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Article

Physical Appearance Design Evaluation of Community Emotional Healing Installations Based on Analytic Hierarchy Process–Fuzzy Comprehensive Evaluation Method

by
Tanhao Gao
1,2,* and
Phillip Bernstein
2
1
College of Design and Innovation, Tongji University, Shanghai 200092, China
2
School of Architecture, Yale University, New Haven, CT 06510, USA
*
Author to whom correspondence should be addressed.
Buildings 2025, 15(5), 773; https://doi.org/10.3390/buildings15050773
Submission received: 28 January 2025 / Revised: 12 February 2025 / Accepted: 24 February 2025 / Published: 26 February 2025
(This article belongs to the Section Architectural Design, Urban Science, and Real Estate)

Abstract

An increasing number of residents are burdened with psychological pressure, and the majority of them refuse to seek professional mental help, falling to a “silent majority” of the untreated. This “silent majority” lives in every corner of cities, and public installations scattered in various spaces have the potential to become community emotional healing touchpoints. Therefore, it is urgent to establish a comprehensive evaluation system for emotional healing installations. This research establishes a physical appearance evaluation system for healing installations based on affinity analysis, thereby combining the Analytic Hierarchy Process (AHP) and Fuzzy Comprehensive Evaluation (FCE) to construct data matrixes and quantitative analysis. The AHP results revealed some trends, including that placing environment is the most critical design indicator for healing installations, saturation is more closely associated with healing than color temperature, and small-scale installations have better healing efficacy. FCE ranked the combined weights of design indicators and revealed preference differences between Western and Eastern scholars regarding emotional healing. Eastern scholars show a clear preference for low-saturation colors and place significant emphasis on the multifunctionality of healing installations. Meanwhile, Western scholars have a stronger inclination toward healing shapes. Furthermore, this research conducts cross-category analysis and sensitive analysis to provide rigorous foundations for future healing research and offer guidance to future designers in healing installation design.

1. Introduction

An increasing number of community residents have been burdened with a range of negative emotions, such as stress, anxiety, depression, and burnout [1]. Worse still, individuals might resist seeking psychological help due to societal judgment or internal shame regarding mental health issues [2]. Most of them choose to silently endure their inner pain, becoming the “silent majority” [3]. Simultaneously, extreme public crises, such as natural disasters, pandemics, economic recessions, political upheavals, and societal unrest, have disrupted daily life, stability, and overall well-being [4]. These crises have also provided insights to government policymakers and social organizations, prompting them to carefully consider alleviating citizens’ psychological stress from multiple perspectives and establishing more emotionally resilient societies to confront sudden public health crises and increasingly uncertain futures. Therefore, analyzing theories and practices related to emotional healing within communities becomes increasingly relevant, urgent, and of practical significance. Because the “silent majority” live in every corner of cities, public installations scattered in various spaces have the potential to become community emotional healing touchpoints [5]. However, design strategies for public installations with healing effects remain ambiguous. Therefore, it is urgent to establish a comprehensive evaluation system for emotional healing installations.
Based on the affinity analysis method [6], this research constructs an evaluation system for the physical appearance of emotional healing installations from six dimensions: color, shape, size, placing environment, material, and multifunctionality. Additionally, it combines the Analytic Hierarchy Process (AHP) and Fuzzy Comprehensive Evaluation (FCE) to construct data matrixes for quantitative analysis. The AHP is a systematic analysis method [7] that organizes complex problems into physical, hierarchical structures [8]. FCE is a quantitative method for evaluating qualitative problems [9]. FCE can incorporate weighting derived from the AHP and has been widely validated as an effective approach to addressing complex and ambiguous issues in design evaluation, such as evaluating smart learning environments in higher education institutions [10], the comprehensive social, cultural and economic benefits of green buildings [11], future planning of urban green spaces [12], and identifying various stakeholders’ needs in student housing [13].
This research makes innovative contributions in two aspects: First, it expands the traditional object-making mindset of public installation design, which typically emphasizes esthetics and functionality, by incorporating considerations of healing value at the societal level. This approach strengthens the role of design as the cross-disciplinary bridge. Specifically, this research examines how the physical design characteristics of public installations (such as color, shape, size, and materials) affect the emotional experiences of community residents. It investigates whether these installations evoke positive emotions (such as happiness, comfort, and joy) or negative emotions (such as anxiety, depression, and sorrow) and the degree of these emotional responses.
In addition, this research employs a combined AHP-FCE method to quantitatively analyze the emotional healing effects of the physical appearances of public installations. Previous research on emotional healing installations generally focused on qualitative studies, such as conceptual introductions [14] and case analysis [15], with limited scientific quantitative research. The AHP-FCE method, as a multi-indicator composite model, integrates quantitative weighting with qualitative indicators. Furthermore, this research not only examines the healing weight of individual indicators but also reveals the comprehensive impact and interactions among various indicator combinations. This approach overcomes the oversimplified assumptions inherent in traditional regression analysis, provides a rigorous empirical foundation for future healing design, and offers strategic guidance for designers in creating emotional healing installations.
The structure of the paper is as follows: Section 2 describes the derivation, development, and bottlenecks of emotional healing design through a literature review. Section 3 introduces the research methodology and data collection process (AHP-FCE). Section 4 documents data analysis and model validation. Section 5 discusses the research insights and explains this study’s limitations. Finally, the conclusion summarizes the key insights and offers recommendations for future research directions.

2. Derivation, Development, and Challenges of Healing Design

Research on healing design first requires clarifying the conceptual distinction between “therapy” and “healing”. “Therapy” usually refers to removing physiological illnesses [16]. In contrast, “healing” encompasses multiple aspects, including physiological, emotional, and social dimensions [17]. Unlike long-term psychological therapy focused on patients with mental health conditions in professional hospitals, community emotional healing embraces a broader group of residents and places and promotes emotional healing through short-term interaction [18]. More specifically, the goal of community emotional healing is to help residents relieve negative emotions (such as anxiety, depression, sorrow, etc..) and attempt to evoke positive emotions (such as happiness, comfort, and joy) [19]. Healing is characterized by its inherent spontaneity and universal wholeness [20]. At the level of design intention, it can aim to create healing social atmospheres to activate the individual’s healing potential [21].
Healing design was originally widely used in professional medical environments. Nightingale emphasized the importance of fresh air, cleanliness, order, natural light, and flowers in fostering patient recovery [22]. Ulrich provided the first rigorous scientific evidence for the healing impact of therapeutic environments [23]. Through a control group comparison study, he found that patients with natural views could recover earlier 75% of the time, resulting in a USD 500 reduction in per-case costs. Additionally, these patients required less heavy medication and had fewer minor complications and better emotional health. To help accelerate evidence-based design into the mainstream, the Academic Health Center [24] has collaborated for years with various healthcare organizations dedicated to improving patient care environments. These collaborative institutions are called “Pebbles”, implying that their studies have a cascading impact on industry expectations [25].
Subsequent developments in healing design have transitioned to designing environments with “psychological support” [26]. This evolution has broadened the healing scope beyond patients to include hospital care staff, professional consultants, and management [27]. Emerging concepts include “nurse-friendly hospital design” and designs for patient families [28]. This evolution has given rise to a series of design studies with healing landscapes as central elements, which could be divided into two main areas: natural and artificial landscapes. Natural elements such as biodiversity and nature demonstrate healing potentials that can positively impact health outcomes [29]. Conversely, artificial gardens combine elements, including biophilic intervention, light therapy, mindfulness, music, fitness, and aromatherapy, showing more significant potential for applications [30].
The built environment can subtly influence the emotions of residents living in surrounding communities. People are easily attracted to forms that resemble nature and pay attention to details that evoke familiarity or emotional connections. These reactions are often subconscious but significantly affect residents’ comfort and behavior in public spaces [31]. Humans have an innate preference for fractal patterns (repetitive, self-similar structures, particularly natural elements with moderate complexity, such as trees, clouds, and snowflakes). Interacting with fractal patterns can significantly reduce stress levels [32]. Incorporating fractal patterns into environmental design to create spaces that promote well-being and alleviate stress aligns with the principles of biophilic design, which aims to establish connections with nature through design, thereby reflecting local ecology and culture [33]. Incorporating natural elements, including green roofs, urban forests, parks, and water features, into cities can significantly improve the physical and mental health of residents and enhance community well-being [34]. From a macro perspective, designs that integrate natural systems with urban environments can create more livable, sustainable, resilient, and inclusive cities, mitigating the impacts of climate change [35].
Although the healing intervention domains have expanded from medical institutions to various buildings and parks, these still present substantial limitations, making it challenging to accommodate a broader population experiencing psychological sub-health. This phenomenon highlights a significant challenge to future healing design: how to engage the “silent majority”? Potential solutions may involve shifting from residents feeling stress and actively going to healing places to residents passively encountering healing touchpoints and engaging in healing experiences. Public installations have the potential to become community emotional healing touchpoints. By creating a series of small-scale interventions in public spaces, residents can unexpectedly encounter them and inadvertently relieve psychological pressure. However, there is currently limited research on public installations for emotional healing, especially empirical studies with data analysis, making it unclear which design strategies or intervention methods are most effective.
Therefore, this research is committed to exploring healing design strategies through data-supported research paths, laying scientific and rigorous empirical foundations for future healing design. At the same time, it seeks to provide systematic practical guidance for future designers, helping them integrate healing elements into installations more effectively, combining esthetic, functional, and emotional considerations to provide more comfortable, healthy, and pleasant experiences to surrounding residents, thereby making positive contributions to future social health and well-being.

3. Methodology

This research focuses on evaluating the physical appearance of emotional healing installations. As shown in Figure 1, the research topic is first analyzed using affinity analysis combined with questionnaires and a literature review, and then multi-level frameworks and an AHP judgment matrix are established. Moreover, the research team visualized and simplified the AHP matrix into a pairwise comparison format and invited experts with related backgrounds (Architecture, Design, Psychology, etc.) to conduct evaluations. All feedback data should pass the independent consistency test. If the data fail to meet the standards, the “M_Outflow” algorithm is used for data correction and matrix weight calculation. Furthermore, the Fuzzy Comprehensive Evaluation (FCE) method analyzes the combined weights and rankings, thereby identifying the most effective design strategies for emotional healing installations.

3.1. Analytic Hierarchy Process (AHP)

The Analytic Hierarchy Process (AHP) is an analytical decision-making method proposed by American scholar Saaty, which can systematize and hierarchize complex multi-objective problems [7]. In design evaluation, the AHP quantifies qualitative design strategies by generating matrices and making pairwise comparisons, thereby obtaining the weights of multi-level indicators through quantitative calculations, thus achieving more objective, precise, and feasible design evaluations and reducing the risk of decision-making bias [36].

3.1.1. Establishing Multi-Level Frameworks

The first step of the AHP is to construct multi-level frameworks. This research initially generated a framework based on KJ affinity analysis [6]. KJ affinity analysis involves refining and categorizing relevant phenomena, opinions, or insights on specific topics to uncover potential relationships within or between themes, thereby finding solutions from complex situations. The research team collected extensive feedback from healing design stakeholders (including mental sub-health residents, design professionals and students, government personnel, and social welfare groups). The data sources included questionnaires and literature reviews to construct the initial evaluation framework for healing installations.
However, after semi-structured interviews with experts in relevant fields and simulation tests, the research team gradually realized that the AHP matrix size needs to be strictly controlled during actual operation and the surveying experience kept within 8 min. Otherwise, participants may lose patience when evaluating the AHP matrix, leading to distorted results. After multiple revisions, this study focused on the physical appearance indicators of healing public installations to determine whether they positively impact participants’ psychological health.
Some equally important indicators that stem from the surrounding environment and can indirectly influence the physical appearance indicators of installations include the following:
  • Environmental Scale (the openness and layout of the space around the installation, as well as the influence of the surrounding pedestrian traffic);
  • Lighting Environment (light intensity, direction, light source type, color temperature, light duration, etc..);
  • Environmental Integration (surrounding environment color, material characteristics, building facades, etc..).
There are some indicators that originate from the surrounding environment but are not within the scope of physical appearance, such as the following:
  • Environmental Temperature (normal range, probability of extreme temperatures, fluctuations, rate of change, etc..);
  • Environmental Humidity (normal humidity levels, distribution, fluctuations, etc..);
  • Environmental Sound (volume, direction of sound sources, duration of sounds, etc..).
Due to the volume limitation of the AHP matrix, indicators derived from the surrounding environment rather than the healing installation itself will be condensed into the “placing environment” category for summarization.
The interactive experience indicators related to healing installations and their healing potentials will be evaluated separately in subsequent studies. Some examples include the following:
  • Interactive Action (how participants engage with, interact with, or respond to the installation’s elements, including jumping, rotating, swinging, hitting, etc..);
  • Interactive Time (the duration and rhythm of the engagement between participants and healing installations);
  • Multi-Sensory Experience (interactions that simultaneously engage two or more senses, creating richer and more immersive experiences to promote relaxation, emotional healing, and well-being, such as smell and sound interaction).
Therefore, the final 6 categories involved in this research are as follows (Figure 2):
  • Color (the overall color atmosphere or using colors in specific areas to evoke certain emotions or enhance healing effects);
  • Shape (the whole installation shapes or combinations of multiple smaller pieces. The shapes may also be functional, inviting people to interact with them—such as leaning on, sitting on, or even being enveloped by the structure);
  • Scale (the relative proportion between installations and participants, ensuring a comfortable and intuitive interaction experience);
  • Placing Environment (the placement setting of the healing installation, such as indoor or outdoor spaces, natural or urban surroundings, and the integration of the installation within its context);
  • Material (the tactile and visual qualities of the materials used in the installation, such as softness, smoothness, transparency, or warmth, which influence the sensory and emotional experience);
  • Multifunctionality (the installation’s ability to serve multiple purposes, such as offering seating, storage, shelter, or visual guidance, to enhance its overall utility and healing effect).

3.1.2. Establishing and Visualizing the AHP Judgment Matrix

Establishing the judgment matrix requires a pairwise comparison of the relative indicators at the same level within the hierarchical model, obtaining membership vectors, and then aggregating different single-factor membership vectors into the matrix through Formula (1).
A = a 11 a 12 a 1 j a 21 a 22 a 2 j a i 1 a i 2 a i j , a i j = 1 a j i i = 1,2 , 3 , n , a n d j = 1,2 , 3 , m
To quantify the judgment matrix, an AHP rating scale from 1 to 9 (Table 1) is used to assign weights to the indicators [37]. This scale expresses the varying degrees of importance among multiple indicators and is evaluated by the selected relevant experts.
Figure 3 shows the visualization and simplification process from the AHP judgment matrix to pairwise comparisons, combined with the images of each indicator (Figure 4), to make an easier and more straightforward evaluation experience for selected experts.
After receiving the evaluation data, use Formula (2) to calculate the eigenvectors and Formula (3) to normalize the vectors to calculate the weights of each design indicator.
M i = j = 1 n   a i j n
W i = M i i = 1 n   M i

3.1.3. Consistency Check

A consistency check is required before calculating the indicator’s weights to ensure that the evaluator’s thinking does not contradict itself while evaluating the AHP matrix. The consistency test steps are as follows:
  • Use Formula (4) to calculate the largest eigenvalues of the matrices.
    λ m a x = 1 n i = 1 n   A ω i ω i
  • Use Formula (5) to calculate the Consistency Index (CI).
    C I = λ m a x n n 1
  • Choose the corresponding Random Index (RI) according to Table 2.
  • Use Formula (6) to calculate the Consistency Ratio (CR).
    C R = C I R I
When CR < 0.1, the judgment matrix passes the consistency test.

3.2. Fuzzy Comprehensive Evaluation

Fuzzy Comprehensive Evaluation (FCE) is based on fuzzy set theory [38]. It uses fuzzy mathematics principles to perform quantitative evaluation and analysis influenced by multiple factors. FCE can be weighted using the AHP, effectively addressing complex and ambiguous problems. In the design field, FCE is often used to discover directions for further optimization or to compare multiple solutions to select the best one [13].

3.3. Sensitivity Analysis

Sensitivity analysis offers multiple advantages during evaluating the AHP framework, which helps decision-makers clearly observe the impact of variations in different input parameters on the output results, thereby enhancing the transparency and credibility of the decision-making process and improving the understanding of key factors in complex problems. The specific steps of sensitivity analysis are as follows:
  • Selecting the Analysis Indicator: Choose an indicator from the AHP matrix as the target of sensitivity analysis, along with its corresponding mirrored indicator in the AHP matrix.
  • Defining the Variation Range: Establish a variation range for the selected indicator. In this study, the range follows Table 3 (from 1/9 to 9).
  • Recalculating Weights: Adjust the selected indicator’s value incrementally within the defined range and recalculate the weights.
  • Checking Consistency: After each adjustment, verify the consistency ratio of the AHP matrix. If the consistency check is passed, the adjusted data will be included in the sensitivity analysis. Otherwise, mark the matrix as unqualified, and its data will be excluded from further analysis.
  • Conducting Sensitivity Analysis: Exclude the directly adjusted indicators from the dataset and analyze the changes in the remaining indicators and their derivative effects. (For example, if there are six indicators—A to E—and this round directly adjusts indicators A and B, then A and B are excluded from the analysis while analyzing the ripple effects on indicators C, D, E, and F).

3.4. Research Ethics

This research focuses on evaluating the physical appearance of healing installations and does not involve any experimental research related to clinical studies, animals, human tissues, or biological samples. In this research, humans only participated in surveys, and all participants were voluntary adults. All participants were informed in advance about the purpose of this study, the survey process, the use of survey data, and their rights as participants. This study does not involve discussions on personal religious beliefs, racial identity, political views, sexual orientation, financial information, or any other personal privacy issues. All data and information were collected and recorded anonymously, and no actions were taken that could infringe upon participants’ privacy, dignity, health, or human rights. Therefore, all research methods and procedures described in this research comply with ethical principles and regulatory requirements.

4. Results

4.1. Experts Participating in the Evaluation

This research invited 12 experts from related fields (Architecture, Design, Psychology, etc..) to participate in the evaluation to ensure the acquisition of comprehensive, scientific, and representative original data. The detailed description of the participants is as follows:
  • One professor from Arizona State University (Architecture)
  • One professor from the University of Pennsylvania (Psychology)
  • One associate professor from Politecnico di Milano (Spatial Design)
  • Two master’s students from Yale University (4a&b. Architecture)
  • Two visiting scholars at Yale University
    (5a. Landscape History; 5b. Ecological Environment)
  • One professor from Tongji University (Environmental Design)
  • Three PhD students from Tongji University
    (7a. Architecture; 7b. Psychology; 7c. Environmental Design)
  • One PhD student from Tsinghua University (Environmental Psychology)

4.2. Geometric Average and Matrix Data Correction

The research team first converted the 12 experts’ pairwise comparison results into an AHP data matrix and conducted an independent consistency test (Figure 5 and Figure 6). The “M_Outflow” algorithm [39] was used for data correction. The advantage of M_Outflow is that it can maintain the original score to the greatest extent. After passing the consistency test, the 12 experts’ matrices were integrated into a single matrix using geometric averaging based on Formula (7).
G = X 1 X 2 X n n

4.3. AHP Matrix Weight Calculation

Table 3, Table 4, Table 5, Table 6, Table 7, Table 8 and Table 9 presents the weight calculation results of the geometrically averaged matrix using Formulas (2) and (3).

4.4. Consistency Test

The consistency test calculation results (Table 10) show that the CR values of all matrices are less than 0.1, indicating that the results have passed the consistency test and the derived weight values are reasonable.

4.5. Fuzzy Comprehensive Evaluation

After passing the consistency test, the research team calculated the combined weights of the design strategy indicators and ranked them (Table 11). The top 10 most important indicators are highlighted in green (No. 1–5: dark green; No. 6–10: light green). The 10 least important indicators are highlighted in yellow (No. 17–21: light yellow; No. 22–26: dark yellow).
Furthermore, the research team conducted a grouped weight analysis of the participating experts from the United States and China (Table 12). This analysis revealed subtle and interesting differences between Western and Eastern scholars in emotional healing design. Detailed insights will be elaborated in Section 5 (Discussion).

5. Discussion

5.1. Healing Design Insights Based on the AHP Data Matrix

Based on the AHP-FCE data analysis results, the research team discovered nine insights (relevant data for specific insights are highlighted in the following figures), and discussed the generated reasons for these insights and their impact on future healing design, providing clear guidance for designers and researchers on healing strategies.
Insight 1: Residents prefer encountering healing installations during leisure activities rather than during work commutes.
Within the environment category, Green Space and Park overwhelmingly dominates the weight ranking (59.715%), reflecting the strong connection between healing potential and natural landscapes (Figure 7). Community Streets (16.56%) and Public Squares (17.141%) share nearly equal weights. In comparison, Business Districts (6.580%) are considered the least important, which reflects that residents prefer to engage with healing installations in relaxed and pleasant living environments rather than in high-pressure, busy scenarios (such as during commutes to work or meetings).
There is a very significant design tendency in the material category. Wood (43.790%) and soft materials (32.623%) are perceived to have significantly greater healing potential compared to stone (9.365%) and metal (4.071%). Surprisingly, materials with lightness and transparent visual characteristics received low weights (9.365%).
Insight 2: Saturation has stronger healing associations than color temperature.
In the color category, an obvious trend is that low-saturation colors are more healing than high-saturation colors, warm colors are more healing than cold colors, while neutral color (7.161%) has the least healing effect (Figure 8). An interesting comparison emerges between saturation and color temperature: cold colors with low saturation (20.726%) are lower than warm colors with low saturation (38.090%), but higher than warm colors with high saturation (19.084%). This reveals that in public installation design, saturation is more closely related to healing effects than color temperature.
Insight 3: Small-scale installations have better healing effects than landmarks.
In the size category, small-scale interactive installations such as 0–1 m3 (31.325%) and 1–5 m3 (38.403%) demonstrate better healing effects. Small installations are generally more accessible and offer better interactivity, allowing surrounding residents to engage with them more comfortably. In contrast, large-scale landmarks have a lower healing association (6.580%) because they usually appear as “public symbols”, carrying historical, social, or cultural significance. However, it is difficult for landmarks to create emotional connections with individuals.
In the shape category, softer shapes such as sphere (42.674%) and ring (37.832%) demonstrate a higher relevance to healing, while angular column (12.836%) and sharp pyramid (6.658%) have lower weights. In the multifunctionality category, practicality (bench, trash can, etc..) ranks first by a significant margin (41.741%), followed by safety (23.790%) and landscape (24.059%). However, intelligence (digital screens, etc..) is considered to have the lowest relevance to healing installation design (10.410%).
Insight 4: Some design strategies rank relatively high, but they are under unimportant categories.
Figure 9 visualizes the FCE (Table 11). Overall, the five most important design strategies are as follows: D1-Environment-Green Space and Park (17.496%); E2-Material-Wood (10.218%); E5-Material-Soft Materials (7.613%); A2-Color-Warm Colors with Low Saturation (6.721%); and F1-Multifunctionality-Practicality (5.394%). Some indicators in less important categories but with relatively high overall weight are noteworthy (Figure 10). For instance, although the multifunctionality category (F) is one of the unimportant categories, practicality (F1) ranks fifth in overall weight. Additionally, the 1–5 m3 interactive installation (C2), from the second least important category (C), ranks eighth in overall weight.
Insight 5: Some design strategies rank relatively low, but they are under important categories
The five least important design strategies are A5-Color-Neutral Color (1.263%); C4-Scale-Over 10 m3 Large Landmark (1.057%); E1-Material-Metal (0.950%); B2-Shape-Column (0.872%); and B3-Shape-Cone (0.452%). Even though the environment category (D) holds the most significant design weight, business district (D4) ranks 20th in overall weight (Figure 10). A similar situation occurs in the second most important material category (E), with metal (E1) ranking 24th, stone (E3) 17th, and transparent (E4) 18th. Despite having three elements at the lower end, the material category remains essential due to the second-ranked wood (E2) and third-ranked soft materials (E5) in overall weight. This reflects the consistency and clarity of experts’ preferences for healing design materials.
Figure 11 visualizes the group weight analysis of the healing installation design by American and Chinese scholars (Table 12), while Figure 12 shows the differences in healing design preferences among American scholars (US), with Chinese scholars (CN) as the baseline. Scholars have consistent preferences towards healing design, such as emphasizing the importance of the placing environment (D) and materials (E). In the environment category, both groups consider the landscape environment (E1) to play the most crucial role, and both agree that shape (B) and scale (C) have weaker correlations with healing design compared to other categories. However, there are some interesting differences in healing tendencies.
Insight 6: CN shows a clear preference for low-saturation colors
In the color category, CN shows a clear preference for low-saturation colors (Figure 13), particularly cold colors with low saturation (A4), which ranks No. 7 in CN’s overall healing weight, while US ranks No. 13. Although warm colors with low saturation (A2) rank high on both groups, CN still shows a greater preference in precise weight percentage (1.824%). This trend can be explained through traditional culture. CN’s traditional philosophy advocates the “Golden Mean,” emphasizing harmony and balance. This concept is also reflected in the softer visual esthetic preference. The tones in Chinese traditional paintings are often grayish with low saturation, concentrating on creating scenarios, and this esthetic has profoundly influenced CN’s modern design styles.
Insight 7: US has a stronger healing shape preference compared to CN.
In the shape category, CN’s shape indicators are concentrated in the much lower ranks (No. 17–No. 26), reflecting CN’s general belief that shape elements are not strongly associated with healing properties. Conversely, US scholars more clearly believe that rounded shapes (B1 = No. 10) are more healing than sharp, angular shapes (B3 = No. 26).
Insight 8: US places greater emphasis on medium-sized public spaces.
In the scale category (Figure 14), a notable difference lies in the perception of 5–10 m3 small landmarks (C3), which the US rates significantly higher (No. 14) compared to CN (No. 21). This can be analyzed together with preferences in the environment category. The US ranks public squares (D3) at No. 4, whereas CN at No. 12. These data reflect that the US places greater emphasis on medium-sized public spaces. This difference may stem from the geographical and developmental contexts of the two countries: the US, with its vast land and low population density, has more extensive public spaces, whereas China, having undergone rapid urbanization in roughly 40 years, has built numerous skyscrapers. However, early urban planning prioritized meeting the urgent housing, transportation, and infrastructure needs. It is difficult for public spaces to generate direct economic benefits, and they were often overlooked during the rapid urbanization.
Insight 9: CN attaches significant importance to the multifunctionality of healing installations compared to the US.
The most significant difference between the US and CN lies in multifunctionality, where CN (20.124%) places significantly more emphasis on it compared to the US (9.178%), especially practicality (F1), which ranks No. 3 in CN. In urban renewal projects in CN, it is difficult for public installations with only aesthetics to receive funding. CN designers usually need to integrate practical functions (such as benches, streetlights, etc..) into the installations to facilitate approval from government departments. The US also has a higher rank for F1 (No. 7), but the specific weight percentage is 8.632% lower than for CN. Additionally, there is a significant difference in intelligence (F4) (CN = No. 16 and US = No. 25).
In summary, future designers could focus on using low-saturation warm colors, incorporating soft shapes such as spheres into installations, and putting these installations in natural forests or gardens to establish connections between landscape and emotional healing. Placing them in community streets and public squares at a smaller scale (0–1 m3 or 1–5 m3) can also achieve the effect of emotional healing through friendly interactivity. For material selection, designers should prioritize wood and soft materials, integrating the installations into residents’ daily activities (resting, playing, socializing, fitness, etc.) to increase interaction frequency. Conversely, in healing installation design, future designers should avoid high-saturation cold colors and neutral colors, avoid placing large landmarks in business districts, and avoid using sharp shapes or tough metal materials.

5.2. Cross-Category Analysis

The interaction among multiple design indicators plays a critical role in the emotional healing effectiveness of public installations. To gain a deeper understanding of how these indicators collaboratively influence the design, the research team conducted four sets of cross-category analyses. These analyses explored the subtle connections, weight variations, and synergistic effects among six categories, color (A), shape (B), scale (C), placing environment (D), material (E), and multifunctionality (E), helping to optimize the design interventions to meet different stakeholders’ demands and adapt to a wider range of scenarios. Figure 15 illustrates the images and weights of the involved indicators.
Combination 1: Color (A) + Shape (B) + Material (E)
Warm colors with low saturation (A2) and wood (E2) both convey warm and comfortable feelings, while the round shape (B1) gives a soft and safe visual impression. The combination of these three indicators (A2 + B1 + E2) has a high comprehensive weight, making it highly suitable for healing installations, especially those with natural style. The round shape easily resonates with natural elements in form. Wood (E2) would also provide comfortable touch sensations while enhancing the emotional healing experience.
Cold colors with low saturation (A4) convey calmness, peace, and quiet emotions, while the circular ring shape (B4) expresses the continuity of visual characteristics. Combined with the lightness of transparent materials (E4), this combination (A4 + B4 + E4) is ideal for environments requiring quiet atmospheres, such as libraries or meditation spaces, to help participants stabilize emotional fluctuations and alleviate anxiety.
By contrast, combinations with lower comprehensive weights, such as neutral color (A5) + column (B2) + stone (E3), convey a stable, durable, and classic visual atmosphere, often seen in public sculptures placed in squares with historical or cultural significance. However, they have clear limitations in emotional expression and applicable scenarios and cannot effectively convey warmth and inclusiveness, making it difficult to evoke emotional resonance from surrounding residents. In addition, the combination of neutral color (A5) + cone (B3) + metal (E1) conveys a cold and sharp visual atmosphere, making it unsuitable for healing installations.
Combination 2: Scale (C) + Placing Environment (D) + Multifunctionality (F)
Green space (D1) + 1–5 m3 interactive installation (C2) + practicality (F1) demonstrates a relatively high combined weight. The healing installations based on this combination can not only meet the esthetic needs of landscape parks but also provide practical functions (such as seating, shading, lighting, etc.). Additionally, the moderate scale allows groups of visitors to experience the installation together, achieving a delicate balance between esthetics and functionality.
The combination 0–1 m3 micro intervention (C1) + community (D2) + safety (F2) seems reasonable, involving small-scale interventions in narrow and crowded community streets. Common forms are street lights, warning signs, etc., which have important visual guidance functions, but the healing potential is quite limited. Therefore, the comprehensive weight value of this combination is low.
Combination 3: Scale (C) + Placing Environment (D) + Material (E)
The combination 1–5 m3 interactive installation (C2) + green space (D1) + wood (E2) has a relatively high comprehensive weight, aiming to create natural, interactive, and friendly spaces. The natural tactile quality of wood echoes the landscape environment, while the proper scale allows residents to interact with the installation comfortably.
In contrast, lower-weight combinations such as stone (E3) + 5–10 m3 small landmark (C3) + public square (D3) demonstrate identity and durability. However, large-scale stone installations easily convey a sense of distance, which contradicts the purpose of emotional healing. Additionally, their surfaces may not be suitable for touch interaction.
Combination 4: Shape (B) + Material (E) + Multifunctionality (F)
High-weight combinations such as round (B1) + soft materials (E5) + practicality (F1) can create a safe, comfortable, and approachable interactive space. The design combining these indicators are similar to a spherical public installation that can be touched, hugged, or climbed, with surfaces covered in soft and elastic materials to provide a comfortable tactile experience. The interior or surrounding areas of the installation can offer opportunities for rest, play, and social interaction, making it suitable for children’s activity areas, community parks, and other spaces aimed at fostering a relaxed and joyful atmosphere.
Similarly, ring (B4) + wood (E2) + landscape (F3) features a circular wooden structure that can be integrated with plants to form flower beds, hedges, or other landscape elements, creating a natural and harmonious ambiance. The ring-shaped space strikes a delicate balance between openness and privacy, allowing participants to share public space while maintaining a comfortable distance. In contrast, low-weight combinations such as column (B2) + metal (E1) + safety (F2) are commonly seen in guardrails or boundary signs, offering stability and durability. However, their healing potential is weaker.

5.3. Sensitivity Analysis

This research conducted three rounds of sensitivity analysis on the six categories of the healing installations’ physical appearance. Figure 16 presents the selected changeable indicators and the visualization of analysis data for each round, while Table 13 provides detailed data on weight variations.
The first round of sensitivity analysis directly adjusted indicators A—color and B—shape, so these two indicators’ weights were excluded from this round of analysis, and then the derivative effects in the remaining indicators were discovered. The results showed that C—scale was not sensitive to changes in A and B indicators (−0.168% to 0.258%). Conversely, D—environment (−0.501% to 0.747%) and E—material (−0.396% to 0.598%) exhibited higher sensitivity. The adjustments of A and B showed a negative correlation with other indicators’ changing trends.
The second round of sensitivity analysis selected C—scale and D—environment for adjustment. The results indicated that A—color (−0.015% to 0.515%) and E—material (−0.016% to 0.684%) were sensitive to these changes, while B—shape (−0.007% to 0.197%) and F—multifunctionality (−0.008% to 0.380%) showed weaker sensitivity. The adjustments of C and D were positively correlated with other indicators’ changing trends because the target indicators’ feature vector in this round was 0.342, while the first round (3.935) and third round (1.940) were both greater than 1 (the baseline for matrix comparison).
The third round of sensitivity analysis selected E—material and F—multifunctionality for adjustment. The results revealed that A—color (−0.661% to 0.273%) and D—environment (−1.097% to 0.454%) were sensitive to changes. Overall, the degree of sensitivity was similar to the original weight distribution, with indicators with high original weights also showing high sensitivity. However, the overall degree of change was not significant, indicating that the weight proportions in the original AHP data matrix possess a high level of stability.

5.4. Healing Installation Prototypes

Based on the above healing design strategies, the research team created two healing installation prototypes around Yale and Tongji University (Figure 17). The prototype placed around Yale University (Tree Seesaw Installation) follows the healing preference of American researchers, choosing a small-scale intervention form (1–5 m3) and situated between two trees in a landscape park. The installation uses multiple rounded shapes to mimic the appearance of trees, with the texture on the base platform featuring linear leaf graffiti, echoing the visual atmosphere of the surrounding environment. Regarding color selection, the tree seesaw installation combined low-saturation and high-saturation warm colors. The interactive method of the tree seesaw installation involves surrounding residents sitting on the longboard, with soft materials used on the seats to ensure a comfortable experience. As the seesaw shakes up and down, the generated mechanical energy will drive the central tree installation to rotate, improving the enjoyment and engagement of the installation.
The prototype placed around Tongji University (spring bee installation) follows the preference of Chinese researchers, choosing a small-scale form (0–1 m3) to integrate into the leftover spaces of the streets. This installation employs low-saturation warm colors and seeks inspiration from bees, and the structure is simple, with some basic shape combinations. The wings are outlined using rounded tubes to achieve their shape. The interactive method of the spring bee installation involves residents and visitors placing their feet through the hollowed-out areas of the wings and grabbing the handles on the bee’s head. By swaying their bodies, they can drive the bottom spring, causing the entire installation to swing.

5.5. Limitations

  • Although relevant field experts were invited to evaluate the indicators and weights, and the surveyed population was carefully selected, some subjectivity still remains (such as the fact that most of the experts are from the United States and China). Although the AHP-FCE method could reduce the subjectivity in determining evaluation indicators, the results still have certain limitations due to the relatively single calculation method and the limited number of experts involved. Future research could expand the number of experts and incorporate multiple calculation methods to make the evaluation more comprehensive.
  • Due to the constraints of the evaluation framework, this research did not evaluate interactive experience indicators for healing installations (including time, speed, actions, multi-sensory experiences, etc.). It also does not include indicators from the surrounding environment, not the healing installation itself (such as antenna, temperature, humidity, etc.). Therefore, potential factors influencing healing efficacy might have been ignored. Future research could focus on evaluating interactive experiences and further integrate interactive experiences with physical appearance for comprehensive evaluation to develop more holistic design strategies.
  • This research conducted cross-category analysis using random combinations of three indicators (such as A + B + E, C + D + F, etc.), but it is still difficult to cover potential connection possibilities, such as the combination analysis of two indicators (A + B and C + F) and four indicators (A + C + D + F and B + D + E + F). Future research could explore the interactions and synergistic effects among multiple design indicators in depth to optimize design strategies.
  • This research focused on expert surveys and data analysis without utilizing psychological scales or physiological data (including biometric stress measurements, heart rate variability, electroencephalogram, etc.) as supplementary tools. This may lead to a less scientific and comprehensive basis for design optimization. Although this study created two healing installation prototypes based on the identified design strategies, further analysis was limited by the scope of this article. Future research could more objectively evaluate the healing potential of healing prototypes with the assistance of psychological scales and physiological indicators.

6. Conclusions

This research establishes a systematic evaluation framework for the physical appearance of healing installations based on affinity analysis, encompassing 3 levels, 6 categories, and 26 design indicators. By integrating the Analytic Hierarchy Process (AHP) and Fuzzy Comprehensive Evaluation (FCE), this research conducts quantitative analyses to derive scientifically robust insights. The results highlight some critical trends, such as that saturation is more closely linked to healing efficacy than color temperature, and small-scale installations have better therapeutic effects. Compared to intuitive and experiential approaches, the combined use of the AHP and FCE ensures a more scientific and rigorous methodology. Unlike singular design evaluation methods, this research incorporates both qualitative and quantitative perspectives, minimizing subjective biases from decision-makers and enhancing the accuracy, validity, and reliability of the evaluation process.
Furthermore, this research reveals delicate and interesting differences in healing design preferences between Western and Eastern scholars. For instance, Chinese scholars exhibit a strong preference for low-saturation colors and place considerable emphasis on the multifunctionality of healing installations. In contrast, American scholars demonstrate a greater inclination toward healing shapes and materials. These findings offer valuable insights into regional design strategies, providing tailored guidance for future healing design practices in different cultural contexts. The AHP-FCE approach offers practical and actionable support for designers, enabling them to systematically analyze diverse stakeholder needs, develop installations with enhanced emotional healing effects, and establish robust scientific foundations for future healing installations’ design.

Author Contributions

Conceptualization, T.G. and P.B.; methodology, T.G.; software, T.G.; validation, T.G. and P.B.; formal analysis, T.G.; investigation, T.G.; resources, T.G. and P.B.; data curation, T.G.; writing—original draft preparation, T.G.; writing—review and editing, T.G. and P.B.; visualization, T.G.; supervision, P.B.; project administration, T.G.; funding acquisition, T.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The authors will supply the relevant data in response to reasonable requests.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. AHP-FCE design decision flow chart.
Figure 1. AHP-FCE design decision flow chart.
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Figure 2. AHP framework of the physical appearance of emotional healing installations.
Figure 2. AHP framework of the physical appearance of emotional healing installations.
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Figure 3. The visualization and simplification process.
Figure 3. The visualization and simplification process.
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Figure 4. Images of all design indicators included in this research.
Figure 4. Images of all design indicators included in this research.
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Figure 5. Evaluation matrix and geometric averages of experts for color, shape, and scale categories.
Figure 5. Evaluation matrix and geometric averages of experts for color, shape, and scale categories.
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Figure 6. Evaluation matrix and geometric averages of 12 experts for environment, material, and multifunctionality categories.
Figure 6. Evaluation matrix and geometric averages of 12 experts for environment, material, and multifunctionality categories.
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Figure 7. Visualization of weights for overall, environmental, and material categories.
Figure 7. Visualization of weights for overall, environmental, and material categories.
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Figure 8. Visualization of weights for color, shape, size, and multifunctionality categories.
Figure 8. Visualization of weights for color, shape, size, and multifunctionality categories.
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Figure 9. Combined weights and rankings of all design strategies.
Figure 9. Combined weights and rankings of all design strategies.
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Figure 10. Highlight diagram for insights 4 and 5.
Figure 10. Highlight diagram for insights 4 and 5.
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Figure 11. Group weights analysis of the installation design by American and Chinese scholars.
Figure 11. Group weights analysis of the installation design by American and Chinese scholars.
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Figure 12. Differences in healing design preferences among American scholars (US), with Chinese scholars (CN) as the baseline.
Figure 12. Differences in healing design preferences among American scholars (US), with Chinese scholars (CN) as the baseline.
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Figure 13. Highlight diagram for insights 6 and 7.
Figure 13. Highlight diagram for insights 6 and 7.
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Figure 14. Highlight diagram for insights 8 and 9.
Figure 14. Highlight diagram for insights 8 and 9.
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Figure 15. The images and weights of the involved indicators.
Figure 15. The images and weights of the involved indicators.
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Figure 16. The selected changeable indicators and the visualization of analysis data for each round.
Figure 16. The selected changeable indicators and the visualization of analysis data for each round.
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Figure 17. Healing installation prototypes design based on healing design strategies.
Figure 17. Healing installation prototypes design based on healing design strategies.
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Table 1. AHP matrix rating scale.
Table 1. AHP matrix rating scale.
Scale ValueImportance LevelImplication
1Equally importantIndicator i is of equal importance compared to indicator j
3Slightly importantIndicator i is marginally important compared to indicator j
5Significantly importantIndicator i is significantly more important than indicator j
7Extremely importantIndicator i is extremely important compared to indicator j
9Absolutely importantIndicator i is absolutely important compared to indicator j
2, 4, 6, 8Eclectic valueThe importance level is between two adjacent levels
1/2, 1/3, …, 1/9Inverse comparisonIf the importance scale of indicator i over indicator j is “n”, the inverse comparison is “1/n”
Table 2. RI values of matrix order 1–9.
Table 2. RI values of matrix order 1–9.
n12345678910
RI0.520.891.121.261.361.411.461.490.520.89
Table 3. Judgment matrix and weights for the category level.
Table 3. Judgment matrix and weights for the category level.
ABCDEFEigenvectorsWeights
A1.0003.9351.6960.4200.6981.4551.19017.644%
B0.2541.0000.6350.3040.3190.5930.4586.795%
C0.5901.5761.0000.3420.4760.6260.67510.004%
D2.3803.2862.9281.0001.2012.1711.97729.300%
E1.4333.1352.1000.8331.0001.9401.57423.335%
F0.6871.6851.5970.4610.5161.0000.87212.922%
Table 4. Judgment matrix and weights for color criteria.
Table 4. Judgment matrix and weights for color criteria.
A1A2A3A4A5EigenvectorsWeights
A11.0000.3261.3731.0893.2221.09419.084%
A23.0681.0002.4681.7573.7402.18438.090%
A30.7280.4051.0000.6222.5170.85714.940%
A40.9180.5691.6081.0002.8221.18920.726%
A50.3100.2670.3970.3541.0000.4117.161%
Table 5. Judgment matrix and weights for shape criteria.
Table 5. Judgment matrix and weights for shape criteria.
B1B2B3B4EigenvectorsWeights
B11.0004.7185.5840.9122.21442.674%
B20.2121.0002.7590.3360.66612.836%
B30.1790.3621.0000.2190.3456.658%
B41.0962.9734.5581.0001.96337.832%
Table 6. Judgment matrix and weights for scale criteria.
Table 6. Judgment matrix and weights for scale criteria.
C1C2C3C4EigenvectorsWeights
C11.0000.6832.0112.7971.40031.325%
C21.4631.0001.9163.0971.71738.403%
C30.4970.5221.0002.3200.88119.706%
C40.3570.3230.4311.0000.47210.566%
Table 7. Judgment matrix and weights for environment criteria.
Table 7. Judgment matrix and weights for environment criteria.
D1D2D3D4EigenvectorsWeights
D11.0004.1524.0966.7013.26759.715%
D20.2411.0000.9992.8060.90616.565%
D30.2441.0011.0003.1660.93817.141%
D40.1490.3560.3161.0000.3606.580%
Table 8. Judgment matrix and weights for material criteria.
Table 8. Judgment matrix and weights for material criteria.
E1E2E3E4E5EigenvectorsWeights
E11.0000.1340.2810.3570.1500.2894.071%
E27.4461.0004.9235.0271.5813.11143.790%
E33.5570.2031.0001.1610.2320.72110.150%
E42.8020.1990.8611.0000.2710.6659.365%
E56.6610.6334.3053.6841.0002.31732.623%
Table 9. Judgment matrix and weights for multifunctionality criteria.
Table 9. Judgment matrix and weights for multifunctionality criteria.
F1F2F3F4EigenvectorsWeights
F11.0001.4842.3313.5281.86941.741%
F20.6741.0000.8142.3481.06523.790%
F30.4291.2291.0002.5561.07724.059%
F40.2830.4260.3911.0000.46610.410%
Table 10. The consistency test calculation results.
Table 10. The consistency test calculation results.
OverallABCDEF
λmax6.0815.0894.0924.0414.0475.0964.045
CI0.0160.0220.0310.0140.0160.0240.015
RI1.261.120.890.890.891.120.89
CR0.0130.020.0340.0150.0180.0210.017
ResultPassPassPassPassPassPassPass
Table 11. The combined weights and ranking of the design strategy indicators.
Table 11. The combined weights and ranking of the design strategy indicators.
Target LayerFirst-Level IndicatorsFirst-Level WeightNo.Secondary IndicatorsSecondary WeightCombined WeightsRank
The Physical Appearance
of Emotional Healing Public Installations
A. Color17.644%A1Warm Colors
(High Saturation)
19.084%3.367%10
A2Warm Colors
(Low Saturation)
38.090%6.721%4
A3Cold Colors
(High Saturation)
14.940%2.636%15
A4Cold Colors
(Low Saturation)
20.726%3.657%09
A5Neutral Color
(Black, White, Gray)
7.161%1.263%22
B. Shape6.795%B1Round (Sphere,
Ellipsoid, etc.)
42.674%2.900%14
B2Column (Cube,
Hexagon, etc.)
12.836%0.872%25
B3Cone (Circular cone, Pyramid, etc.)6.658%0.452%26
B4Ring (Circular ring,
Square ring, etc.)
37.832%2.571%16
C. Scale10.004%C10–1 m3 Micro
Intervention
31.325%3.134%11
C21–5 m3 Interactive Installation38.403%3.842%08
C35–10 m3 Small
Landmark
19.706%1.971%19
C4Over 10 m3 Large Landmark10.566%1.057%23
D. Placing Environment29.300%D1Green Space
and Park
59.715%17.496%01
D2Community
and Street
16.565%4.854%07
D3Public Building
and Square
17.141%5.022%06
D4Business District
and Shopping Mall
6.580%1.928%20
E. Material23.335%E1Metal (Stainless Steel, Aluminum, etc..)4.071%0.950%24
E2Wood (Logs, Composite Boards, etc..)43.790%10.218%02
E3Stone (Marble,
Concrete, etc..)
10.150%2.369%17
E4Transparent (Glass, Plastic, etc..)9.365%2.185%18
E5Soft Materials (Rubber, Textile, etc..)32.623%7.613%03
F. Multifunc-tionality12.922%F1Practicality (Bench,
Trash Can, etc..)
41.741%5.394%05
F2Safety (Street Lights, Warning Signs, etc..)23.790%3.074%13
F3Landscape (Flower Beds, Tree Fences, etc..)24.059%3.109%12
F4Intelligence (Digital Screens, etc..)10.410%1.345%21
Table 12. Differences in design indicator weights between American and Chinese scholars.
Table 12. Differences in design indicator weights between American and Chinese scholars.
American Scholars and DesignersChinese Scholars and Designers
No.First-Level WeightNo.Secondary WeightCombined WeightsRankNo.First-Level WeightNo.Secondary WeightCombined WeightsRank
A15.973%A122.935%3.663%09A19.563%A114.378%2.813%13
A236.619%5.849%05A239.225%7.674%04
A315.314%2.446%15A314.065%2.752%14
A417.145%2.739%13A426.344%5.154%07
A57.988%1.276%22A55.988%1.171%22
B7.232%B145.673%3.303%10B6.008%B138.171%2.293%17
B214.039%1.015%24B211.138%0.669%24
B37.103%0.514%26B35.983%0.359%26
B433.185%2.400%16B444.709%2.686%15
C10.538%C127.186%2.865%11C8.973%C136.800%3.302%11
C235.398%3.730%08C241.467%3.721%10
C323.652%2.492%14C314.704%1.319%21
C413.764%1.450%21C47.029%0.631%25
D32.038%D159.240%18.979%01D24.940%D158.846%14.676%01
D213.108%4.200%06D222.401%5.587%06
D320.671%6.623%04D312.851%3.205%12
D46.981%2.237%20D45.902%1.472%20
E25.041%E14.664%1.168%23E20.392%E13.354%0.684%23
E240.378%10.111%02E244.931%9.162%02
E311.017%2.759%12E38.245%1.681%19
E49.138%2.288%18E410.211%2.082%18
E534.804%8.715%03E533.259%6.782%05
F9.178%F140.691%3.735%07F20.124%F142.892%8.632%03
F224.596%2.257%19F222.514%4.531%08
F325.947%2.381%17F321.462%4.319%09
F48.766%0.805%25F413.131%2.642%16
Table 13. Detailed data from three rounds of sensitivity analysis.
Table 13. Detailed data from three rounds of sensitivity analysis.
First round (manual adjustment of A and B indicators)
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AConsistency Check Failed−5.653%−3.337%−0.703%0.634%1.554%2.262%
B3.718%1.903%0.346%−0.297%−0.694%−0.977%
C0.258%0.192%0.049%−0.043%−0.112%−0.168%
D0.747%0.553%0.135%−0.134%−0.337%−0.501%
E0.598%0.443%0.110%−0.104%−0.265%−0.396%
F0.332%0.246%0.062%−0.057%−0.146%−0.219%
Second round (manual adjustment of C and D indicators)
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A−0.732%−0.553%−0.326%−0.015%0.515%Consistency Check Failed
B−0.283%−0.214%−0.127%−0.007%0.197%
C−2.051%−1.623%−1.022%−0.048%2.312%
D4.565%3.520%2.141%0.095%−4.088%
E−0.965%−0.728%−0.429%−0.016%0.684%
F−0.534%−0.402%−0.237%−0.008%0.380%
Third round (manual adjustment of E and F indicators)
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AConsistency Check Failed0.273%0.165%−0.150%−0.364%−0.528%−0.661%
B0.104%0.062%−0.059%−0.142%−0.205%−0.256%
C0.158%0.097%−0.082%−0.203%−0.296%−0.372%
D0.454%0.274%−0.249%−0.604%−0.876%−1.097%
E−5.665%−2.242%1.548%3.428%4.704%5.676%
F4.677%1.644%−1.008%−2.114%−2.800%−3.291%
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Gao, T.; Bernstein, P. Physical Appearance Design Evaluation of Community Emotional Healing Installations Based on Analytic Hierarchy Process–Fuzzy Comprehensive Evaluation Method. Buildings 2025, 15, 773. https://doi.org/10.3390/buildings15050773

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Gao T, Bernstein P. Physical Appearance Design Evaluation of Community Emotional Healing Installations Based on Analytic Hierarchy Process–Fuzzy Comprehensive Evaluation Method. Buildings. 2025; 15(5):773. https://doi.org/10.3390/buildings15050773

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Gao, Tanhao, and Phillip Bernstein. 2025. "Physical Appearance Design Evaluation of Community Emotional Healing Installations Based on Analytic Hierarchy Process–Fuzzy Comprehensive Evaluation Method" Buildings 15, no. 5: 773. https://doi.org/10.3390/buildings15050773

APA Style

Gao, T., & Bernstein, P. (2025). Physical Appearance Design Evaluation of Community Emotional Healing Installations Based on Analytic Hierarchy Process–Fuzzy Comprehensive Evaluation Method. Buildings, 15(5), 773. https://doi.org/10.3390/buildings15050773

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