Applications of virtual reality technology on a 3D model based on a fuzzy mathematical model in an urban garden art and design setting

2.1 Research gap

The existing research on urban garden design and VR integration provides valuable insights into various aspects, such as resource optimization, ecological management, and emotional responses in virtual environments. However, there is a notable gap in exploring the intersection of immersive VR technology and advanced fuzzy logic models specifically tailored for urban garden art and design. While VR has been utilized for spatial visualization and community engagement, there is limited research on its application in the creation of sustainable, resource-efficient, and aesthetically impactful urban garden environments. More studies focus on isolated components such as irrigation systems, 3D modeling, or emotional responses, yet a holistic framework that combines these elements with real-time, adaptive VR-based design remains largely unexplored. The research integration of AGA-FLMM for optimizing garden spaces and fostering community interaction remains underexplored, which should focus on developing comprehensive models that address these gaps, enabling a more immersive, sustainable, and user-centric approach to urban garden design.

3.1 Data collection

Dataset 1 (https://www.kaggle.com/datasets/ziya07/urban-green-space-model-data/data), the Urban Green Space (UGS) Model Data, offers a comprehensive collection of urban garden and landscape layout plans. It includes high-resolution 2,000 × 2,000 px JPEG images of garden blueprints and design metadata that detail plant species, object placements, and terrain. This dataset is valuable for advanced modeling, simulation tasks, and urban planning using AI-driven techniques, 3D modeling, and VR environments. Dataset 2 (https://www.kaggle.com/datasets/ziya07/garden-space-planning-data/data), “Garden Space Planning Data,” is a curated collection of high-resolution urban garden landscape plans (2,000 × 2,000 px) in JPEG format. This dataset is designed to support research and development in areas such as 3D modeling, VR simulation, and fuzzy logic-based design optimization. It provides essential resources for designing smart, sustainable, and visually engaging green spaces in urban environments, contributing to the advancement of urban planning and landscape design techniques. The data for the research were gathered from (https://www.kaggle.com/datasets/zoya77/3m-urban-blue-green-gray-dataset) website. UBGG-3m (Urban Blue-Green-Gray 3-meter) dataset is a high-resolution urban landscape resource developed to address the lack of fine-grained urban landscape data. It focuses on classifying urban areas into three primary categories: Urban Blue Spaces, which include water bodies such as rivers, lakes, and ponds; UGS, which encompass vegetation areas such as trees, grasslands, and farmlands; and Urban Impervious Surfaces, which are man-made structures such as buildings, roads, and pavements. This dataset provides valuable insights into the composition of urban landscapes, aiding in urban planning, environmental sustainability efforts, and the assessment of ecosystem services, such as water management, green space availability, and urban heat island effects. By offering high-resolution data, UBGG-3m supports detailed analysis and decision-making for sustainable urban development.

3.2 Data pre-processing using min-max normalization

Min-max normalization is often used to scale numerical properties within a certain range. In machine learning, it is often used to prepare data for models. To improve diabetes prediction accuracy, min-max normalization can be used to the dataset’s input features. To compare results fairly before and after normalization, min-max normalization makes linear adjustments to the original data.

Z new = scaled-down version of the original number, Z = obsolete price, max ( z ) = the maximum possible score in a dataset, and min ( z ) = dataset minimum value.

3.3 Data feature extraction using PCA

To reduce urban data dimensionality while preserving key information, PCA is applied. PCA helps eliminate redundancy, reduce noise, and transform correlated evaluation indices into a smaller set of uncorrelated principal components, thus enhancing urban landscape garden design data interpretability without significant information loss.

Let the evaluation data matrix be defined as follows:

where B is the number of observation samples (e.g., different sporting events), A is the number of original evaluation indices (e.g., crowd size, weather conditions, and injury rates), and E _ji is the value of the ith index in the jth sample.

The score for the jth observation on the ith principal component is given as follows:

where S j denotes the matrix representing the correlation coefficient’s major component, and the normalized eigenvector is f i .

Compute the correlation matrix Q A ⁎ A of the indices, perform eigenvalue decomposition on Q , obtaining eigenvalues λ 1 , λ 2 , … , λ A and eigenvectors f 1 , f 2 , … , f A (each is a principal component direction). Select the top components such that their cumulative contribution rate exceeds 86% the following:

where b i is the contribution rate of the ith principal component.

Once principal components are extracted, the overall risk rating W for a given event is computed using a weighted sum of selected components:

where X is an eigenvalue of the eigenvector a and w denotes the normalized index’s original data. Figure 2 illustrates that the relative importance of features extracted using PCA highlights which components contribute most significantly to the model’s predictive performance.

Figure 2

Feature importance from PCA features.

Design quality in this context is typically assessed using algorithmic benchmarks rather than purely subjective user ratings. PCA, as visualized in the provided image, reduces dimensionality by identifying components that explain the most variance in the dataset. The bar plot indicates the relative importance of each principal component. In this example, the first component (index ∼1) has the highest importance score, contributing over 70% to the model’s predictive power. This suggests that the features most aligned with this component are key contributors often capturing dominant trends or correlations in the data. These might include composite measures of performance, structural integrity, or thermal efficiency, depending on the domain. Such insights allow for refining feature selection and improving model sensitivity and robustness.

3.4 AGA-FLMM

3.4.2 Advanced genetic algorithm

A kind of randomized search algorithm called a genetic algorithm is one that depends on the genetics and natural selection of creatures. More suitable personalities are chosen from the problem-solving groups using some metric. To create newer generations of potential answers, each person is merged by genetic operators. This procedure is continued before the convergence index is reached. The four major parts of a genetic algorithm are control parameters: selection, crossover, variation genetic operators, and coding technique. When an issue is solved using a genetic algorithm, the potential answers are encoded into chromosomes or people. An early problem-solving group is made up of several people. After determining the fitness function, the algorithm can be terminated by printing the persons who meet the termination requirements. If not, people will mix with each other, change, and recombine to create the following new population. The preceding generation’s positive traits are passed down to the next population, which is superior to it, allowing for a more favorable outcome to eventually emerge. The following are some examples of the genetic algorithm’s steps.

3.4.2.1 Creating the first population and coding

Select the suitable coding method for the given trouble. And make a populace of M chromosomes with a prearranged length at random.

(18) pop j ( s ) , s = 1 , j = 1 , 2 , … M .

3.4.2.2 Calculating fitness value

Each chromosome’s fitness t pop ( s ) in populace pop ( s ) is calculated as follows:

(19) e j = fitness ( pop j ( s ) ) .

Determine whether the convergence need is met. With the output explore outcomes, continue with the next steps.

3.4.2.3 Choose action

According to each person’s fitness, the chance of selection is determined as follows:

(20) O j = e j ∑ j = 1 M e j , j = 1 , 2 , 3 , … M .

To create the new population in the next-generation population, a random sample of the probability distributions mentioned earlier is taken from the TPOP ( s ) current generation population:

(21) newpop ( s + 1 ) = { pop i ( s ) ∣ i = 1 , 2 , … M } .

3.4.2.4 Cross-action

A collection of M chromosomes t crosspop ( s + 1 ) results from the union of probability O c .

3.4.2.5 Operation of mutation

Use a lower probability O n to induce gene mutations in chromosomal regions. There develops a new population, t mutpop ( s + 1 ) . Pop ( t ) = Mutpop ( s + 1 ) is the term given to the new population that results from a genetic operation. In addition, it returns to 2 and serves as the father of the subsequent genetic surgery.

Algorithm 1: Advanced Genetic Algorithm

Step 1: Create an n-chromosome population of random kind e ( x )

Step 2: Fitness estimation for each chromosome x’s fitness e ( x ) among the populace

Step 3: Iterate the following processes until you reach the new required population.

Selection: selects a few parent’s chromosomes from a population based on fitness Crossover: To determine a new offspring, parents conduct crossover based on a crossover probability. The child can be a perfect replica of the parent if the crossover is not performed. Mutation: Create new children with a mutation probability at each locus. Accepting: Add a fresh generation to a brand-new population.

Step 4: Utilize freshly created population in a subsequent algorithm run.

Step 5: If the criteria for termination are met, stop the procedure and provide the best response from the current group of people.

Step 6: Step 2 is next.

Urban garden planning and designing a landscape is a comprehensive procedure that begins with the gathering of the fundamental data needed for planning, continues with the creation of detailed design plans, and ends with the execution of the design on the substance of the planning. Planning objectives and planning pointers into physical places is the process of creating urban planning, which forms the basis of all other planning and design work. The system’s most important features are security and dependability. These features effectively ensure the integrity and security of the system’s data. The proposed system can be adapted for different climatic zones, cultural aesthetics, or ecological requirements. The integration of VR and the AGA-FLMM allows for flexible design solutions. By adjusting the parameters and models based on local climate, cultural preferences, and ecological needs, the system can offer tailored, context-specific urban garden designs that optimize space usage, resource management, and community engagement while ensuring environmental and aesthetic relevance.

A number of models can be automatically built in the 3D scene based on the urban garden landscape design’s chosen area’s landscape (Figure 3). This additionally offers a quick and easy way to generate models, but it can also be used to evaluate models created manually by other designers. The planner can change the chosen model’s size, orientation, coordinates, and other characteristics, as well as completely swap out the chosen model. This gives designers an opportunity for horizontal and vertical comparison, enabling them to choose their perfect strategy. The place is chosen in the planning interface using the landscape models’ replacements and modification functions.

Figure 3

Using VR technology, a 3D virtualized urban garden landscape design was created (source: https://www.sciencedirect.com/science/article/abs/pii/S2352186421003862).

4.1 Distribution of aesthetic scores

The histogram displays the distribution of aesthetic scores across a dataset, with most samples clustering near the mean around zero. This bell-shaped pattern suggests a roughly normal distribution, indicating balanced evaluations of design aesthetics. These scores are likely derived from either algorithmic model trained on annotated datasets or user rating aggregation, depending on the methodology. Figure 4 shows the presence of scores across a broad range from approximately −1.2 to 1.2, which implies sensitivity to diverse design attributes. While subjective ratings can influence initial training, the final assessment is often quantitatively modelled to ensure consistency, objectivity, and scalability across large datasets.

Figure 4

Distribution of aesthetic scores.

4.2 Comparison of dataset

The UGS Model Data (Dataset 1) and Garden Space Planning Data (Dataset 2) provide high-resolution (2,000 × 2,000 px) JPEG images and detailed metadata for urban garden and landscape layouts, enabling AI-driven modeling, 3D simulation, and VR-based urban planning. Both datasets contribute significantly to sustainable and smart green space design. Sourced from the UBGG-3m dataset, which classifies urban areas into blue, green, and gray spaces, they support environmental sustainability and urban ecosystem analysis. Figure 5 shows that the Dataset-1 achieved 98.2% accuracy; Dataset-2 reached 98.5%, while the proposed research model outperformed both with 98.8% accuracy.

Figure 5

Comparison of accuracy dataset.

4.3 Design quality

The VR platform should include a wide variety of design components to provide a complete and adaptable garden art design experience. Various kinds of vegetation, flowers, trees, hardscape components, sculptures, and water features are included in this. Designers will have freedom and alternatives to modify the diverse components. Figure 6 depicts the design quality of the proposed and existing methods. Realistic, interactive, user-friendly, and performance-optimized VR design is essential for creating 3D-based garden art. Table 2 depicts the outcomes of the design quality. Designers can develop a potent and compelling virtual environment that encourages creativity and aids in the realization of remarkable garden art ideas by giving these elements the highest priority. Compared with the existing one, the design quality for the proposed model is high (92.89%).

Figure 6

Design quality of the proposed and existing method.

4.4 Design efficiency

To keep the garden art design focused, and on the course, it is crucial to have well-stated design goals and objectives. The design process is guided, and superfluous iterations are avoided by defining the goal and intended aesthetic effect of the artwork. Efficiency depends on selecting the right materials that complement the design intent and the surrounding area. Garden art projects that include sustainable design concepts are more effective and beneficial for the environment. Design effectiveness of the proposed and current methodologies is shown in Figure 7. Design efficiency data are shown in Table 3. Long-term maintenance expenses and resource consumption can be decreased by implementing sustainable techniques, such as adopting native plants, water-efficient irrigation systems, and energy-efficient lighting. The proposed method achieves high efficiency than the existing methods. The proposed method achieves the greatest effective design (97.23%).

Figure 7

Design efficiency of the proposed and existing methods.

4.5 Accuracy

The competence and knowledge of the craftsmen or artisans engaged in its creation have a significant impact on how accurately the garden art design is executed. It is crucial to engage with seasoned experts who can operate precisely and pay attention to detail. The correctness of the design can be impacted by site-specific elements, including geography, soil characteristics, and climate. For the design to be implemented successfully, the site circumstances must be taken into consideration. Figure 8 illustrates the precision of the suggested and current approaches. Results from accuracy research are shown in Table 4.

Figure 8

Accuracy of the proposed and existing methods.

4.6 Prediction

The amount of upkeep given to the garden will have an effect on how it develops as a whole. Regular weeding, fertilizer, and trimming can result in a well-kept and lively landscape, while neglect can provide a less appealing look. The landscape of the garden can be influenced by environmental variables, including rainfall, temperature, and nearby fauna. For instance, heavy rain or drought can harm a plant’s health and development. Figure 9 shows the agreement between the proposed and current approaches for prediction. Table 5 illustrates the outcome of the garden landscape forecast.

Figure 9

Prediction of the proposed and existing methods.

4.7 Fitness rate

The degree to which a garden art design satisfies the demands, goals, and limits specified by the customer or other project stakeholders is referred to as the design’s fitness rate. It serves as a gauge of how well and efficiently the garden art design satisfies both the expectations of the target audience and the purpose for which it was created. The aesthetic appeal and aesthetic features of a garden art design also influence how suitable it is. In keeping with the overall garden idea, the design should blend in with the surrounding terrain. Safety should be considered in the design of any garden sculpture. It needs to be safe for both people and the environment, managed, and upgradable over time. The relative fitness of the new and old approaches is shown in Figure 10. The results of the fitness rate are shown in Table 6. It shows that the proposed method reaches the highest fitness rate (95.71%) among the existing ones.

Figure 10

Fitness rate of the proposed and existing methods.

4.8 Sensitivity

Designing garden art requires sensitivity to the natural world. A design can be ecologically conscious by using eco-friendly procedures, using sustainable materials, and including native flora. The natural rhythms of the site, such as seasonal changes, light patterns, and animal habits, ought to be respected while designing garden art. Instead of obstructing these organic features, the design should acknowledge and embrace them. Figure 11 depicts the sensitive results. Table 7 shows the sensitivity analysis. When compared to the existing methods, the proposed method has a greater sensitivity (97.91).

Figure 11

Sensitivity of the existing and proposed methods.