perceived resilience across ecological, neighborhood, and central park types, highlighting the importance of context-specific and user-adaptive strategies. The study finally proposes four optimization pathways, emphasizing the role of feedback mechanisms in enhancing urban park resilience and shaping “cognitive-friendly” spaces, providing a systematic modeling foundation and strategic reference for perception-driven urban public space optimization.

1. Introduction

Amid the growing uncertainties faced by global cities—ranging from climate change and public health crises to surging challenges in mental well-being—the traditional governance paradigm centered on “emergency response and physical recovery” is becoming increasingly inadequate [1,2]. Urban systems are now frequently exposed to non-disastrous, low-intensity but high-frequency stressors such as chronic anxiety, social withdrawal, and latent health risks [3]. Unlike acute disasters, these pressures manifest subtly in daily life, accumulating over time to erode residents’ mental and physical resilience. This constitutes a “slow variable” risk mechanism [4], which calls for a shift in urban governance: from post-disaster repair to fostering “everyday resilience”—that is, the capacity of urban space to support emotional regulation, cognitive restoration, and social reintegration in response to persistent environmental micro-stressors [5,6,7].

In this context, urban parks are undergoing a functional redefinition. No longer limited to ecological beautification or recreational amenities, they are increasingly recognized as critical spatial infrastructures that bolster psychological resilience, emotional recovery, and social connectivity for urban residents [8,9,10]. Historically, the social role of parks has evolved in tandem with shifting urban risk structures. In the 19th century, they were designed to mitigate pollution and green space scarcity during industrialization; in the 20th century, they were developed into multifunctional public spaces integrating leisure, culture, and community life. Entering the 21st century—particularly in the post-COVID-19 era—urban parks have emerged as core arenas for addressing chronic psychological stress and social isolation, functioning as crucial carriers of “non-structural resilience” [11,12,13].

While the notion of “urban resilience” has gradually extended to social and psychological domains, many subtle spatial stressors remain systematically overlooked due to their non-disastrous, intangible nature [14]. In reality, a wide array of factors that impair emotional recovery and social engagement—such as spatial confinement-induced stress, wayfinding ambiguity, thermal discomfort due to lack of shade, or visual signs of spatial decay—constitute what can be termed “micro-risks” [15,16]. These elements may not immediately trigger discomfort, but repeated exposure accumulates psychological burdens that compromise users’ sense of safety, trust, and belonging [17]. Compared with catastrophic events, these slow-accumulating, non-disruptive risks are more insidious yet prevalent in everyday park experiences. Their subtle and subjective nature makes them difficult to capture using traditional “hard” indicators, resulting in their exclusion from current evaluation systems and spatial policy designs. To address this blind spot, it is necessary to introduce the lens of “perceptual erosion under everyday scenarios” into resilience theory, thereby filling the conceptual and operational gap in daily spatial adaptability [18,19,20].

Most current research on public space behavior still adopts a linear “perception → behavior” model, wherein variables like safety perception, aesthetic satisfaction, or restorative potential are treated as one-way predictors of spatial behavior (e.g., dwell time, revisit intentions, or social participation) [21]. However, in real-world environments, user behavior is rarely a passive response to perception. Instead, it involves recursive loops of experience, evaluation, and re-experience [22]. A single negative encounter, for instance, may cause prolonged vigilance, undermining trust even in well-designed spaces [23]. This “perception–behavior–reperception” loop more accurately reflects the experiential logic of spatial use. Although recent urban resilience research has increasingly emphasized the integration of public perception, most existing evaluation models remain grounded in incomplete or overly linear cognitive mechanisms. For instance, some studies focus solely on climate change adaptation or are confined to physical and social dimensions shaped by institutional contexts [1,19,24]. Others merely examine linear associations between environmental attributes and psychological responses, overlooking the dynamic complexity of perception feedback mechanisms [22,25,26]. Still, a number of models remain anchored in static frameworks that rely on unidirectional “perception–satisfaction” pathways [5,8]. Even among studies attempting to develop more comprehensive evaluation systems, commonly employed methods such as structural equation modeling (PLS-SEM), Analytic Hierarchy Process (AHP), or intuition-based scoring approaches have largely failed to uncover the internal dependency structures and feedback paths among perception indicators [17,18,27].

To address these theoretical and empirical gaps—including micro-risk invisibility, perception–behavior feedback deficiencies, and group-level variability—this study proposes an integrated multi-criteria decision-making (MADM) framework that synthesizes the Fuzzy Delphi Method (FDM), DEMATEL-based Analytic Network Process (DANP), and the VIKOR compromise ranking method [25,27]. This hybrid model incorporates both expert knowledge and public preference, enabling dynamic modeling of feedback loops, trade-off behaviors, and perceptual conflicts. The result is a structural perceptual–behavioral coupling framework for evaluating urban park perceptual resilience. Specifically, FDM is used to consolidate expert opinions and extract 17 core indicators across dimensions such as restorative potential, safety, and social accessibility [27]; DANP uncovers causal pathways and hierarchical dependencies among indicators, yielding a perceptual network embedded with feedback mechanisms [28,29]; and VIKOR introduces a multi-group perspective to simulate public trade-offs among competing goals (e.g., safety, comfort, and sociability), identifying dynamic equilibria between maximum group satisfaction and minimum individual regret [25].

Based on this foundation, the present study addresses the following three research questions:

(1)

Under the lens of micro-risks, which factors significantly influence residents’ perceptual resilience in urban parks, and what causal feedback relationships exist among them?

(2)

Do users exhibit cognitive conflicts or preference differences across perceptual dimensions? Are their behavioral choices shaped by compromise-seeking strategies?

(3)

How can we construct an integrated evaluation model that reflects both causal feedback and user preference heterogeneity to optimize urban park perceptual resilience?

The remainder of this paper is organized as follows: Section 2 reviews the theoretical evolution of urban resilience, environmental perception, and MCDM evaluation models. Section 3 outlines the case study sites, data collection strategies, and hybrid modeling procedures. Section 4 presents empirical findings and model outputs. Section 5 discusses key causal drivers, preference trade-offs, and proposes cognitively friendly spatial design strategies. Section 6 summarizes the research contributions, outlines limitations, and offers directions for future work.

2. Literature Review

2.1. Perceived Resilience: Theoretical and Structural Shifts

Perceived resilience, as an emerging concept to measure urban spatial adaptability and public sense of safety, has its theoretical roots in environmental psychology’s framework of “restorative environments” [30]. Ref. [31] Stress Recovery Theory emphasized the potential of natural elements and spatial features to alleviate physiological stress and psychological anxiety in built environments. Building on this, ref. [32] further developed the Attention Restoration Theory, which argued that cognitive clarity, exploratory potential, and the sense of order within a space can effectively restore attention fatigue and enhance individual recovery experiences. This growing body of evidence later inspired broader biophilic design theories, such as those advanced by Stephen Kellert, which emphasize the restorative value of natural elements in built environments—such as vegetation, water, and organic forms—and their contribution to human psychological resilience [33]. Ref. [34] introduced the concept of sense of control, suggesting that the predictability and boundary recognition of spaces positively contribute to safety and cognitive resilience [31,32,35].

In practical research, many scholars have focused on the influence of urban spatial elements on psychological recovery, safety perception, and social support, attempting to explain how public spaces support individual psychological restoration and behavioral participation from the perspective of subjective perception. For example, open green spaces, visual permeability, and boundary clarity are generally regarded as factors that reduce anxiety and enhance a sense of belonging [36,37,38]. These studies typically develop related measurement indicators from dimensions such as restorative experience, safety perception, environmental accessibility, and social inclusivity, aiming to explain residents’ spatial preferences and behavioral responses [39,40]. However, despite advancements in subjective scales, behavioral observation, and physiological data collection, the current research still predominantly views perceived resilience as a static outcome variable. It is treated as an explanatory factor for spatial satisfaction, revisit intention, or subjective health, rather than being constructed as a system variable network with causal structural logic [40,41]. This analytical paradigm limits the identification of dynamic relationships, structural mechanisms, and feedback pathways between spatial factors, and restricts the guiding role of perceived resilience in complex urban contexts.

Furthermore, existing research models commonly adopt linear structures, assuming indicator independence and static preferences. While this approach facilitates implementation and statistical analysis, it fails to reveal the underlying non-linear and multi-path interaction mechanisms in the perception reconstruction, behavioral feedback, and subjective judgment evolution that occur during public space use [42]. Particularly in complex public spaces such as urban parks, where perception factors are often coupled and exhibit feedback loops, the one-way “perception → behavior” model struggles to reflect the dynamic adaptation logic in real usage scenarios [43].

2.2. Micro-Risk and Perception Feedback Mechanisms in Urban Resilience

In traditional urban resilience studies, individual adaptation to spatial environments has primarily been discussed in the context of sudden, catastrophic situations, such as earthquakes, floods, and pandemics, focusing on emergency response and functional recovery. However, with the rise of “perceived resilience” research, scholars are increasingly paying attention to chronic stress adaptation mechanisms in non-disaster contexts, particularly in everyday urban spaces, where individuals regulate their cognition and reconstruct behavior under continuous environmental exposure [44,45].

In recent years, concepts like “micro-risk” and “slow variables” have been introduced in fields such as social psychology, public health, and urban design to describe spatial factors that, although lacking strong sudden impacts, exert erosive psychological effects over prolonged exposure. For instance, social disturbances in high-density environments, reduced feelings of safety from hidden corners, and the disorientation caused by path confusion are all considered micro-risks. While not immediate urgent threats, these factors gradually accumulate psychological burdens, weakening the public’s trust, sense of belonging, and resilience toward public spaces [45,46].

The chronic erosion of these “micro-context—micro-risk” pathways has been identified in specific areas such as children’s mental health, women’s sense of safety, and campus design. Studies show that urban environments with high density, restricted views, and social interference significantly affect women’s subjective perception of safety, especially in high-risk areas [47]. Another study in Iran on elderly women found that “psychological safety,” such as fears of falling, loss of orientation, and social anxiety, occupies a central position in their overall sense of safety [48]. However, most of these studies are based on interviews or static questionnaires and lack structured modeling and causal path depiction, making them difficult to apply in strategic design or spatial interventions.

At the same time, spatial usage behavior has traditionally been viewed as a passive result of perception, with research often assuming a unidirectional “perception → behavior” pathway, predicting dwell time, path choices, or social engagement through methods like structural equation modeling or Logit regression. However, cognitive psychology and social ecology theories suggest that spatial behavior can, in turn, influence an individual’s perception, forming a feedback loop of “perception—behavior—reperception.” For example, a study found that when women rated the safety of street scenes, their direct experiences (e.g., negative events) significantly influenced their subsequent perception and established a lasting sense of security [49]. If an individual experiences a negative event in a space, even if the physical conditions are favorable, anxiety and distrust may lead to decreased perceptions, thereby weakening behavior participation and revisit intentions [50].

Current micro-risk mechanism modeling faces three main challenges: (1) micro-risk factors are highly subjective and subtle, making them difficult to incorporate into traditional “hard” indicator systems; (2) mainstream models are based on assumptions of “instantaneous preference” or “stable attitudes,” failing to capture the gradual psychological impact of prolonged exposure; (3) there is a lack of theoretical tools that can simultaneously depict the dynamic interaction paths between variables and the cognitive regulation strategies of the public, making it difficult to close the “perception feedback gap” in practice. Especially in urban spaces with diverse groups, such as the elderly, women, and youth, significant disparities exist in risk perception and behavioral responses to the same space. Spatial experience feedback is not only reflected in individual-level cognitive reconstruction but also manifests as preference tensions and structural conflicts between groups.

2.3. Expanding Pathways for Multi-Criteria Decision Making (MADM) in Urban Resilience Assessment

When faced with the multi-objective, conflicting, and uncertain problems in urban space evaluation, MADM methods have become an important modeling tool in urban planning, transportation optimization, and environmental assessment due to their advantages in integrating expert knowledge, constructing indicator structures, and preference ranking [25,51,52]. Traditional methods like AHP and TOPSIS are operationally strong and suitable for optimizing structural indicators. However, their theoretical assumptions often rely on indicator independence and static weighting structures, making it difficult to capture the interdependencies, feedback mechanisms, and non-additive effects between variables. In addition to quantitative frameworks, timeless pattern-based heuristics—such as Christopher Alexander’s A Pattern Language—continue to inform spatial decisions, particularly in the design of resilient public areas like parks, squares, and pedestrian networks. Patterns such as “Accessible Green” and “Positive Outdoor Space” embody the perceptual and behavioral logic that contemporary MADM models attempt to quantify [53].

To overcome the limitations of these traditional methods, researchers have progressively developed a series of integrated methodologies that are capable of modeling causal feedback and nonlinear relationships. One such modeling chain that has gained traction is the combination of FDM, DANP, and VIKOR, forming a systematic modeling paradigm. FDM can be used to gather expert consensus and construct a structural evaluation system that incorporates complex subjective factors; DEMATEL combined with ANP reveals the bidirectional causal paths and hierarchical dependencies between factors, allowing the construction of feedback-looped network models [25,26,28]; VIKOR is particularly suitable for resolving preference trade-offs in multi-group and multi-objective conflicts, balancing the logic of “minimum individual regret” and “maximum group satisfaction” [26].

This methodological framework has been widely validated in complex engineering systems such as real estate site selection [54], transportation service optimization [55], green supply chains [56], and potential evaluations of characteristic towns [57]. Its advantage lies in not only uncovering the intrinsic dependencies between variables but also simulating the ranking logic of public preference conflicts, providing a systematic tool for multi-objective decision making with behavioral regulation capacity.

3. Case Context and the Modeling Process of the Hybrid MADM Approach

To address the multidimensional evaluation requirements of the complex perception system in urban parks, this study constructs a hybrid MADM modeling approach, incorporating FDM, DANP, and VIKOR, to support the assessment of perceived resilience and strategy optimization. As shown in Figure 1, the modeling process consists of three stages: first, FDM is used to extract representative perceived resilience indicators; second, DANP identifies the causal relationships and weight structures between dimensions and indicators; third, the VIKOR model is applied to simulate the comprehensive ranking logic under multi-group preference conflicts.

Figure 1. Modeling process of the hybrid MADM model.

3.1. Indicator System Construction and Fuzzy Delphi Method

This study, based on the theoretical frameworks of “restorative environments” in environmental psychology [31,58], urban resilience theory [59], environmental safety perception models [60], and the perspective of social ecology [61], systematically reviews the existing literature on urban space adaptability and public perception–feedback mechanisms. The research identifies and refines five primary dimensions: resilience, safety, sociability, controllability, and adaptability. This theoretical framework aims to integrate micro-risk identification, perception feedback, and behavioral regulation processes in urban park use at multiple scales and through various pathways, constructing a perception-based evaluation foundation for the “everyday resilience” of urban parks.

Guided by this theoretical framework, a scientifically valid, effective, and operational secondary indicator system is constructed, serving as a key component of the model development. Given the challenges in existing studies, such as a large number of perception evaluation indicators, overlapping definitions, and difficulties in practical implementation [25,62], the FDM is introduced to integrate expert consensus, select core factors, and enhance the focus and applicability of the indicator system. Table 1 presents the perception resilience evaluation indicator system for the five dimensions, along with their primary sources in the literature.

FDM is a qualitative–quantitative hybrid approach that integrates expert knowledge and fuzzy logic, suitable for subjective perception, multi-factor evaluation, and scenarios involving cognitive uncertainty. The basic logic of FDM involves collecting expert opinions through multiple rounds, constructing indicator interval scores using fuzzy triangular numbers, and using the “gray zone verification method” to determine the degree of expert consensus, thus identifying whether to retain each indicator [63].

This study implements the following steps in the FDM process:

(1)

Expert questionnaire design and distribution: Based on a systematic literature review and interviews with five senior experts, a preliminary resilience assessment indicator system is developed, including five primary dimensions and 23 secondary indicators. Subsequently, 15 experts from fields such as urban planning, architecture, and social space are invited to rate the importance of each indicator using a Likert five-point scale.

(2)

Triangular fuzzy number calculation: The conservative value, optimistic value, and single value for each indicator are collected from experts. Triangular fuzzy score functions are constructed for each indicator, and the geometric mean and bounds are calculated.

(3)

Extreme value removal and gray zone verification: Extreme values exceeding two standard deviations are removed, and the gray zone verification method is used to assess the consistency of expert scores. If the gray zone value is positive, expert opinions are consistent; if negative, the scoring process is re-conducted or the indicator is discarded.

(4)

Consensus value calculation and threshold setting: The consensus value “G_i” and consensus difference “M_i − Z_i” for each indicator are calculated. Core indicators are retained if their consensus value is above the average threshold, while those with insufficient consensus are excluded.

Table 1. Perceived resilience indicators and their literature source.

Dimension	Indicators	Description	References
Resilience—the park’s ability to support psychological restoration and reduce cumulative stress from daily urban environments. It focuses on elements such as calmness, green views, and sensory relief that help users recover mentally. This dimension is most relevant under chronic, low-level stress conditions like urban fatigue.	Environmental Psychological Restorativeness	Whether the space can relieve stress and promote psychological restoration.	[64,65]
	Emotional Comfort	Whether the space has relaxing lighting, colors, and textures.	[65,66]
	Spatial Quietness	Whether the space is quiet and free from traffic or crowd noise.	[67]
	Green Space Visibility	Whether there are visible green plants and open landscapes.	[68]
	Spatial Openness	Whether there is enough open space without spatial oppression.	[69,70]
Safety—the perceived sense of physical and emotional protection within the park. It is shaped by spatial visibility, lighting, and social cues that reduce fear and anxiety. Unlike resilience, safety addresses perceived risk rather than stress recovery.	Suitability of Nighttime Lighting	Whether lighting is appropriate and not fear-inducing at night.	[71,72]
	Accessibility for Emergency Evacuation	Whether there are emergency escape routes and shelters.	[73]
	Clarity of Spatial Boundaries	Whether the functional boundaries and usage of space are clearly defined.	[69,70]
Sociability—the capacity of a park to support social interaction, group presence, and community inclusion. It emphasizes social affordances like shared spaces, diverse activity zones, and welcoming design. While safety reduces threat, sociability fosters positive connection.	Availability of Stay Space	Whether the space provides seating facilities such as benches and tables that support prolonged stay and encourage social interaction.	[74,75,76]
	Design for Social Interaction	Whether the space encourages communication between strangers and has interaction nodes.	[75,76]
	Perceived Neighborhood Interaction Atmosphere	Whether the space conveys a vibrant, inclusive, and socially engaging atmosphere that encourages users to perceive active neighborhood presence and informal social interactions.	[76]
	Inclusiveness for Diverse Groups	Whether people of different identities or age groups can share the space.	[77,78]
	Perceived Social Safety	Whether there is a sense of safety during social interactions.	[79]
Controllability—the degree to which users feel they can navigate and regulate their experience within the park. It depends on clear layout, signage, and flexible spatial settings that enable autonomy. This dimension centers on personal agency rather than interaction or recovery.	Freedom of Path Choice	Whether users have the freedom to choose among multiple walking routes and avoid congested areas.	[80]
	Transparency of Spatial Rules	Whether the management rules and usage boundaries of the space are publicly available.	[81]
	Clarity of Signage System	helps users find directions and exits.	[82,83]
	Visual Permeability	Whether there are no blind spots and clear, visible spatial interfaces.	[84]
Adaptability—the flexibility of the park to accommodate different users, time periods, and unexpected situations. It includes features like multifunctional infrastructure, movable elements, and climate responsiveness. Adaptability operates at the system level, enabling resilience and usability over time.	Functional Diversity	Whether the space supports diverse functions such as recreation and fitness.	[85,86]
	Microclimate Adaptability	Whether the space provides mechanisms for shade, ventilation, and rain protection.	[87,88]
	Flexibility of Use	Whether the space layout can be flexibly adjusted according to activity needs.	[89,90]
	Ease of Maintenance and Renewal	Whether facilities can be repaired, replaced, or updated quickly.	[91,92]
	Pandemic Adaptability	Whether the space supports social distancing, ventilation, and crowd dispersal.	[93]
	Crowd Tolerance Capacity	Whether the space remains orderly and comfortable under high foot traffic.	[94]

Table 1. Perceived resilience indicators and their literature source.

Dimension	Indicators	Description	References
Resilience—the park’s ability to support psychological restoration and reduce cumulative stress from daily urban environments. It focuses on elements such as calmness, green views, and sensory relief that help users recover mentally. This dimension is most relevant under chronic, low-level stress conditions like urban fatigue.	Environmental Psychological Restorativeness	Whether the space can relieve stress and promote psychological restoration.	[64,65]
	Emotional Comfort	Whether the space has relaxing lighting, colors, and textures.	[65,66]
	Spatial Quietness	Whether the space is quiet and free from traffic or crowd noise.	[67]
	Green Space Visibility	Whether there are visible green plants and open landscapes.	[68]
	Spatial Openness	Whether there is enough open space without spatial oppression.	[69,70]
Safety—the perceived sense of physical and emotional protection within the park. It is shaped by spatial visibility, lighting, and social cues that reduce fear and anxiety. Unlike resilience, safety addresses perceived risk rather than stress recovery.	Suitability of Nighttime Lighting	Whether lighting is appropriate and not fear-inducing at night.	[71,72]
	Accessibility for Emergency Evacuation	Whether there are emergency escape routes and shelters.	[73]
	Clarity of Spatial Boundaries	Whether the functional boundaries and usage of space are clearly defined.	[69,70]
Sociability—the capacity of a park to support social interaction, group presence, and community inclusion. It emphasizes social affordances like shared spaces, diverse activity zones, and welcoming design. While safety reduces threat, sociability fosters positive connection.	Availability of Stay Space	Whether the space provides seating facilities such as benches and tables that support prolonged stay and encourage social interaction.	[74,75,76]
	Design for Social Interaction	Whether the space encourages communication between strangers and has interaction nodes.	[75,76]
	Perceived Neighborhood Interaction Atmosphere	Whether the space conveys a vibrant, inclusive, and socially engaging atmosphere that encourages users to perceive active neighborhood presence and informal social interactions.	[76]
	Inclusiveness for Diverse Groups	Whether people of different identities or age groups can share the space.	[77,78]
	Perceived Social Safety	Whether there is a sense of safety during social interactions.	[79]
Controllability—the degree to which users feel they can navigate and regulate their experience within the park. It depends on clear layout, signage, and flexible spatial settings that enable autonomy. This dimension centers on personal agency rather than interaction or recovery.	Freedom of Path Choice	Whether users have the freedom to choose among multiple walking routes and avoid congested areas.	[80]
	Transparency of Spatial Rules	Whether the management rules and usage boundaries of the space are publicly available.	[81]
	Clarity of Signage System	helps users find directions and exits.	[82,83]
	Visual Permeability	Whether there are no blind spots and clear, visible spatial interfaces.	[84]
Adaptability—the flexibility of the park to accommodate different users, time periods, and unexpected situations. It includes features like multifunctional infrastructure, movable elements, and climate responsiveness. Adaptability operates at the system level, enabling resilience and usability over time.	Functional Diversity	Whether the space supports diverse functions such as recreation and fitness.	[85,86]
	Microclimate Adaptability	Whether the space provides mechanisms for shade, ventilation, and rain protection.	[87,88]
	Flexibility of Use	Whether the space layout can be flexibly adjusted according to activity needs.	[89,90]
	Ease of Maintenance and Renewal	Whether facilities can be repaired, replaced, or updated quickly.	[91,92]
	Pandemic Adaptability	Whether the space supports social distancing, ventilation, and crowd dispersal.	[93]
	Crowd Tolerance Capacity	Whether the space remains orderly and comfortable under high foot traffic.	[94]

To further refine the representative perceived resilience indicators, the FDM was applied to analyze expert consensus on the initially constructed secondary indicator system. The results show that most of the indicators achieved a high level of consistency, with consensus values (G_i) ranging between 6.5 and 7.7, indicating strong agreement among experts on the proposed indicator system. Among them, “Functional Diversity” (C1, G_i = 7.707), “Environmental Psychological Restorativeness” (C2, G_i = 7.574), and “Perceived Neighborhood Interaction Atmosphere” (C3, G_i = 7.559) ranked the highest, reflecting experts’ consensus that multi-functional adaptability, psychological recovery, and enhanced community interaction are key factors in improving perceived resilience in public spaces.

At the same time, some indicators, such as “Spatial Quietness” (C7, G_i = 7.118) and “Flexibility of Use” (C13, G_i = 6.768), were considered important, but there was some disagreement among experts, indicating that their significance may vary depending on specific contexts and professional backgrounds. For example, “Flexibility of Use” exhibited a negative consensus difference (M_i − Z_i = –1.425), suggesting relatively low support among certain expert groups, and requiring further validation in subsequent empirical studies.

To determine which indicators to retain, we adopted a slope-based thresholding approach rather than using a fixed cut-off value. Specifically, the consensus values of the 23 indicators were ranked in descending order and plotted as a slope curve (Figure 2). The first and steepest drop in the curve—representing the largest decline in consensus between adjacent indicators—was identified as the empirical threshold. This inflection point is marked in red in Figure 2. Indicators above this point were retained, while those below were excluded.

Figure 2. Slope chart and threshold values.

Based on the consensus value ranking and expert evaluation, 17 indicators were finally selected for inclusion in the subsequent DANP-VIKOR modeling process, supporting the construction of the causal network structure and multi-objective preference ranking analysis. Table 2 presents the FDM analysis results for each secondary indicator in this study, including their conservative values, optimistic values, geometric means, consensus differences, and final consensus values. Additionally, to visually present the consensus level of indicators and the selection logic, a slope chart (see Figure 2) was created to display the ranking trend of consensus values and the FDM retention threshold.

Table 2. FDM results.

Indicators	Conservative Value C		Optimistic Value O		Geometric Mean M		Verification Values	Consensus Values
	Cl	Cu	Ol	Ou	Cm	Om	Mi − Zi	Gi
Functional Diversity (C1)	5	9	8	10	6.646	8.769	1.123	7.707
Environmental Psychological Restorativeness (C2)	5	8	7	10	6.388	8.759	1.371	7.574
Perceived Neighborhood Interaction Atmosphere (C3)	5	7	7	10	6.358	8.759	2.402	7.559
Accessibility for Emergency Evacuation (C4)	5	8	7	10	6.472	8.623	1.151	7.547
Visual Permeability (C5)	5	8	7	10	6.340	8.272	0.932	7.306
Microclimate Adaptability (C6)	5	8	6	10	6.427	7.995	−0.432	7.211
Spatial Quietness (C7)	6	8	6	10	6.430	7.807	−0.623	7.118
Emotional Comfort (C8)	5	7	6	10	6.240	7.935	0.695	7.087
Inclusiveness for Diverse Groups (C9)	5	7	7	9	6.102	7.966	1.865	7.034
Clarity of Signage System (C10)	5	7	6	9	6.240	7.735	0.495	6.988
Transparency of Spatial Rules (C11)	5	8	6	9	6.220	7.735	−0.485	6.978
Suitability of Nighttime Lighting (C12)	5	8	6	10	5.992	7.859	−0.133	6.926
Flexibility of Use (C13)	4	8	5	9	5.981	7.556	−1.425	6.768
Spatial Openness (C14)	5	7	5	9	6.079	7.370	−0.709	6.724
Clarity of Spatial Boundaries (C15)	5	7	6	9	5.894	7.331	0.436	6.612
Ease of Maintenance and Renewal (C16)	5	7	6	9	5.834	7.388	0.554	6.611
Perceived Social Safety (C17)	5	7	6	9	5.774	7.263	0.489	6.519

3.2. DEMATEL-ANP Method

To reveal the interdependencies among the evaluation dimensions and their subordinate indicators, and to overcome the theoretical assumptions of criterion independence in traditional ANP methods, this study introduces the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method to construct a causal influence matrix, combining it with the Analytic Network Process (ANP) to form the DANP integrated model. This approach identifies the inter-influence paths among multidimensional factors within the system, enhancing the alignment of weight distribution with the real cognitive structure, and compensating for the limitations of traditional linear weighted models in handling factor coupling and feedback mechanisms [95].

3.2.1. Expert Questionnaire

To support the systematic judgment of causal paths between indicators in the construction of the hybrid MADM model, a Chinese expert questionnaire was designed to collect the necessary data for analyzing causal relationships. The structure of this questionnaire was based on previous studies [27,28] and the 17 key indicators of perceived resilience proposed in this study. A five-point scale with equal intervals (0 = no influence, 4 = very strong influence) was used to score the degree of influence between pairs of indicators.

Considering that the DANP method focuses on “expert depth” rather than “sample breadth,” it is suggested that the number of experts be reasonably controlled between 5 and 15 [96]. Therefore, the research team invited 10 experts from urban planning, architecture, sociology, and related fields to participate in the survey via email and phone. A total of 8 valid responses were received. Before distributing the questionnaire, the research team provided a guide to ensure that experts completed the scoring under a unified understanding.

All participating experts hold a master’s degree or higher, with half having a doctoral degree. They each have more than five years of professional experience in urban design, spatial governance, environmental psychology, and related fields. The experts have a clear understanding of the conceptual system of perceived resilience assessment and are familiar with the “resilience–adaptability” dual design concept in urban spaces. Expert information is provided in Table 3.

Table 3. Basic information of experts in the DANP questionnaire.

Department	ID	Degree	Years of Experience	Position	Expertise
Land Management	1	PhD	6	Researcher	Urban Design, Public Space Planning
Urban Planning	2	PhD	8	Associate Professor	Urban Planning, Spatial Design
Architecture	3	PhD	7	Assistant Professor	Architectural Design, Urban Renewal
Urban Planning	4	PhD	10	Assistant Professor	Urban Planning, Green Space Design
Environmental Psychology	5	PhD	5	Expert	Environmental Psychology, Perceived Resilience
Public Health	6	Master’s	15	Expert	Social Space, Public Health, Social Resilience
Planning Department	7	Master’s	16	Deputy General Manager	Social Space, Social Design
Government	8	Master’s	8	Section Chief	Land Management, Planning Policy

In addition, a consistency validation was conducted based on expert feedback. The results showed a consensus rate of 95.45%, with an average consensus gap of 4.55%, which is below the 5% threshold. This indicates a high level of agreement among the experts and confirms the reliability of the data for proceeding to the second-stage modeling process.

3.2.2. DEMATEL-Based Interdependency Analysis

The Decision-Making Trial and Evaluation Laboratory (DEMATEL) method was originally developed by the Battelle Memorial Institute of Geneva under the United Nations system in 1972, aimed at analyzing complex systems characterized by multiple interacting factors [95]. This approach quantitatively reveals causal mechanisms and dynamic feedback structures by assessing the influence paths and interdependencies among system components. One of its core outputs, the Influential Network Relation Map (INRM), has been widely applied in fields such as sustainable development, urban governance, and multi-criteria decision making to identify critical factors and support strategic planning [97].

In this study, DEMATEL was employed to uncover the interrelationships among the dimensions in the perceived resilience evaluation framework, with a particular focus on the coupling logic among core dimensions such as restorativeness, safety, and sociability. By constructing a dimension-level causal influence map (INRM), the study clarifies both the strength and directionality of influence between dimensions. This not only provides the causal basis for structural weight assignment in the subsequent integrated DEMATEL–ANP model but also lays the groundwork for informed optimization strategies in urban public space design and perceptual regulation.

The modeling process proceeds as follows:

Expert pairwise ratings were aggregated to construct the initial direct-relation matrix $\mathit{Z}$, representing the influence strength among each pair of dimensions.

$$\mathit{Z}=\left[\begin{array}{ccccc}{\mathit{z}}_{\mathrm{c}}^{11}& \dots & {\mathit{z}}_{\mathrm{c}}^{1\mathrm{j}}& \dots & {\mathit{z}}_{\mathrm{c}}^{1\mathrm{n}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{z}}_{\mathrm{c}}^{\mathrm{i}1}& \dots & {\mathit{z}}_{\mathrm{c}}^{\mathrm{i}\mathrm{j}}& \dots & {\mathit{z}}_{\mathrm{c}}^{\mathrm{i}\mathrm{n}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{z}}_{\mathrm{c}}^{\mathrm{n}1}& \dots & {\mathit{z}}_{\mathrm{c}}^{\mathrm{n}\mathrm{j}}& \dots & {\mathit{z}}_{\mathrm{c}}^{\mathrm{n}\mathrm{n}}\end{array}\right]$$

(1)

According to Equation (2), the original direct influence data were normalized to obtain the standardized matrix, which satisfies the following structural conditions: the main diagonal elements are zero, and the maximum sum of each row or column is equal to 1.

$$\begin{gathered} \mathit{D}=\mathrm{y}\mathit{Z} \\ \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{y}=\underset{\mathrm{i}\mathrm{j}}{\mathrm{m}\mathrm{i}\mathrm{n}}\left\{{\displaystyle \frac{1}{\underset{\mathrm{i}}{\mathrm{m}\mathrm{a}\mathrm{x}}\sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathit{z}}_{\mathrm{c}}^{\mathrm{i}\mathrm{j}}}},{\displaystyle \frac{1}{\underset{\mathrm{j}}{\mathrm{m}\mathrm{a}\mathrm{x}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathit{z}}_{\mathrm{c}}^{\mathrm{i}\mathrm{j}}}}\right\}, \mathrm{i},\mathrm{j}\in \{\mathrm{1,2},\dots ,\mathrm{n}\} \end{gathered}$$

(2)

The matrix $\mathit{D}$ is expanded using a power series, and by summing under the condition of h → ∞, the resulting matrix ${\mathit{T}}_{\mathit{c}}$ represents the total influence exerted by each factor within the evaluation system.

$${\mathit{T}}_{\mathit{c}}={\left[\begin{array}{ccccc}& & & & \\ {\mathit{T}}_{\mathit{c}}^{11}& \dots & {\mathit{T}}_{\mathit{c}}^{1\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{c}}^{1\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{c}}^{\mathrm{i}1}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathrm{i}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathrm{i}\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{c}}^{\mathrm{m}1}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathrm{m}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathrm{m}\mathrm{m}}\end{array}\right]}_{\mathrm{n}\times \mathrm{n}|\mathrm{m}<\mathrm{n},\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{m}}_{\mathrm{j}}=\mathrm{n}}$$

(3)

The analytical process among the dimensions is largely consistent with the aforementioned procedures applied at the criterion level, through which the total influence relation matrix at the dimensional level can be derived accordingly.

$${\left.{\mathit{T}}_{\mathit{D}}=\left[\begin{array}{ccccc}{\mathit{T}}_{\mathit{D}}^{11}& \dots & {\mathit{T}}_{\mathit{D}}^{1\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{1\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{D}}^{\mathrm{i}1}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathrm{i}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathrm{i}\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{D}}^{\mathrm{m}1}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathrm{m}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathrm{m}\mathrm{m}}\end{array}\right.\right]}_{\mathrm{n}\times \mathrm{n}|\mathrm{m}<\mathrm{n},\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{m}}_{\mathrm{j}}=\mathrm{n}}$$

(4)

Subsequently, according to Equations (5) and (6), the row sums and column sums of the total influence matrix are calculated to obtain the row vector R_i and column vector S_i, respectively. The value of R_i represents the total (both direct and indirect) influence that a given dimension or indicator exerts on other components within the system, reflecting its “influencing capacity” or “output strength.” Conversely, the value of S_i captures the extent to which a particular factor is affected by others, indicating its “receptive attribute” or “input strength.”

Furthermore, the value of R_i + S_i represents the overall degree of interaction or prominence of a factor within the system, serving as a proxy for its centrality in the network structure. In contrast, R_i − S_i is used to determine the causal role of a factor; a positive value indicates that the factor primarily exerts influence (a “cause” factor), whereas a negative value suggests it is predominantly influenced by others (an “effect” factor).

Finally, based on the computed values of R_i + S_i and R_i − S_i, an INRM is constructed to visualize the causal pathways and interrelationships among the dimensions or indicators.

$$R={\left[\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{t}}_{\mathrm{i}\mathrm{j}}\right]}_{\mathrm{n}\times 1}={\left[R_{\mathrm{i}}\right]}_{\mathrm{n}\times 1}^{\mathrm{\prime }}=\left(R_1,\dots ,R_{\mathrm{j}},\dots ,R_{\mathrm{n}}\right)$$

(5)

$$S={\left[\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{t}}_{\mathrm{i}\mathrm{j}}\right]}^{\mathrm{\prime }}={\left[{\mathrm{t}}_{\mathrm{j}}\right]}_{\mathrm{n}\times 1}^{\mathrm{\prime }}={\left(S_1,\dots ,S_{\mathrm{j}},\dots S_{\mathrm{n}}\right)}^{\mathrm{\prime }}$$

(6)

3.2.3. Derivation of Evaluation Weights Based on the DANP Method

After clarifying the interdependencies among the dimensions and indicators within the evaluation framework, the next step involves embedding these causal relationships into the computation of relative weights. While the traditional ANP improves upon the AHP by allowing interdependence among criteria, it still relies on a predefined network structure and often assumes uniform influence across clusters—typically by assigning normalized column values equally based on the number of clusters. This assumption implicitly treats all dimensions as equally influential, which is rarely realistic in complex social-ecological systems [25].

To address this limitation, the DANP method integrates causal path information obtained from the DEMATEL technique into the ANP framework. Specifically, the DANP method utilizes the total influence matrix among dimensions and the normalized influence matrices among indicators within each dimension, both derived from the DEMATEL procedure, to construct the weighted supermatrix that more accurately captures real-world interdependencies. This mechanism avoids arbitrary assumptions and empirically verifies the inter-criteria relationships based on expert judgments [98].

As a result, the DANP model not only retains the logical foundation of ANP but also enhances its explanatory capacity in dealing with complex feedback structures. It captures the interactive and evolving characteristics among resilience-related indicators, allowing the derived weights to represent not just static importance, but also dynamic influence pathways. This feature is particularly valuable in perception-based evaluations, where psychological trade-offs and perception feedback loops are critical to understanding user behavior.

In this study, the DANP method is employed to calculate the structural weights of both primary dimensions and secondary indicators, thereby identifying the critical factors that influence perceived resilience in urban parks. The specific modeling procedure is as follows:

First, the total influence relation matrix obtained from the DEMATEL analysis is normalized to produce the standardized influence matrix ${\mathit{T}}_{\mathit{c}}^{\mathit{b}}$:

$${\mathit{T}}_{\mathit{c}}^{\mathit{b}}={\left[\begin{array}{ccccc}{\mathbf{T}}_{\mathbf{c}}^{\mathbf{b}11}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathit{b}1\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathit{b}1\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{c}}^{\mathit{b}\mathrm{i}1}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathit{b}\mathrm{i}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{c}}^{b\mathrm{i}\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{c}}^{\mathit{b}\mathrm{m}1}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathit{b}\mathrm{m}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{c}}^{\mathit{b}\mathrm{m}\mathrm{m}}\end{array}\right]}_{\mathrm{n}\times \mathrm{n}|\mathrm{m}<\mathrm{n}, \sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{m}}_{\mathrm{j}}=\mathrm{n}}$$

(7)

${\mathit{T}}_{\mathit{c}}^{\mathit{b}\mathrm{m}\mathrm{m}}$ is computed as follows:

$$\begin{gathered} {\mathit{T}}_{\mathit{C}}^{\mathit{b}11}=\left[\begin{array}{ccccc}{\displaystyle \frac{{\mathrm{t}}_{\mathrm{C}11}^{11}}{{\mathrm{e}}_1^{11}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{C}1\mathrm{j}}^{11}}{{\mathrm{e}}_1^{11}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{C}1{\mathrm{m}}_1}^{11}}{{\mathrm{e}}_1^{11}}}\\ ⋮& & ⋮& & ⋮\\ {\displaystyle \frac{{\mathrm{t}}_{\mathrm{C}\mathrm{i}1}^{11}}{{\mathrm{e}}_{\mathrm{i}}^{11}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{C}\mathrm{i}}^{11}}{{\mathrm{e}}_{\mathrm{i}}^{11}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{C}\mathrm{i}{\mathrm{m}}_1}^{11}}{{\mathrm{e}}_{\mathrm{i}}^{11}}}\\ ⋮& & ⋮& & ⋮\\ {\displaystyle \frac{{\mathrm{t}}_{{\mathrm{C}}^{{\mathrm{m}}_{11}}}^{11}}{{\mathrm{e}}_{{\mathrm{m}}_1}^{11}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{{\mathrm{C}}^{{\mathrm{m}}_1\mathrm{j}}}^{11}}{{\mathrm{e}}_{{\mathrm{m}}_1}^{11}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{{\mathrm{C}}^{{\mathrm{m}}_1{\mathrm{m}}_1}}^{11}}{{\mathrm{e}}_{{\mathrm{m}}_1}^{11}}}\end{array}\right] \\ \begin{array}{rr}& \\ & \\ & \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}{\mathrm{e}}_{\mathrm{i}}^{11}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{m}}}{\mathrm{t}}_{{\mathrm{c}}^{\mathrm{i}\mathrm{j}}}^{11}, \mathrm{i}=\mathrm{1,2},\dots ,{\mathrm{m}}_1.\end{array} \end{gathered}$$

(8)

Similarly, the total influence relation matrix of the dimension layer (T_D) is also normalized, yielding the normalized total influence relation matrix denoted as ${\mathit{T}}_{\mathit{D}}^{\mathit{b}}$:

$$\begin{array}{rr}{\mathit{T}}_{\mathit{D}}^{\mathit{b}}& ={\left[\begin{array}{ccccc}& & & & \\ {\mathit{T}}_{\mathit{D}}^{\mathit{b}11}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}1\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}1\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{i}1}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{i}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{i}\mathrm{m}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{m}1}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{m}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{m}\mathrm{m}}\end{array}\right]}_{\mathrm{n}\times \mathrm{n}|\mathrm{m}<\mathrm{n}, \sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{m}}_{\mathrm{j}}=\mathrm{n}}\end{array}$$

(9)

${\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{m}\mathrm{m}}$ is computed using the following formula:

$$\begin{gathered} {\mathit{T}}_{\mathit{D}}^{\mathit{b}11}=\left[\begin{array}{ccccc}{\displaystyle \frac{{\mathrm{t}}_{\mathrm{e}11}^{11}}{{\mathrm{e}}_1}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{e}1\mathrm{j}}^{11}}{{\mathrm{e}}_1}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{e}1}^{11{\mathrm{m}}_1}}{{\mathrm{e}}_1}}\\ ⋮& ⋮& & & ⋮\\ {\displaystyle \frac{{\mathrm{t}}_{\mathrm{e}\mathrm{i}1}^{11}}{{\mathrm{e}}_{\mathrm{i}}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{e}\mathrm{i}\mathrm{j}}^{11}}{{\mathrm{e}}_{\mathrm{i}}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{\mathrm{e}\mathrm{i}{\mathrm{m}}_1}^{11}}{{\mathrm{e}}_{\mathrm{i}}}}\\ ⋮& & ⋮& & ⋮\\ {\displaystyle \frac{{\mathrm{t}}_{{\mathrm{e}}^{{\mathrm{m}}_{11}}}^{11}}{{\mathrm{e}}_{{\mathrm{m}}_1}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{{\mathrm{e}}^{{\mathrm{m}}_1\mathrm{j}}}^{11}}{{\mathrm{e}}_{{\mathrm{m}}_1}}}& \dots & {\displaystyle \frac{{\mathrm{t}}_{{\mathrm{e}}^{{\mathrm{m}}_1{\mathrm{m}}_1}}^{11}}{{\mathrm{e}}_{{\mathrm{m}}_1}}}\end{array}\right] \\ \begin{array}{c}\\ \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}{\mathrm{e}}_{\mathrm{i}}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}}{\mathrm{t}}_{\mathrm{D}}^{\mathrm{j}},\mathrm{i}=\mathrm{1,2},\dots ,\mathrm{n}.\end{array} \end{gathered}$$

(10)

By transposing ${\mathit{T}}_{\mathit{c}}^{\mathit{b}}$, the unweighted supermatrix $\mathit{W}={\left({\mathit{T}}_{\mathit{c}}^{\mathit{b}}\right)}^{\mathit{\prime }}$ is obtained. Subsequently, ${\mathrm{T}}_{\mathrm{D}}^{\mathrm{b}}$ is multiplied by W to derive the weighted supermatrix ${\mathit{W}}^{\mathit{b}}={\mathit{T}}_{\mathit{D}}^{\mathit{b}}\mathit{W}$:

$${\left.\mathit{W}={\left({\mathit{T}}_{\mathit{c}}^{\mathit{b}}\right)}^{\mathrm{\prime }}=\left[\begin{array}{ccccc}{\mathit{W}}^{11}& \dots & {\mathit{W}}^{\mathrm{i}1}& \dots & {\mathit{W}}^{\mathrm{m}1}\\ ⋮& & ⋮& & ⋮\\ {\mathit{W}}^{1\mathrm{j}}& \dots & {\mathit{W}}^{\mathrm{i}\mathrm{j}}& \dots & {\mathit{W}}^{\mathrm{m}\mathrm{j}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{W}}^{1\mathrm{m}}& \dots & {\mathit{W}}^{\mathrm{i}\mathrm{m}}& \dots & {\mathit{W}}^{\mathrm{m}\mathrm{m}}\end{array}\right.\right]}_{\mathrm{n}\times \mathrm{n}\mid \mathrm{m}<\mathrm{n},}\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{m}}_{\mathrm{j}}=\mathrm{n}$$

(11)

$$\begin{array}{rrr}{\mathit{W}}^{\mathit{b}}& =& {\mathit{T}}_{\mathit{D}}^{\mathit{b}}\mathit{W}\hfill \\ & =& {\left[\begin{array}{ccccc}{\mathit{T}}_{\mathit{D}}^{\mathit{b}11}\times {\mathit{W}}^{11}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{i}1}\times {\mathit{W}}^{\mathrm{i}1}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{m}1}\times {\mathit{W}}^{\mathrm{m}1}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{D}}^{\mathit{b}1\mathrm{j}}\times {\mathit{W}}^{1\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{i}\mathrm{j}}\times {\mathit{W}}^{\mathrm{i}\mathrm{j}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{m}\mathrm{j}}\times {\mathit{W}}^{\mathrm{r}\mathrm{m}\mathrm{j}}\\ ⋮& & ⋮& & ⋮\\ {\mathit{T}}_{\mathit{D}}^{\mathit{b}1\mathrm{m}}\times {\mathit{W}}^{1\mathrm{m}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{i}\mathrm{m}}\times {\mathit{W}}^{\mathrm{i}\mathrm{m}}& \dots & {\mathit{T}}_{\mathit{D}}^{\mathit{b}\mathrm{m}\mathrm{n}}\times {\mathit{W}}^{\mathrm{m}\mathrm{m}\mathrm{n}}\end{array}\right]}_{\mathrm{n}\times \mathrm{n}|\mathrm{m}<\mathrm{n}, \sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{m}}_{\mathrm{j}}=\mathrm{n}}\end{array}$$

(12)

The DANP weights are computed by raising the weighted supermatrix to sufficiently large powers until convergence is achieved, resulting in a stable structure from which the global priority vector is extracted: w = (w₁, w₂, …, w_n). The values of w fall within the range [0, 1], representing the overall influence intensity of each indicator.

3.3. Public Preference Ranking and Compromise Analysis: The VIKOR Method

To further evaluate whether a given urban park in Guangzhou has achieved spatial sustainability under the lens of perceived resilience, this study introduces an improved version of the VIKOR method, building upon the structural weights obtained through the DANP model. The conventional VIKOR approach typically adopts “1” as the positive ideal solution and “0” as the negative ideal, and is primarily designed for ranking and selecting among multiple alternatives. However, it is not well suited for performance assessment of a single case. More importantly, the traditional method is often interpreted as identifying a “relatively optimal” solution among several suboptimal options, offering limited guidance for proposing concrete improvement strategies for a specific object [96].

To address this limitation, refs. [99,100] proposed a modified VIKOR method based on Simon’s (1978) “aspiration–worst” theory, which expands its application to single-case evaluations and enables the identification of performance gaps across multiple indicators.

A key feature of the modified VIKOR method is the introduction of an “aspiration level” framework, where a score of 10 represents the ideal state and 0 denotes the worst-case scenario. This allows for performance evaluation without requiring multiple comparative alternatives. Moreover, the method quantifies the “performance gaps” across different dimensions, providing empirical support for strategic adjustments and spatial optimization.

Accordingly, this study employs the improved VIKOR model to construct a multidimensional gap diagnosis framework for perceived resilience in urban parks. Three cases—Haizhu Wetland Park, Tianhe Park, and Huacheng Square—are selected for empirical analysis. The modeling procedure is as follows:

First, the gap between each case and its aspiration level is calculated, based primarily on two indicators:

(1)

The weighted mean gap value $S_u$, which reflects the overall degree of deviation from the expected performance level;

(2)

The maximum individual gap value $Q_u$, which identifies the most underperforming aspect of the case.

This diagnostic process is instrumental in pinpointing key performance shortcomings and provides empirical support for subsequent optimization strategies.

$$S_u=L_u^{p=1}=\sum _{j=1}^n\left[w_j\left(\left|f_j^{*}-f_{uj}\right|\right)/\left(\left|f_j^{*}-f_j^{-}\right|\right)\right]$$

(13)

$$Q_u=L_u^{p=\infty }=\underset{j}{max}\left\{\left(\left|f_j^{*}-f_{uj}\right|\right)/\left(\left|f_j^{*}-f_j^{-}\right|\right)|j=\mathrm{1,2},\dots ,\mathrm{n}\right\}$$

(14)

Here, $\mathrm{u}$ denotes the number of evaluated alternatives. $f_j^{*}$ and $f_j^{-}$ represent the ideal (aspiration) level (set to 10) and the worst-case level (set to 0), respectively. The subscript $j$ refers to the set of 17 proposed evaluation criteria, and $w_j$ denotes the weights obtained from the DANP method.

To obtain an optimal compromise solution, the parameter $\nu$ is introduced as a critical coefficient that balances “maximum group utility” and “minimum individual regret.” Based on this, the aggregated resilience performance value $R_u$ for each urban park is calculated as follows:

$$R_u=\nu \left(S_u-S^{*}\right)/\left(S^{-}-S^{*}\right)+\left(1-\nu \right)\left(Q_u-Q^{*}\right)/\left(Q^{-}-Q^{*}\right)$$

(15)

In this study, the ${{\mathrm{m}\mathrm{i}\mathrm{n}}_{\mathrm{u}}S}_u$ and ${{\mathrm{m}\mathrm{i}\mathrm{n}}_{\mathrm{u}}Q}_u$ principles are adopted. For the former, the normalization is set as $S^{*}={{min}_{u}S}_u$ (i.e.,$S^{*}=0$) and $S^{-}={{max}_{u}S}_u$ (i.e., $S^{-}=1$); for the latter, the setting is $Q^{*}={{min}_{u}Q}_u$ (i.e.,$Q^{*}=0$) and $Q^{-}={{max}_{u}Q}_u$ (i.e.,$Q^{-}=1$). Accordingly, Equation (15) is reformulated as follows:

$$R_u=\mathsf{\nu }{S}_u+\left(1-\mathsf{\nu }\right)Q_u$$

(16)

By integrating the weights derived from the DANP model with the improved VIKOR method, this study aims to identify and minimize both the overall and dimension-specific average performance gaps—also conceptualized as “perceptual regrets.” Furthermore, by leveraging the INRM constructed through the DEMATEL method, the analysis clarifies the priority paths for improvement.

The core emphasis lies in how to systematically identify key bottleneck dimensions based on the causal structure revealed by the INRM and to formulate targeted optimization strategies that enhance the perceived resilience of urban parks toward the aspiration level.

3.4. Case Background and Selection Rationale

To validate the applicability and explanatory power of the multidimensional evaluation model of perceived resilience in urban parks, this study selects three representative public spaces in Guangzhou as empirical cases: Haizhu Wetland Park, Tianhe Park, and Huacheng Square (see Figure 3). These parks differ significantly in terms of spatial characteristics, functional positioning, and usage frequency, respectively representing ecological, neighborhood, and central urban park types. Their diversity provides a robust basis for comparison and complementary analysis, offering a comprehensive reflection of perceived resilience across different urban contexts.

Figure 3. Study area and selected cases.

In this study, “perceived experience” is specifically defined as perceived resilience, which is operationalized through five key perceptual dimensions—resilience, safety, sociability, controllability, and adaptability—and 17 validated indicators derived from environmental psychology, social ecology, and spatial governance theory. Among them, dimensions such as safety, controllability, and adaptability are particularly sensitive to user density and crowd-related stressors, as they capture public perceptions of environmental pressure, spatial legibility, and systemic flexibility under real-use conditions. Although the three cases differ in spatial form and population dynamics, a unified questionnaire and evaluation framework was applied across all sites. Importantly, each site was analyzed independently using a modified VIKOR method, which compares the actual performance of each park with an ideal reference level, rather than assuming comparability among parks.

(1)

Haizhu Wetland Park: Resilience Challenges in Ecological Spaces

• As the largest urban wetland in Guangzhou, Haizhu Wetland Park typologically represents an ecological park model characterized by natural integrity and biodiversity. Its functions center on ecological restoration, microclimate buffering, and environmental education, making it a benchmark for nature-oriented public spaces. However, the park faces clear vulnerabilities under stress conditions. Its low-lying terrain and insufficient drainage lead to frequent waterlogging, often forcing boardwalk closures and restricting access. The spatial layout is fragmented, with narrow winding paths, limited evacuation nodes, and poor circulation continuity, reducing its adaptability in extreme weather. Management prioritizes ecological conservation over spatial usability, which, while beneficial for biodiversity, limits interventions to enhance flexibility or accessibility. This trade-off highlights the resilience challenges faced by ecologically-driven public spaces under growing urban risk conditions.

(2)

Tianhe Park: Adaptability Demands in Neighborhood Spaces

• Located in the dense Tianhe CBD, Tianhe Park functions as a high-use neighborhood park supporting daily recreation, fitness, and social interaction. It typifies multifunctional spaces operating under sustained pressure from diverse user needs. The park is exposed to spatial stressors such as congestion, user conflict, and zoning ambiguity. Clashes between quiet leisure users and active groups like square dancers are frequent, exacerbated by the lack of clear signage or designated activity zones. Additionally, repetitive vegetation and limited shelters reduce adaptability to changing weather or time-of-day conditions. Its fragmented governance—shared by local committees, service contractors, and sanitation units—leads to inconsistent maintenance and delayed spatial responses. This case underscores how spatial adaptability is shaped by user intensity and decentralized management.

(3)

Huacheng Square: Controllability Issues in Central Urban Spaces

• Huacheng Square exemplifies a multifunctional central plaza, integrating administrative, cultural, and commercial activities at the heart of Guangzhou. Its open form and symbolic prominence offer strong accessibility and visibility. Yet, the square experiences frequent disruptions from large-scale events requiring temporary installations, fences, and rerouting, which compromise spatial legibility and circulation. Nighttime safety is also a concern due to poor lighting near fountain zones and vegetation clusters. Its governance involves multiple overlapping authorities, often prioritizing image and security over user experience. This complexity makes Huacheng Square a critical case for examining how controllability is constrained by both functional overload and fragmented oversight.

3.5. Survey Design and Data Collection

To operationalize the evaluation framework developed through the FDM–DEMATEL–ANP model, we designed a structured questionnaire based on the finalized indicator system, which comprises five perceptual dimensions—resilience, sociability, safety, controllability, and adaptability—and 17 refined indicators (see Table 2). Each indicator was translated into a perception-oriented question using a 5-point Likert scale, enabling the quantification of users’ subjective evaluation across spatial and psychological dimensions.

The on-site survey was conducted during daytime hours over a two-week period in March–April 2025, covering both weekdays and weekends to account for variation in user profiles and spatial usage. A random intercept sampling method was employed at each park entrance and major activity node. Visitors aged 16 and above who had spent at least 15 min in the park were invited to participate. Investigators briefly explained the study purpose and obtained informed consent before administering the questionnaire.

A total of 512 valid responses were collected, distributed across the three sites as follows: Haizhu Wetland Park (168 responses), Tianhe Park (169 responses), and Huacheng Square (175 responses). These data served as input for the subsequent VIKOR analysis, which evaluates the extent to which each urban park aligns with user expectations under the multidimensional framework.

4. Results

4.1. Causal Network Path Analysis of Dimensions and Indicators

To identify the interrelationships among the evaluation indicators of perceived resilience in urban parks, this study applies the DEMATEL method to model expert judgment data and construct the INRM. The analysis involves building a direct influence matrix, normalizing the data, computing the total influence matrix, and deriving causal values. The results are visualized in Figure 4, which displays the causal networks both among the five resilience dimensions and within each dimension’s indicator set. These visualizations facilitate the identification of dominant influencing factors and structural bottlenecks in the perceived resilience system.

Figure 4. INRM.

Figure 4 illustrates the INRM of the five perceived resilience dimensions and their respective sub-indicators. The overall structure reveals differentiated roles across dimensions and indicators based on the R_i (influence) and S_i (influenced) scores.

At the dimensional level (Figure 4a), resilience (1.753, 0.182), adaptability (1.637, 0.173), and safety (1.717, 0.061) are positioned above the horizontal axis (R_i − S_i > 0), indicating their roles as net causal dimensions. Conversely, controllability (1.830, −0.201) and sociability (1.726, −0.216) fall below the axis, acting as net result dimensions that tend to absorb rather than transmit influence.

Within the resilience dimension (Figure 4b), E1 (2.702, 0.221) and E2 (2.670, 0.080) are identified as key causal indicators, whereas E3 (2.581, −0.123) and E4 (2.619, −0.178) appear as more reactive elements. Similarly, in the adaptability dimension (Figure 4c), E5 (2.129, 0.132) and E6 (2.276, 0.038) exert moderate causal impact, while E7 (2.356, −0.024) and E8 (2.403, −0.147) stand out as a primary result-type indicator. The controllability dimension (Figure 4d) presents a more unidirectional structure, where E9 (1.750, 0.092) operates as the only causal contributor, with E10 (1.646, −0.022) and E11 (1.609, −0.070) positioned as passive outcomes. In the safety dimension (Figure 4e), E12 (1.789, 0.031) and E13 (1.723, 0.025) show slight causal predominance, while E14 (1.750, −0.057) serves as a moderately passive indicator. Within the sociability dimension (Figure 4f), E15 (1.454, 0.039) and E17 (1.429, 0.022) retain a marginally positive net influence, whereas E16 (1.462, −0.061) is more strongly driven by other components.

Together, the INRM results capture the asymmetric and non-uniform structure of perceived resilience, offering an analytical foundation for subsequent weight modeling and strategy prioritization.

To clarify the mutual influences among the evaluation criteria, experts were invited to conduct pairwise comparisons, based on which average scores were calculated to construct the initial direct influence matrix $\mathit{Z}$ (see Table 4).

Table 4. Initial direct influence matrix $\mathit{Z}$.

	E1	E2	E3	E4	E5	E6	E7	E8	E9	E10	E11	E12	E13	E14	E15	E16	E17	Total
E1	0.000	3.250	3.625	3.750	2.500	1.625	1.625	1.500	3.250	1.875	2.125	1.125	2.375	2.000	1.625	2.375	2.125	36.750
E2	2.625	0.000	3.625	3.500	1.875	2.000	2.125	1.750	2.875	2.125	1.625	0.375	2.625	0.875	2.750	2.000	2.125	34.875
E3	2.000	2.500	0.000	2.875	2.250	2.000	1.875	1.875	2.375	1.500	1.875	1.625	1.000	1.250	2.875	2.125	2.125	32.125
E4	1.250	2.000	2.625	0.000	2.750	2.375	2.625	0.625	2.625	2.000	1.875	2.750	1.000	1.625	2.625	2.125	2.375	33.250
E5	2.000	1.125	2.125	2.375	0.000	1.875	3.000	2.875	1.125	2.125	2.125	2.000	2.000	2.250	1.375	1.625	1.125	31.125
E6	2.375	1.750	2.000	2.250	1.375	0.000	2.500	2.375	2.375	1.375	1.875	1.750	2.250	2.000	2.000	2.125	2.000	32.375
E7	2.000	1.500	1.250	2.000	1.250	2.250	0.000	2.500	3.000	1.375	1.875	2.000	2.000	2.125	2.750	2.875	2.625	33.375
E8	2.125	1.750	1.250	2.000	1.750	2.125	1.625	0.000	1.625	2.875	2.875	2.250	3.125	2.000	1.250	1.500	2.250	32.375
E9	2.125	2.375	1.125	2.250	1.750	2.000	2.125	1.875	0.000	2.375	2.250	2.125	2.000	2.000	1.625	0.875	2.000	30.875
E10	1.250	1.250	0.250	1.250	1.750	1.500	1.250	2.000	2.125	0.000	2.625	2.250	1.875	2.250	1.375	2.000	1.875	26.875
E11	0.875	1.750	0.875	0.500	1.750	1.125	1.375	1.875	1.500	2.500	0.000	2.375	1.500	2.125	1.625	2.125	2.125	26.000
E12	2.625	2.875	2.875	2.625	1.000	1.250	1.375	1.750	2.375	3.000	2.750	0.000	2.500	1.625	0.875	1.875	1.750	33.125
E13	2.500	2.500	2.500	2.125	1.375	1.875	1.625	1.750	1.375	2.000	0.750	2.250	0.000	3.000	1.375	1.375	1.625	30.000
E14	2.250	2.000	2.125	2.125	1.625	1.875	1.625	2.250	2.625	1.500	2.375	2.000	1.375	0.000	1.625	1.750	2.000	31.125
E15	1.500	1.500	1.750	0.875	1.375	1.375	1.875	2.500	1.750	1.250	1.750	1.250	1.500	2.375	0.000	2.500	1.375	26.500
E16	1.375	1.125	1.500	0.750	1.125	1.500	1.875	2.250	1.000	2.000	1.875	2.375	1.250	1.750	2.000	0.000	1.375	25.125
E17	1.500	1.125	1.250	0.625	1.125	1.250	1.250	2.125	1.500	2.000	1.625	2.125	1.500	2.250	2.000	2.250	0.000	25.500
Total	30.375	30.375	30.750	31.875	26.625	28.000	29.750	31.875	33.500	31.875	32.250	30.625	29.875	31.500	29.750	31.500	30.875	36.750

Based on the initial direct influence matrix $\mathit{Z}$, the normalized direct influence matrix $\mathit{D}$ is calculated using Equations (1) and (2) (see Table 5). Subsequently, the total influence matrices ${\mathit{T}}_{\mathit{c}}$ and ${\mathit{T}}_{\mathit{D}}$ are derived using Equations (3) and (4), as presented in Table 6 and Table 7, respectively. Following this, the given values ${\mathit{R}}_{\mathit{i}}$ and received values ${\mathit{S}}_{\mathit{i}}$ for each indicator are computed using Equations (5) and (6), with the results summarized in Table 8. Based on the causal values in Table 8, the INRM is generated to visualize the causal structure among indicators.

Table 5. Normalized direct influence matrix $D$.

	E1	E2	E3	E4	E5	E6	E7	E8	E9	E10	E11	E12	E13	E14	E15	E16	E17
E1	0.000	0.088	0.099	0.102	0.068	0.044	0.044	0.041	0.088	0.051	0.058	0.031	0.065	0.054	0.044	0.065	0.058
E2	0.071	0.000	0.099	0.095	0.051	0.054	0.058	0.048	0.078	0.058	0.044	0.010	0.071	0.024	0.075	0.054	0.058
E3	0.054	0.068	0.000	0.078	0.061	0.054	0.051	0.051	0.065	0.041	0.051	0.044	0.027	0.034	0.078	0.058	0.058
E4	0.034	0.054	0.071	0.000	0.075	0.065	0.071	0.017	0.071	0.054	0.051	0.075	0.027	0.044	0.071	0.058	0.065
E5	0.054	0.031	0.058	0.065	0.000	0.051	0.082	0.078	0.031	0.058	0.058	0.054	0.054	0.061	0.037	0.044	0.031
E6	0.065	0.048	0.054	0.061	0.037	0.000	0.068	0.065	0.065	0.037	0.051	0.048	0.061	0.054	0.054	0.058	0.054
E7	0.054	0.041	0.034	0.054	0.034	0.061	0.000	0.068	0.082	0.037	0.051	0.054	0.054	0.058	0.075	0.078	0.071
E8	0.058	0.048	0.034	0.054	0.048	0.058	0.044	0.000	0.044	0.078	0.078	0.061	0.085	0.054	0.034	0.041	0.061
E9	0.058	0.065	0.031	0.061	0.048	0.054	0.058	0.051	0.000	0.065	0.061	0.058	0.054	0.054	0.044	0.024	0.054
E10	0.034	0.034	0.007	0.034	0.048	0.041	0.034	0.054	0.058	0.000	0.071	0.061	0.051	0.061	0.037	0.054	0.051
E11	0.024	0.048	0.024	0.014	0.048	0.031	0.037	0.051	0.041	0.068	0.000	0.065	0.041	0.058	0.044	0.058	0.058
E12	0.071	0.078	0.078	0.071	0.027	0.034	0.037	0.048	0.065	0.082	0.075	0.000	0.068	0.044	0.024	0.051	0.048
E13	0.068	0.068	0.068	0.058	0.037	0.051	0.044	0.048	0.037	0.054	0.020	0.061	0.000	0.082	0.037	0.037	0.044
E14	0.061	0.054	0.058	0.058	0.044	0.051	0.044	0.061	0.071	0.041	0.065	0.054	0.037	0.000	0.044	0.048	0.054
E15	0.041	0.041	0.048	0.024	0.037	0.037	0.051	0.068	0.048	0.034	0.048	0.034	0.041	0.065	0.000	0.068	0.037
E16	0.037	0.031	0.041	0.020	0.031	0.041	0.051	0.061	0.027	0.054	0.051	0.065	0.034	0.048	0.054	0.000	0.037
E17	0.041	0.031	0.034	0.017	0.031	0.034	0.034	0.058	0.041	0.054	0.044	0.058	0.041	0.061	0.054	0.061	0.000

Table 6. Total influence relation matrix $T_c$.

	E1	E2	E3	E4	E5	E6	E7	E8	E9	E10	E11	E12	E13	E14	E15	E16	E17
E1	0.293	0.377	0.389	0.403	0.326	0.316	0.331	0.344	0.406	0.357	0.365	0.327	0.348	0.354	0.333	0.364	0.355
E2	0.344	0.280	0.372	0.380	0.297	0.311	0.328	0.335	0.380	0.346	0.337	0.294	0.339	0.312	0.346	0.340	0.339
E3	0.307	0.321	0.259	0.341	0.286	0.290	0.301	0.317	0.344	0.310	0.322	0.302	0.280	0.299	0.327	0.321	0.317
E4	0.297	0.316	0.332	0.275	0.303	0.305	0.326	0.295	0.358	0.329	0.330	0.338	0.286	0.316	0.328	0.329	0.330
E5	0.302	0.283	0.307	0.323	0.223	0.282	0.321	0.335	0.307	0.319	0.323	0.308	0.299	0.318	0.283	0.303	0.288
E6	0.320	0.307	0.314	0.329	0.267	0.241	0.318	0.332	0.347	0.310	0.325	0.309	0.314	0.321	0.307	0.324	0.318
E7	0.315	0.305	0.298	0.325	0.266	0.302	0.258	0.340	0.366	0.315	0.330	0.320	0.312	0.329	0.329	0.346	0.337
E8	0.312	0.305	0.292	0.320	0.274	0.293	0.293	0.268	0.326	0.346	0.347	0.320	0.334	0.320	0.285	0.306	0.321
E9	0.303	0.311	0.281	0.318	0.266	0.282	0.298	0.308	0.275	0.323	0.323	0.307	0.298	0.310	0.286	0.282	0.306
E10	0.247	0.248	0.222	0.254	0.234	0.237	0.241	0.276	0.289	0.227	0.296	0.276	0.260	0.281	0.244	0.272	0.267
E11	0.230	0.252	0.230	0.228	0.227	0.220	0.237	0.266	0.265	0.283	0.221	0.271	0.244	0.269	0.243	0.268	0.265
E12	0.332	0.342	0.341	0.346	0.264	0.279	0.295	0.320	0.354	0.357	0.352	0.269	0.325	0.316	0.285	0.323	0.318
E13	0.310	0.312	0.314	0.314	0.254	0.276	0.281	0.300	0.308	0.309	0.281	0.305	0.241	0.328	0.277	0.290	0.293
E14	0.307	0.304	0.307	0.317	0.265	0.280	0.287	0.318	0.343	0.304	0.328	0.305	0.283	0.258	0.288	0.304	0.308
E15	0.252	0.253	0.259	0.245	0.224	0.234	0.256	0.287	0.279	0.257	0.272	0.249	0.249	0.281	0.209	0.284	0.254
E16	0.238	0.233	0.241	0.230	0.208	0.226	0.244	0.269	0.249	0.265	0.265	0.266	0.233	0.255	0.249	0.209	0.242
E17	0.243	0.234	0.237	0.229	0.209	0.221	0.230	0.268	0.262	0.267	0.260	0.262	0.240	0.269	0.250	0.268	0.207

Table 7. Dimension-level total influence matrix $T_D$.

	Resilience	Adaptability	Controllability	Safety	Sociability	Ri
Resilience	0.330	0.313	0.349	0.316	0.336	1.644
Adaptability	0.310	0.288	0.330	0.317	0.312	1.557
Controllability	0.260	0.258	0.278	0.279	0.270	1.346
Safety	0.320	0.285	0.326	0.292	0.298	1.522
Sociability	0.241	0.240	0.264	0.256	0.241	1.242
Si	1.462	1.384	1.547	1.461	1.458

Table 8. Summary of causal values and total influence weights.

Dimension/Indicator	Ri	Si	Ri + Si	Ri − Si
Resilience (D1)	1.644	1.462	1.753	0.182
Environmental Psychological Restorativeness (E1)	1.461	1.240	2.702	0.221
Emotional Comfort (E2)	1.375	1.295	2.670	0.080
Spatial Quietness (E3)	1.229	1.352	2.581	−0.123
Spatial Openness (E4)	1.220	1.398	2.619	−0.178
Adaptability (D2)	1.557	1.384	1.637	0.173
Functional Diversity (E5)	1.161	1.029	2.191	0.132
Microclimate Adaptability (E6)	1.157	1.119	2.276	0.038
Flexibility of Use (E7)	1.166	1.190	2.356	−0.024
Ease of Maintenance and Renewal (E8)	1.128	1.275	2.403	−0.147
Controllability (D3)	1.346	1.547	1.830	−0.201
Visual Permeability (E9)	0.921	0.829	1.750	0.092
Clarity of Signage System (E9)	0.812	0.834	1.646	−0.022
Transparency of Spatial Rules (E11)	0.769	0.840	1.609	−0.070
Safety (D4)	1.522	1.461	1.717	0.061
Accessibility for Emergency Evacuation (E12)	0.910	0.879	1.789	0.031
Suitability of Nighttime Lighting (E13)	0.874	0.849	1.723	0.025
Clarity of Spatial Boundaries (E14)	0.847	0.903	1.750	−0.057
Sociability (D5)	1.242	1.458	1.726	−0.216
Perceived Neighborhood Interaction Atmosphere (E15)	0.746	0.707	1.454	0.039
Inclusiveness for Diverse Groups (E16)	0.701	0.762	1.462	−0.061
Perceived Social Safety (E17)	0.725	0.703	1.429	0.022

After identifying the causal relationships among the indicators, the DANP method is introduced to calculate the structural weights. Based on the INRM network, the normalized influence matrix is transposed to generate the initial unweighted supermatrix (see Table 9).

Table 9. Unweighted supermatrix $W$.

	E1	E2	E3	E4	E5	E6	E7	E8	E9	E10	E11	E12	E13	E14	E15	E16	E17
E1	0.200	0.250	0.250	0.243	0.249	0.252	0.254	0.254	0.250	0.254	0.245	0.244	0.248	0.249	0.250	0.252	0.257
E2	0.258	0.204	0.261	0.259	0.233	0.242	0.245	0.248	0.256	0.255	0.268	0.251	0.249	0.246	0.250	0.247	0.249
E3	0.266	0.270	0.211	0.272	0.253	0.247	0.240	0.238	0.232	0.229	0.245	0.251	0.251	0.249	0.257	0.256	0.251
E4	0.276	0.276	0.278	0.225	0.266	0.259	0.262	0.260	0.262	0.262	0.243	0.254	0.251	0.256	0.243	0.244	0.243
E5	0.248	0.234	0.240	0.247	0.192	0.230	0.228	0.243	0.231	0.237	0.239	0.228	0.229	0.230	0.222	0.219	0.225
E6	0.240	0.245	0.243	0.248	0.243	0.209	0.259	0.260	0.245	0.240	0.232	0.241	0.248	0.227	0.232	0.238	0.238
E7	0.251	0.258	0.252	0.265	0.277	0.275	0.221	0.260	0.258	0.244	0.249	0.254	0.253	0.232	0.254	0.258	0.248
E8	0.261	0.263	0.265	0.240	0.288	0.287	0.292	0.238	0.267	0.279	0.280	0.276	0.270	0.258	0.285	0.284	0.289
E9	0.360	0.357	0.352	0.352	0.324	0.354	0.362	0.320	0.299	0.356	0.345	0.333	0.343	0.352	0.345	0.320	0.332
E10	0.317	0.326	0.318	0.324	0.336	0.316	0.312	0.339	0.351	0.280	0.368	0.336	0.344	0.312	0.318	0.340	0.338
E11	0.324	0.317	0.330	0.324	0.340	0.331	0.326	0.341	0.350	0.364	0.287	0.331	0.313	0.336	0.337	0.340	0.330
E12	0.318	0.311	0.343	0.359	0.332	0.328	0.333	0.329	0.336	0.338	0.346	0.296	0.348	0.361	0.247	0.282	0.278
E13	0.338	0.359	0.318	0.305	0.324	0.332	0.324	0.343	0.326	0.318	0.311	0.357	0.276	0.334	0.320	0.309	0.312
E14	0.344	0.330	0.339	0.336	0.344	0.340	0.342	0.329	0.339	0.343	0.344	0.347	0.376	0.305	0.361	0.338	0.349
E15	0.317	0.338	0.339	0.332	0.324	0.324	0.325	0.312	0.328	0.312	0.313	0.308	0.323	0.320	0.280	0.355	0.344
E16	0.346	0.332	0.333	0.333	0.347	0.341	0.342	0.335	0.322	0.348	0.345	0.349	0.337	0.338	0.380	0.299	0.370
E17	0.337	0.331	0.328	0.335	0.329	0.335	0.333	0.352	0.350	0.341	0.341	0.343	0.341	0.342	0.340	0.346	0.286

After performing the calculations based on Equations (7)–(12), the structural influence weights of each dimension and indicator are obtained using the DANP method. The results are summarized in Table 10.

Table 10. Weighted supermatrix $W^b$.

	E1	E2	E3	E4	E5	E6	E7	E8	E9	E10	E11	E12	E13	E14	E15	E16	E17
E1	0.045	0.056	0.057	0.055	0.056	0.057	0.057	0.057	0.056	0.057	0.055	0.053	0.054	0.054	0.058	0.058	0.059
E2	0.058	0.046	0.059	0.059	0.053	0.055	0.055	0.056	0.058	0.057	0.060	0.054	0.054	0.053	0.058	0.057	0.057
E3	0.060	0.061	0.048	0.062	0.057	0.056	0.054	0.054	0.052	0.052	0.055	0.054	0.054	0.054	0.059	0.059	0.058
E4	0.062	0.062	0.063	0.051	0.060	0.059	0.059	0.059	0.059	0.059	0.055	0.055	0.054	0.055	0.056	0.056	0.056
E5	0.047	0.045	0.046	0.047	0.040	0.048	0.048	0.051	0.049	0.051	0.051	0.049	0.050	0.050	0.048	0.047	0.048
E6	0.046	0.047	0.046	0.047	0.051	0.043	0.054	0.054	0.052	0.051	0.050	0.052	0.054	0.049	0.050	0.051	0.051
E7	0.048	0.049	0.048	0.051	0.058	0.057	0.046	0.054	0.055	0.052	0.053	0.055	0.055	0.050	0.054	0.055	0.053
E8	0.050	0.050	0.051	0.046	0.060	0.060	0.061	0.050	0.057	0.060	0.060	0.060	0.059	0.056	0.061	0.061	0.062
E9	0.064	0.064	0.063	0.063	0.060	0.066	0.067	0.060	0.054	0.064	0.062	0.064	0.066	0.067	0.064	0.059	0.062
E10	0.056	0.058	0.057	0.058	0.063	0.059	0.058	0.063	0.063	0.050	0.066	0.064	0.066	0.060	0.059	0.063	0.063
E11	0.058	0.056	0.059	0.058	0.063	0.062	0.061	0.063	0.063	0.065	0.052	0.063	0.060	0.064	0.062	0.063	0.061
E12	0.070	0.068	0.075	0.079	0.068	0.067	0.069	0.068	0.071	0.071	0.073	0.059	0.070	0.072	0.051	0.058	0.057
E13	0.074	0.079	0.070	0.067	0.067	0.068	0.067	0.071	0.069	0.067	0.066	0.071	0.055	0.067	0.065	0.063	0.064
E14	0.075	0.072	0.074	0.074	0.071	0.070	0.071	0.068	0.071	0.072	0.072	0.070	0.075	0.061	0.074	0.069	0.071
E15	0.052	0.056	0.056	0.055	0.056	0.056	0.056	0.054	0.056	0.053	0.054	0.054	0.057	0.056	0.046	0.059	0.057
E16	0.057	0.055	0.055	0.055	0.060	0.059	0.059	0.058	0.055	0.059	0.059	0.061	0.059	0.059	0.063	0.050	0.061
E17	0.056	0.055	0.054	0.055	0.057	0.058	0.058	0.061	0.060	0.058	0.058	0.060	0.060	0.060	0.056	0.057	0.047

As shown in Table 11, the weights of the 17 secondary indicators were derived using the DANP method, reflecting their relative influence within the perception–resilience framework.

Table 11. DANP weights of secondary indicators.

Indicator	E1	E2	E3	E4	E5	E6	E7	E8	E9	E10	E11	E12	E13	E14	E15	E16	E17
Weights (DANP)	0.056	0.056	0.056	0.058	0.048	0.050	0.053	0.057	0.063	0.061	0.061	0.068	0.068	0.072	0.055	0.058	0.058

4.2. VIKOR-Based Decision Ranking Analysis

To systematically evaluate the perceived resilience of different urban park types, this study applied the VIKOR method to 512 valid responses across 17 core indicators, incorporating globally weighted scores derived from the DANP model. Based on this, each park’s weighted satisfaction scores were aggregated to yield a Total Performance score and a corresponding Total Gap, enabling a comprehensive understanding of both perceived quality and the degree of expectation alignment. The results reveal distinct variations among the three parks (see Table 12). Haizhu Wetland Park achieved the highest Total Performance (3.966) and the lowest Total Gap (0.194), indicating a strong alignment between spatial delivery and public expectations. Tianhe Park ranked second with a Total Performance of 3.459 and a moderate Total Gap of 0.292, suggesting generally positive perceptions but moderate mismatches in specific aspects. In contrast, Huacheng Square showed the lowest Total Performance (2.929) and the highest Total Gap (0.389), reflecting significant dissonance between user expectations and perceived experience in this central public space.

Table 12. VIKOR results of indicator weights, performance, and gap values.

Dimension/Indicator	Local Weight	Global Weight (DANP Weight)	Haizhu Wetland Park		Tianhe Park		Huacheng Square
			Performance	Gap	Performance	Gap	Performance	Gap
Resilience (D1)	0.216		0.908	0.045	0.762	0.074	0.646	0.097
Environmental Psychological Restorativeness (E1)	0.247	0.056	1.009	0.045	0.861	0.075	0.712	0.105
Emotional Comfort (E2)	0.249	0.056	0.990	0.051	0.856	0.077	0.715	0.106
Spatial Quietness (E3)	0.248	0.056	1.011	0.046	0.842	0.080	0.710	0.106
Spatial Openness (E4)	0.256	0.058	0.997	0.057	0.803	0.096	0.714	0.113
Adaptability (D2)	0.199		0.844	0.040	0.721	0.065	0.591	0.091
Functional Diversity (E5)	0.232	0.048	0.934	0.045	0.809	0.070	0.687	0.094
Microclimate Adaptability (E6)	0.241	0.050	0.984	0.045	0.831	0.075	0.665	0.108
Flexibility of Use (E7)	0.254	0.053	1.022	0.050	0.894	0.075	0.721	0.110
Ease of Maintenance and Renewal (E8)	0.273	0.057	1.101	0.053	0.919	0.089	0.759	0.121
Controllability (D3)	0.177		0.732	0.043	0.661	0.057	0.565	0.075
Visual Permeability (E9)	0.341	0.063	1.326	0.076	1.161	0.109	1.022	0.137
Clarity of Signage System (E9)	0.328	0.061	1.302	0.078	1.227	0.092	1.022	0.132
Transparency of Spatial Rules (E11)	0.331	0.061	1.314	0.076	1.171	0.104	1.000	0.137
Safety (D4)	0.198		0.819	0.044	0.724	0.065	0.645	0.081
Accessibility for Emergency Evacuation (E12)	0.327	0.068	1.282	0.071	1.154	0.096	1.023	0.123
Suitability of Nighttime Lighting (E13)	0.327	0.068	1.290	0.071	1.151	0.109	1.022	0.133
Clarity of Spatial Boundaries (E14)	0.345	0.072	1.373	0.071	1.183	0.109	1.060	0.133
Sociability (D5)	0.164		0.664	0.022	0.591	0.032	0.483	0.044
Perceived Neighborhood Interaction Atmosphere (E15)	0.323	0.055	1.272	0.068	1.121	0.099	0.926	0.138
Inclusiveness for Diverse Groups (E16)	0.341	0.058	1.316	0.077	1.189	0.103	0.965	0.147
Perceived Social Safety (E17)	0.336	0.058	1.284	0.080	1.137	0.109	0.924	0.152
Total Performance			3.966		3.459		2.929
Total Gap				0.194		0.292		0.389

At the dimension level, Haizhu Wetland Park outperformed the other sites in resilience, adaptability, and controllability. Notably, it received the highest scores in psychological restorativeness (E₁ = 1.009), functional diversity (E₅ = 0.934), and all indicators under the spatial control dimension (E₉–E₁₁ averaged above 1.3), demonstrating effective delivery of both emotional and spatial clarity. Tianhe Park presented relatively balanced performance, with moderate strengths in emotional comfort (E₂ = 0.856) and functional diversity (E₅ = 0.809); however, lower scores in Flexibility of Use (E₇ = 0.894) and higher Total Gap values in adaptability-related indicators suggest crowding and zoning ambiguity as key constraints. Huacheng Square consistently underperformed in sociability and safety, with low values for inclusiveness (E₁₆ = 0.965), perceived social safety (E₁₇ = 0.924), and clarity of spatial boundaries (E₁₄ = 1.060), aligning with known issues such as weak nighttime lighting, spatial disorder, and over-programmed event disruptions.

5. Results and Discussion

5.1. Key Dimensions and Causal Drivers

This study, through the integrated application of the FDM–DEMATEL–DANP method, systematically identified the causal relationships, influence weights, and pathway dominance among five primary dimensions and 17 indicators within the “Perceived Resilience–Spatial Adaptability” framework for public spaces. According to the structural identification results from DEMATEL and the INRM network, resilience and adaptability exhibit significant causal driving characteristics, both positioned at the “Cause” end of the network. This suggests that restorative experiences and environmental adaptability are not only key triggers of subjective public perception, but also source variables that drive perceptual changes in other dimensions such as safety, sociability, and controllability. Notably, in the resilience dimension, E₁ and E₂ exhibit strong external influence (R_i − S_i = 0.221 and 0.080, respectively), indicating their role as cognitive anchors. In the adaptability dimension, E₆ and E₇ constitute the perceptual adaptation foundation for spatial environments, laying the groundwork for higher-level perceptions.

It is worth noting that although sociability and controllability rank at a moderate level in DANP weights, they are located at the “Effect” end in the R_i − S_i analysis (−0.216 and −0.201, respectively), meaning they are more susceptible to changes in other dimensions and serve as passive response indicators. This structural distribution implies that merely enhancing E₁₇ or E₁₂ may yield a limited effect. Systematic improvement must start from the causal variables of resilience and adaptability to trigger chain reactions throughout the entire perceptual system.

From the perspective of DANP global weights, resilience holds the highest overall weight (0.216), indicating that the public places the greatest emphasis on the psychological and emotional restorative capacity of spaces when evaluating perceived resilience—especially under high-stress, fast-paced urban contexts. Adaptability (0.199) and safety (0.198) follow closely, suggesting that environmental flexibility and safety trust together form the “functional foundation” of perceived resilience. In contrast, controllability (0.177) and sociability (0.164), while structurally important, primarily serve as indirect effectors rather than core drivers.

At the indicator level, integrating DANP weights and R_i − S_i values identifies several critical causal factors. E₁ not only demonstrates the strongest causal influence but also ranks high in perceived performance (1.009), confirming its dual importance as both a system core and user priority—hence a key entry point for enhancing perceived resilience. Additionally, E₆ and E₁₁ represent essential elements for spatial adaptability and control, with strong system-adjustment potential. Within the safety dimension, E₁₃ and E₁₄, though moderate in weight, show weak causal roles in the DEMATEL structure and offer tactical adjustability.

Of note, E₉ and E₄, though not core causal factors, display relatively large gap values in public perception (0.121 and 0.105, respectively), revealing perceptual shortcomings that deserve attention as “secondary optimization targets” in spatial renovation strategies.

Compared with existing studies, the findings of this research extend the structural perspective on perceived resilience. The traditional literature often emphasizes safety and sociability as key predictors of public space satisfaction. For instance, some studies highlight the decisive role of spatial safety in user perception and satisfaction—especially in high-frequency, open street spaces [101]. Likewise, in peri-urban and high-density contexts, the social functions of public space significantly impact users’ sense of belonging, satisfaction, and behavioral patterns [102]. This study, however, reveals through DEMATEL and the INRM network that resilience–adaptability are the true origin dimensions of perception structure. This aligns with the emerging trend of “restorative urbanism” in urban mental health research [103], and echoes SDG 11.7’s call for cognitively friendly urban spaces.

Practically speaking, urban planners and decision-makers should prioritize the enhancement of resilience and adaptability dimensions when optimizing public spaces. Specifically, emphasis should be placed on improving visual permeability, microclimate comfort, spatial flexibility, and restorative features—thereby systematically enhancing the perception of passive dimensions like controllability and sociability. Special attention should also be given to the causal chain among E₁₁, safety trust, and E₁₇, facilitating a shift from “accessible” to “trustworthy” and “belonging” spaces.

In conclusion, through the integration of causal network analysis and structural weight judgment, this study identifies resilience and adaptability as source variables of perceived resilience, and designates E₁, E₆, and E₁₁ as key indicators for prioritized optimization—thus providing actionable theoretical support and empirical basis for the construction and intervention of public space perception systems.

5.2. Multidimensional Path Optimization and Strategic Combination

Based on the results of the integrated DANP–VIKOR model, this study identified not only the causal relationships and influence structures among key dimensions and indicators, but also revealed performance shortfalls in the system—offering a clear prioritization logic and actionable intervention roadmap for enhancing the perceived resilience of public spaces. To systematically improve multidimensional perception, interventions must be grounded in causal nodes and guided by performance gap analysis.

Within the INRM network, the dimensions resilience and adaptability are driven by the representative indicators E₁ (R_i − S_i = 0.221) and E₆ (R_i − S_i = 0.132), respectively. These indicators exhibit high causal strength and high subjective performance (performance = 1.009 and 0.942), forming a cluster of “high-weight—high-cause—high-performance” variables and warranting top priority in optimization.

In contrast, indicators such as E₉ (R_i − S_i = −0.147, Gap = 0.121) and E₃ (R_i − S_i = −0.123, Gap = 0.105), though less causally influential, show substantial perceptual gaps and are thus recommended as “secondary optimization targets” through lightweight interventions.

Four critical optimization paths are outlined as follows:

Path 1: From E₁ → E₃ → E₁₇

This pathway represents the transmission from psychological restoration to spatial tranquility and finally to social trust (i.e., perceived social safety). Interventions should focus on enhancing restorative and tranquil environments using features like water elements, meditation platforms, and noise-buffering vegetation.

Path 2: From E₆ → E₈ → E₁₃

This path illustrates the structural logic of “flexibility–order–controllability” under adaptability. Strategies should include modular spatial layouts, movable furniture, and flexible zoning to improve perceived order and predictability.

Path 3: From E₁₂ → E₁₆ → E₁₅ → E₁₇

This visual-cognition-driven trust mechanism highlights the importance of visual accessibility and lighting quality in cultivating a secure and controllable social environment. Enhancements should include unobstructed sightlines, layered lighting systems, and clear boundary articulation.

Path 4: From E₇ → E₂ → E₁₈

This path suggests that local microclimate regulation indirectly influences social behavior by improving emotional comfort. Recommended strategies include permeable pavements, shading pergolas, and adjustable ventilation corridors.

Although indicators such as E9 and E3 are less central in the causal network, their noticeable perception gaps suggest they should be addressed through micro-renovation measures such as minor repairs, landscape cleaning, or greenery supplementation.

The proposed “restoration–transparency–adaptability” tri-core optimization strategy echoes the perceptual resilience paradigm in [42,104] and structurally extends the perception–satisfaction causal framework established by [105]. By integrating structural weights, causal pathways, and perceptual gaps, this study provides a clear, operable model for resilience-oriented intervention in public space design.

Beyond the specific context of urban parks, the modified VIKOR model based on aspiration–worst thresholds, as adopted in this study, is designed to support single-case evaluations rather than comparative rankings. This extension of VIKOR is particularly suitable for public spaces where the goal is to diagnose performance shortfalls relative to user expectations across multiple perceptual dimensions, rather than to select from among competing alternatives. As such, the model is applicable to a wide range of urban public spaces—including multifunctional plazas, transit station forecourts, informal green spaces, and school campuses—where diverse psychological and social demands converge. The model remains valid under the following conditions: (1) user expectations and spatial outcomes can be meaningfully mapped to indicator-level scores; (2) aspiration and worst-case thresholds can be reasonably calibrated through normative standards or participatory stakeholder input; and (3) the evaluation objective is to identify dimension-specific performance gaps and optimize perceptual alignment, rather than determine a best option. These features make the modified VIKOR framework a valuable diagnostic tool for perception-centered spatial governance beyond the park typology.

6. Conclusions and Policy Implications

This study aimed to develop a mechanism-oriented evaluation framework to assess the perceived resilience of urban parks by integrating user feedback, spatial attributes, and expert-informed causal logic. By embedding a perception–behavior–reperception loop into a hybrid FDM–DEMATEL–ANP–VIKOR model, the framework captures not only the relative importance of resilience factors but also their interdependencies and preference gaps across user groups. The results demonstrate that the proposed model successfully identifies latent spatial dissonances and prioritizes context-sensitive interventions. Therefore, the original research purpose—to develop an adaptive, perception-driven tool for evaluating urban park resilience under micro-risk scenarios—has been effectively achieved.

Compared with traditional MADM-based resilience models that typically rely on fixed indicator weights or one-directional satisfaction assessments, our approach introduces a feedback-sensitive structure. It uses causal mapping (DEMATEL) to construct dimension-level total influence matrices and weighted supermatrices (via DANP), thereby avoiding equal-weight assumptions and better reflecting perceptual interdependencies. The integration with VIKOR further allows the identification of systemic preference dissonances between user expectations and perceived delivery, which cannot be revealed through simple performance ranking. This diagnostic capacity makes the framework particularly suitable for real-world urban settings where perception, behavior, and space interact dynamically.

Empirical findings from three representative urban parks in Guangzhou show that perception gaps vary significantly across park types and dimensions. For instance, indicators under the controllability and safety dimensions revealed larger Total Gap values in high-density civic spaces, while issues related to restorativeness were more critical in ecological parks. This reinforces the argument that resilience is not a static or universal trait but is typologically and perceptually contingent. Furthermore, the identification of four strategic optimization paths highlights how different spatial qualities—such as shaded rest areas, noise-buffering edges, or legible circulation—can address perceptual mismatches with relatively targeted interventions.

To enhance translational utility, the model provides several practice-oriented insights. Indicators with Total Gap values exceeding 0.30 should be treated as perceptually critical, as they reflect the most pronounced mismatch between user expectations and spatial performance. Prioritizing such indicators—particularly those that can be addressed through low-cost design interventions—can generate visible and rapid improvements in perceived satisfaction. Moreover, spatial optimization strategies should be sensitive to the typological characteristics of different park types. In ecological parks such as Haizhu Wetland, design improvements should emphasize the continuity of circulation, terrain adaptability, and the facilitation of immersive human–nature interactions. In neighborhood parks like Tianhe Park, managing spatial congestion, clarifying functional zoning, and mitigating noise disruptions emerge as key concerns. For multifunctional civic plazas such as Huacheng Square, spatial legibility, controllability under high-use or event conditions, and the assurance of night-time safety are particularly critical to enhancing perceptual resilience.

Third, a perceptual design toolkit can be developed based on model outputs—for example, integrating shaded rest zones, low-noise edges, transparent signage, and modular activity platforms to enhance adaptive usability. Finally, these spatial insights should inform broader urban planning frameworks, especially in the context of post-pandemic mental health recovery, aging-friendly cities, and restorative urban design.

Nonetheless, several methodological limitations should be acknowledged. First, the expert panel used for FDM and DANP stages was geographically concentrated in Guangzhou and largely composed of planning and design professionals. This disciplinary and regional concentration may constrain the diversity of evaluative perspectives, particularly those from community management, public health, or operational domains. Second, empirical validation was limited to three parks within a single metropolitan area. Although these parks span different typologies, the findings may not fully generalize to other urban or cultural contexts. Public space perceptions are shaped by climate, social norms, and governance models, necessitating cross-regional validation. Third, while demographic diversity was acknowledged in data collection, the model did not incorporate subgroup-specific simulations. Understanding how perception gaps vary by age, gender, or user role would enhance the model’s granularity and inclusivity.

Future research can proceed along several directions. Cross-regional replication, especially in cities with different governance models and cultural attitudes toward public space, would help verify the robustness of identified pathways. Introducing participatory weighting mechanisms or fuzzy linguistic modeling can enhance the inclusivity and adaptability of the evaluation process. The framework can also be applied to post-occupancy evaluation of newly renovated or designed parks, testing its capacity to predict alignment between planning intentions and user experiences. Finally, integrating multi-stakeholder perspectives—not only from users but also planners, maintenance personnel, and policy actors—will enable more collaborative, equitable, and sustainable approaches to urban space resilience planning.

In summary, this study offers both a theoretical and practical contribution by advancing a dynamic, feedback-sensitive evaluation framework that bridges environmental psychology, resilience planning, and spatial design. It transforms abstract resilience constructs into actionable diagnostic tools and planning strategies, providing a timely response to the growing need for adaptive, perception-oriented public space design.