Research on Teaching Evaluation of Landscape Bridge Aesthetics Creation Ability Based on Sustainable Development Concept

1. Introduction

In today's society, bridges are not only transportation infrastructures but also important components of urban landscapes. With the continuous improvement in people's quality-of-life requirements, the importance of the aesthetic landscape design of bridges has become increasingly prominent [1,2,3,4,5]. In this context, the evaluation of students' ability in the aesthetic landscape design of bridges is of crucial importance in teaching. On the one hand, a good evaluation system can accurately measure students' knowledge mastery and practical ability in the aesthetic landscape design of bridges, providing a basis for teachers to adjust their teaching strategies. On the other hand, through scientific evaluation, students' learning enthusiasm and creativity can be stimulated, prompting them to pay more attention to the combination of aesthetics and engineering and cultivating bridge design talent with both solid professional knowledge and innovative design capabilities to meet society's demand for high-quality bridge landscapes and add beautiful scenery to urban construction and development [6,7,8,9,10,11,12,13]. The output-oriented evaluation method has gradually gained attention in this field and has achieved relevant research results.

The concept of output-oriented education has been widely applied in the field of engineering education [14,15,16,17]. In bridge aesthetics courses, many universities focus on cultivating students' practical abilities and innovative thinking by using actual project outputs as an important basis for evaluating their design abilities. Foreign scholars emphasize the integration of real engineering projects into curriculum design, allowing students to exercise their landscape bridge design skills in practical situations. By collaborating with enterprises and participating in actual project bidding, students can be exposed to the latest design concepts and technologies and improve their design skills. In the evaluation process, we not only focus on the aesthetic value and engineering feasibility of the design scheme but also pay attention to students' teamwork, communication skills, and problem-solving abilities in the project. We are constantly exploring new evaluation methods and tools. For example, some scholars have used multi-index evaluation methods, such as fuzzy comprehensive evaluation and the analytic hierarchy process, to comprehensively evaluate students' landscape bridge design. At the same time, use of digital technologies, such as 3D modeling and virtual reality, allows students to present design proposals more intuitively, improving the accuracy and objectivity of evaluations.

Some universities have begun to introduce the concept of output-oriented education to bridge aesthetics courses, emphasizing student learning outcomes as the guide and focusing on cultivating students' practical design abilities. In the teaching process, practical design tasks are set, guiding students to combine theoretical knowledge with practice and improving their design level. In terms of evaluation, scholars are also actively exploring suitable evaluation methods. Some universities adopt a combination of teacher evaluation, student peer evaluation, and self-evaluation to achieve more objective and comprehensive evaluation results. At the same time, some scholars have attempted to establish a scientific and reasonable evaluation index system, including design creativity, aesthetic value, engineering feasibility, environmental coordination and other aspects, to comprehensively evaluate students' design ability. In addition, some studies have focused on the feedback effect of evaluation. When timely feedback on evaluation results is provided to students, they can understand their strengths and weaknesses and make targeted improvements and enhancements. Moreover, teachers can adjust teaching content and methods on the basis of the evaluation results to improve teaching quality.

In summary, active exploration and practice have been carried out in the evaluation of students' landscape bridge design abilities in output-oriented bridge aesthetics courses. However, there are still some shortcomings in the current research. For example, the scientific validity and rationality of the evaluation index system need to be further improved, and the operability and universality of the evaluation methods need to be strengthened. In addition, how to better leverage the feedback role of evaluation and promote students' sustainable development is a problem that needs to be addressed in future research. The evaluation of students' landscape bridge design ability in bridge aesthetics courses on the basis of output orientation is a research field with important theoretical and practical significance. In the future, it will be necessary to further strengthen communication and cooperation at home and abroad, constantly explore innovation, improve evaluation systems and methods, and provide strong support for the cultivation of high-quality bridge aesthetics professionals. This study aims to comprehensively evaluate students’ landscape design ability in bridge aesthetics course, using the output-oriented approach of landscape design ability and the principles of a comprehensive radar chart and fuzzy analytic hierarchy process.

The main structural framework of this article is as follows. First, the main content of the Bridge Aesthetics course and the logical relationship between each piece of con - tent are introduced. In this process, the significance of sustainable development in bridge design is emphasized, such as the use of environmentally friendly materials and energy - efficient designs that blend harmoniously with the surrounding environment. Second, corresponding output - oriented training objectives for landscape bridge design abilities are developed on the basis of the learning content of the course. These objectives include not only traditional design aspects but also the integration of sustainable principles, like minimizing the ecological footprint during construction and operation. Next, on the basis of the learning content and training objectives, an evaluation system for students' landscape bridge design abilities is constructed. Sustainable factors are incorporated into the evaluation criteria, for example, the recyclability of materials and the long - term durability that reduces the need for frequent replacements. Interval re - liability theory was subsequently used to construct an ability evaluation system for students in the process of landscape bridge creation. Finally, practical cases are used to illustrate the applicability of the method proposed in this article. These cases showcase how students' designs that embrace sustainable development concepts can achieve better overall performance in the evaluation system, highlighting the importance of integrating sustainability into bridge aesthetics education.

2. Bridge Aesthetics Course Content

The Bridge Aesthetics course covers a wide range of content, including the following aspects.

2.1. Theoretical Basis

Principles of Aesthetics: Introduce the basic concepts, categories, and development history of aesthetics, enabling students to understand the essence of beauty and the rules of formal beauty, and lay a theoretical foundation for understanding bridge aesthetics.

Introduction to Bridge Engineering: An overview of the types, structural forms, and development history of bridges, providing students with a preliminary understanding of bridge engineering.

Art History and Design History: Through the study of art history and design history, students learn to understand the art styles and design concepts of different periods and gain inspiration and references for bridge aesthetic design.

2.2. Design Elements

Form and proportion: Study the formal beauty of bridges, including lines, shapes, and proportions, and explore how to achieve visual harmony and beauty through reasonable design.

Color and Material: Analyze the impact of bridge color and material selection on aesthetic effects and learn how to use color and material to enhance the expressiveness of bridges.

Landscape and Environment: Emphasize the coordination between bridges and surrounding landscapes and environments, including natural landscapes and urban landscapes. Explore how to integrate bridges into the environment and create a beautiful scenic line.

2.3. Design Method

Creativity and conceptualization: Cultivate students' innovative thinking and design creativity and guide them to propose unique bridge aesthetic design solutions from different perspectives.

Hand drawing and model making: Using hand drawing and model making, teach students to intuitively express their design concepts and improve their design expression ability.

Computer-aided design: Introduce commonly used computer software in bridge aesthetic design, such as CAD and 3DMAX, to enable students to master digital design methods.

The specific content of the Bridge Aesthetics course is shown in Table 1.

3. Goal of Cultivating Output-Oriented Ability

The cultivation goals of output-oriented ability in bridge aesthetics mainly include the following aspects.

3.1. Professional Knowledge and Skills

The basic theories and methods of bridge aesthetics, including the principles of formal beauty, the use of color and material, and the coordination between landscape and environment, should be mastered. Students should be able to accurately analyze and evaluate the aesthetic value of bridges and possess a solid foundation in aesthetic theory.

Students should be familiar with the design and construction process of bridge engineering and understand the structural characteristics and technical requirements of different types of bridges. They should be able to combine aesthetic concepts with engineering practice while ensuring the safety and functionality of bridge structures, to achieve the maximization of aesthetic effects.

Students should be proficient in drawing and model making and able to accurately express their design concepts. They should have mastered computer-aided design software, such as CAD and 3DMAX, to improve design efficiency and quality.

3.2. Innovative Thinking and Design Ability

Students' innovative consciousness and ability should be cultivated, and they should be encouraged to boldly try new forms, materials, and technologies in bridge aesthetic design. They also should be capable of proposing unique design solutions to meet the needs of different clients and environments.

Students' design thinking ability should be improved, and comprehensive analysis and design should be conducted from multiple perspectives, such as user needs, environmental factors, and cultural backgrounds. They should be able to take into account various factors, such as aesthetics, engineering, and society, to achieve sustainable development in design.

Students' teamwork and communication skills should be strengthened, and their ability to collaborate with professionals from different fields should be cultivated during the design process. They must be able to effectively express their design intentions, listen to others' opinions and suggestions, and jointly complete high-quality design work.

3.3. Practical Ability and Professional Ethics

Through practical teaching and curriculum design, students' practical operation ability and problem-solving ability can be improved. They should be capable of independently completing bridge aesthetic design tasks in practical projects and dealing with various complex situations and challenges.

Students' professional ethics and sense of responsibility should be cultivated so they are able to understand the importance and social impact of bridge engineering. A rigorous work attitude, good professional ethics, and team spirit lay a solid foundation for future career development.

Students' social adaptability and competitiveness should be enhanced, and they should be equipped with the ability to engage in bridge aesthetic design work in different fields and industries. They should be able to continuously learn and update knowledge and adapt to developments and changes of society.

4. Evaluation System for Landscape Bridge Design Capability

The evaluation system for landscape bridge design capability can be constructed on the basis of the following aspects.

4.1. Design Creativity

Innovation: Whether the design has unique, creative, and innovative ideas and whether it can break through traditional design patterns.

Cultural integration: Whether local cultural characteristics, historical elements, etc., can be integrated into the design to reflect the regional cultural environment.

Function expansion: Whether the design has expanded other functions, such as leisure, sightseeing, etc., on the basis of meeting the transportation function.

4.2. Structural Rationality

Mechanical performance: Whether the structural design is reasonable and meets the mechanical requirements, such as those related to the bearing capacity and stability of the bridge.

Material selection: Whether the selected materials are suitable, have good durability, workability, etc.

Construction feasibility: Whether the design scheme is convenient for construction and whether the construction difficulty level and cost are within a reasonable range.

4.3. Aesthetic Expression

Formal beauty: Whether the shape of the bridge is beautiful, the lines are smooth, and the proportions are coordinated.

Color matching: Whether the selection of colors is in harmony with the surrounding environment and can create a good visual effect.

Landscape integration: Whether the bridge can blend with the surrounding natural and cultural landscapes to become a beautiful scenic line.

4.4. Environmental Coordination

Ecological and Environmental Protection: Whether the design considers the impact on the ecological environment and takes corresponding environmental protection measures.

Coordination with surrounding buildings: Whether the bridge and surrounding buildings are coordinated and together can form a harmonious whole.

Transportation convenience: Whether the design considers the rationality of traffic flow and can facilitate the passage of pedestrians and vehicles.

4.5. Plan Expression

Drawing quality: Whether the design drawings are standardized, clear, and accurate and whether they can fully express the design intent.

Scheme Explanation: Whether the explanation of the design scheme is clear and organized and can enable others to fully understand the design concept.

In the evaluation process, a combination of quantitative and qualitative methods can be used to set corresponding weights and scoring criteria for each evaluation indicator. Objective and accurate evaluation results can be obtained through a comprehensive evaluation of students' design work. At the same time, the evaluation system should also have a certain degree of flexibility and operability and be able to adjust and improve according to different teaching requirements and design tasks. Table 2 provides information about the landscape bridge design capability evaluation system.

5. Fuzzy Analytic Hierarchy Process Based on Interval Reliability Theory

5.1. Establishment of the Evaluation Index System

This study uses the fuzzy analytic hierarchy process to construct a hierarchical structure model for evaluating students’ aesthetic creation ability as it relates to landscape bridges [18]. The landscape creation capability evaluation (A) is targeted as the objective layer. The key factors for (B) evaluating the aesthetic creation ability of landscape bridges form the criterion layer, such as design creativity, structural rationality, aesthetic expression, and environmental coordination. The sub-element (C) of the criterion layer indicators, such as cultural integration, mechanical stability, and clarity of the plan, etc., is used as the indicator layer.

Figure 1. Evaluation System for Landscape Bridge Creation Ability.

Figure 1. Evaluation System for Landscape Bridge Creation Ability.

5.2. Indicator Weight

The evaluation system involves many indicators, and determining the role of each indicator in the evaluation is the key to the accuracy of the evaluation. This article uses the methods of the fuzzy judgment matrix and fuzzy consistency matrix to determine the indicator weights [19].

The recognition of the importance of each indicator is presented using a fuzzy judgment matrix, such as the fuzzy judgment matrix composed of each indicator under criterion layer B1, as follows.

(1)

This study uses three scales: 0, 0.5, and 1. Zero indicates that indicator i is more important than indicator i, 0.5 indicates that indicator j is as important as indicator i, and 1 indicates that indicator i is more important than indicator j. In the formula, b_ij represents the evaluation results of experts on the indicators in the i-th row and j-th column. Further transformation yields the fuzzy consistent matrix R as follows.

(2)

(3)

In the formula, r_i and r_j represent the sum of the indicators in the i-th and j-th rows of judgment matrix B1, and n is the number of indicators in B.

(4)

From this, the weights of each indicator in criterion layer B1 can be obtained, W₁=[w₁, w₂..., w_n]. The same method can be used to obtain W₂, W₃, W_n, and the weights W of each criterion layer in engineering geological suitability A.

5.3. Determination of the Single-Factor Evaluation Matrix

The individual indicators in the landscape bridge indicator layer will not be the same in specific projects but instead will vary. If we generalize the binary thinking of "good" and "poor", it will cause information loss and inaccurate evaluation. Therefore, this article uses interval numbers to express the ambiguity of each indicator [20]. The evaluation matrix for the interval numbers of each indicator in criterion layer B is shown in Table 3.

Among them, l_ij represents the membership interval [X_ij, Y_ij] of indicator C_i to scheme F_i, and the single factor evaluation matrix L_n is

(5)

5.4. Calculation of the Evaluation and Ranking Results

The evaluation result D_n of each criterion layer is obtained by multiplying the evaluation matrix L_n of each criterion by the weight W_n of each indicator of that criterion.

(6)

The final evaluation result E is obtained by multiplying the set of evaluation results D of each criterion layer item by the weight W of each criterion layer item in the overall evaluation.

$$E=W=\left[\begin{array}{l}{D}_1\\ D_2\\ \mathrm{...}\\ D_n\end{array}\right]=\left[p_1,p_2,\mathrm{...},p_n\right]$$

(7)

where p_i(i=1,2,…,m) is the final evaluation result for the i-th plan. The evaluation results can be divided into 4 levels on the basis of the rating: 0.75–1 is level 1, indicating good suitability; 0.5–0.75 is level 2, indicating moderate suitability; 0.25–0.5 is level 3, indicating moderate suitability; and 0–0.25 is level 4, indicating poor suitability.

Because of the interval form of P, the sorting of each interval adopts the ideal point method, which ranks indicators by comparing the evaluation results with the closeness of the optimal and worst solutions.

6. Evaluation Process for Landscape Bridge Design Ability

The specific process of evaluating students' landscape bridge design ability in the bridge aesthetics course using the output-oriented interval number fuzzy analytic hierarchy process is as follows.

6.1. Determine the Evaluation Index System

Analyze the teaching objectives of the Bridge Aesthetics course and the requirements for students' landscape bridge design abilities, and determine the main dimensions of evaluation, such as design creativity, structural rationality, aesthetic expression, environmental coordination, etc.

Further subdivide each major dimension and determine specific evaluation indicators. For example, design creativity can include indicators such as innovation and cultural integration; structural rationality can include indicators such as mechanical stability and material selection rationality.

6.2. Build a Hierarchical Structure Model

Set the evaluation objective (the student’s landscape bridge design ability evaluation) as the highest level.

Use the determined evaluation indicators as the middle and bottom layers, and construct a hierarchical structure model according to different hierarchical relationships.

6.3. Determine the Interval Number Fuzzy Judgment Matrix

Invite relevant experts (such as bridge designers, aesthetic experts, and teachers) to assess the relative importance of each evaluation indicator.

Because of the uncertainty and ambiguity of the evaluation process, expert judgments are represented in the form of interval numbers and fuzzy numbers. For example, for two indicators, A and B, experts may judge that "A is much more important than B", represented by interval fuzzy numbers [7,9].

On the basis of expert judgment, a fuzzy judgment matrix for interval numbers is constructed.

6.4. Calculate the of Indicator Weights

Using the calculation method of the interval number fuzzy analytic hierarchy process, process the interval number fuzzy judgment matrix and calculate the weights of each evaluation indicator.

Consistency checks are required during the calculation process to ensure the rationality of the judgment matrix. If the consistency check fails, it is necessary to invite experts to make a new judgment or adjust the judgment matrix.

6.5. Student Work Evaluation

Collect students' landscape bridge design works, including design drawings, scheme explanations, etc.

According to the evaluation index system, score each student's work. The scoring also adopts the form of interval fuzzy numbers to represent the uncertainty of the evaluation.

Weigh and sum the scores of various indicators for each student's work to obtain a comprehensive score of their work.

6.6. Result Analysis and Feedback

Analyze the comprehensive scores of students' works to understand their performance in different aspects.

On the basis of the evaluation results, provide specific feedback to students, highlight the strengths and weaknesses of the work, and provide guidance for further learning and improvement.

Teachers can also adjust teaching content and methods on the basis of evaluation results to improve teaching quality.

7. Application

7.1. Design Cases

Case background: Taking the actual creation of four landscape bridges as examples, evaluate their aesthetic creation ability. The description of each landscape bridge creation plan is as follows.

Plan A (see Figure 2): This plan is a concrete beam–style landscape bridge with a courtyard-like structure that spans a 10-m river.

Scheme B (see Figure 3): This scheme involves a wooden truss beam landscape bridge spanning a 300 m river.

Scheme C (see Figure 4): This scheme is a cable-stayed landscape bridge connecting three small islands in the center of a lake.

Scheme D (see Figure 5): This scheme is a cable-stayed landscape bridge connecting five intersections.

7.2. Construct a Judgment Matrix

1. Judgment matrix of the criterion layer on the target layer (landscape bridge creation ability)

Invite experts to make pairwise comparisons of the five elements of the criterion layer and provide interval number judgments. The obtained judgment matrix is as follows:

$$\left[\begin{array}{lllll}\left[(1,1),(1/2,2/3)\right]& \left[(3/2,2),(1,1)\right]& \left[(1/3,1/2),(1,2)\right]& \left[(1/4,1/3),(1/2,1)\right]& \left[(1/2,2),(3/2,1/2)\right]\\ \left[(2/3,3/2),(1,1)\right]& \left[(1,1),(1/2,2/3)\right]& \left[(1/2,1),(1/3,1/2)\right]& \left[(1/3,1/2),(1/4,1/3)\right]& \left[(1/3,1/2),(1/2,2/3)\right]\\ \left[(1/2,1),(2,3)\right]& \left[(2,3),(1,1)\right]& \left[(1,1),(1/2,2/3)\right]& \left[(1/3,1/2),(1/4,1/3)\right]& \left[(1/4,1/2),(3/4,1/2)\right]\\ \left[(1,2),(3/2,4)\right]& \left[(2,3),(3/2,4)\right]& \left[(3/2,4),(2,3)\right]& \left[(1,1),(1/2,2/3)\right]& \left[(1/2,1/4),(3/2,1/3)\right]\\ \left[(2/3,3/2),(1,2)\right]& \left[(3/2,4),(2,3)\right]& \left[(4,5),(3,4)\right]& \left[(2,3),(1,2)\right]& \left[(1,2),(3/2,1/4)\right]\end{array}\right]$$

2. Judgment matrix between the indicator layer and the criterion layer

The judgment matrix for design creativity (B1) based on innovation (C11) and cultural integration (C12) is as follows:

$$\left[\begin{array}{ll}\left[(1,1),(1/2,2/3)\right]& \left[(3/2,2),(1,1)\right]\\ \left[(2/3,3/2),(1,1)\right]& \left[(1,1),(1/2,2/3)\right]\end{array}\right]$$

The judgment matrix for the structural rationality (B2) based on the mechanical stability (C21) and material rationality (C22) is as follows:

$$\left[\begin{array}{ll}\left[(1,1),(1/3,1/2)\right]& \left[(2,3),(1,1)\right]\\ \left[(1/3,1/2),(1/4,1/3)\right]& \left[(1,1),(1/3,1/2)\right]\end{array}\right]$$

The judgment matrix for aesthetic expression (B3) based on formal aesthetics (C31) and color coordination (C32) is as follows:

$$\left[\begin{array}{ll}\left[(1,1),(1/4,1/3)\right]& \left[(3/2,3),(1,1)\right]\\ \left[(2/3,3/2),(1,1)\right]& \left[(1,1),(1/4,1/3)\right]\end{array}\right]$$

The natural environment (C41) and human environment (C42) have an impact on environmental coordination (B4), and the judgment matrix is as follows:

$$\left[\begin{array}{ll}\left[(1,1),(1/5,1/4)\right]& \left[(4/3,3/2),(1,1)\right]\\ \left[(2/3,3/4),(1,1)\right]& \left[(1,1),(1/5,1/4)\right]\end{array}\right]$$

The judgment matrix for the standardization of drawings (C51) and clarity of schemes (C52) in relation to the expression of schemes (B5) is as follows:

$$\left[\begin{array}{ll}\left[(1,1),(1/6,1/5)\right]& \left[(5/4,3/2),(1,1)\right]\\ \left[(2/3,4/5),(1,1)\right]& \left[(1,1),(1/6,1/5)\right]\end{array}\right]$$

7.3. Calculate the Weight Vector

(1) For the criterion layer judgment matrix

First, the root of the product of each row of elements is calculated.

First line:

$${\left[(1,1)\times (3/2,2)\times (1/3,1/2)\times (1/4,1/3)\times (1/2,1)\right]}^{1/5},$$

where $\left[(0.745,0.873),(0.623,0.762)\right]$.

In addition, other rows are calculated.

(2) For the indicator layer judgment matrix

The judgment matrix of innovation (C11) and cultural integration (C12) on design creativity (A) is taken as an example. The root of the product of each row of elements is calculated.

First line:

$${\left[(1,1)\times (3/2,2)\right]}^{1/2},$$

where $\left[(1.225,1.414),(1,1)\right]$.

Second line:

$${\left[(2/3,3/2)\times (1,1)\right]}^{1/2},$$

where the calculated

$$\left[(0.816,1.061),(1,1)\right].$$

Normalize processing: Assuming that the sum of weights under this criterion layer is 1, the weight interval of innovation (A11) in design creativity (A) obtained after normalization is

$$\left[(0.556,0.607),(0.476,0.538)\right].$$

The weight range of cultural integration (A12) in design creativity (A) is

$$\left[(0.444,0.393),(0.524,0.462)\right].$$

7.4. Perform a Consistency Check

The consistency index (CI) and consistency ratio (CR) are calculated. After calculation, the CI interval of the criterion layer judgment matrix is $\left[5.01,5.09\right]$. When the CR is calculated, the CR interval is $\left[0.005,0.045\right]$.

If the CR interval value is less than 0.1, the judgment matrix has satisfactory consistency.

For the indicator layer judgment matrix, the above steps are also performed for consistency testing.

7.5. Evaluate the Results of Landscape Creation Ability

The interval reliability theory proposed in this article is used to evaluate the aesthetic landscape design capability of bridges. For the four schemes in this case, the corresponding detailed evaluation results are as follows.

The weights between the four aesthetic design schemes for landscape bridges are as follows. The settlement results indicate that the order of the four creative schemes is as follows: the first is Plan D, the second is Plan B, the third is Plan C, and the fourth is Plan A.

$$A=\left[0.121,0.231,0.189,0.459\right]$$

The results between the five elements of the criterion layer corresponding to each design scheme are as follows. From the calculation results, one can see that for Plan A, the first ranking is structural rationality, the second ranking is aesthetic expression, the third ranking is scheme expression, the fourth ranking is environmental coordination, and the fifth ranking is design creativity. For Plan B, the first priority is aesthetic expression, the second priority is structural rationality, the third priority is environmental coordination, the fourth priority is scheme expression, and the fifth priority is design creativity. In terms of Plan C, the first priority is aesthetic expression, the second priority is environmental coordination, the third priority is design creativity, the fourth priority is scheme expression, and the fifth priority is structural rationality. For Plan D, the first priority is aesthetic expression, the second priority is structural rationality, the third priority is environmental coordination, the fourth priority is scheme expression, and the fifth priority is design creativity.

$$B_a=\left[0.188,0.212,0.203,0.197,0.200\right]$$

$$B_b=\left[0.125,0.231,0.302,0.207,0.135\right]$$

$$B_{\mathrm{c}}=\left[0.200,0.150,0.250,0.225,0.175\right]$$

$$B_d=\left[0.083,0.241,0.306,0.215,0.155\right]$$

On the basis of the above calculation and analysis results, the interval analytic hierarchy process is highly important for evaluating the creative ability of landscape bridges. First, it can make the evaluation more scientific, comprehensively consider multiple factors that affect creative ability, and determine reasonable weights to avoid subjective one-sidedness. Second, by quantifying the results it is possible to clearly compare the advantages and disadvantages of different creators or design schemes in various aspects. For example, its contribution to overall creative ability in terms of structural innovation and integration with the surrounding landscape can be accurately measured. These results provide a basis for selecting outstanding creators, optimizing design schemes, and promoting a better balance and development of landscape bridges in terms of art and function.

7.6. Discussion

By combining the interval reliability theory proposed in this article with the fuzzy analytic hierarchy process to evaluate the aesthetic landscape creation ability of bridges, and analyzing and discussing them in relation to the traditional analytic hierarchy process, the following three aspects are considered: scientific and accurate evaluation, risk and reliability assessment, and multi-scheme comparison and decision optimization.

(1) Improving the scientific basis and accuracy of evaluation

The weight determination of the general analytic hierarchy process in evaluating students’ ability to create landscape bridges often relies on the subjective judgment of experts. Although it has some rationality, there is uncertainty. The analytic hierarchy process for interval reliability introduces interval numbers and considers more fuzzy and uncertain factors.

For the evaluation of landscape bridge creation ability, the results of the interval reliability analytic hierarchy process have more advantages in terms of scientific accuracy. It can more finely depict the range of evaluation indicators; for example, when evaluating the aesthetic value of bridges, it not only considers the traditional aesthetic appearance but also reflects the fuzzy influence of cultural elements through interval numbers. This method can more accurately reflect the complex interrelationships between different factors in landscape bridge creation, avoid errors caused by single-value evaluation, and make the evaluation results closer to the actual level of creative ability.

(2) Improvement of risk and reliability assessment

The general analytic hierarchy process rarely involves risk- and reliability-related content in the evaluation process. The interval reliability analytic hierarchy process can provide a risk-and-reliability perspective for evaluating students’ ability to create landscape bridges through calculation results.

There are many risk factors in the design and creation of landscape bridges, such as the reliability of structural safety under different environmental conditions and the uncertainty of material durability. By using the interval reliability analytic hierarchy process, these risk factors can be included in the evaluation system, and the impact of risk on creative ability can be quantified through calculated results. For example, if a landscape bridge has a low level of reliability in its ability to withstand natural disasters such as floods, during its design, the student’s overall creative ability evaluation will be affected accordingly, prompting them to pay attention to potential risks during the design phase and improving the reliability of their work.

(3) Multi-scheme comparison and decision support optimization

When faced with multiple landscape bridge creation schemes, the general analytic hierarchy process can make basic comparisons, but its ability to handle complex conditions and uncertain information is limited. The results of the interval reliability analytic hierarchy process can better support multi-scheme comparisons and decisions.

Different landscape bridge creation schemes may have their own advantages and disadvantages in terms of functional implementation, cost control, and environmental adaptability. The calculation results of this method can clearly present the interval range of each scheme on various evaluation indicators, which can help decision-makers gain a more comprehensive understanding of the potential and risks of each scheme. For example, a scheme that excels in artistic innovation but has low reliability in the construction cost range can be compared with other schemes under a unified standard. Decision-makers can weigh the pros and cons of different solutions on the basis of the calculation results, choose the optimal solution in terms of comprehensive evaluation of creative ability, and improve the quality and efficiency of landscape bridge construction.

Compared with the general analytic hierarchy process, the interval reliability analytic hierarchy process has outstanding advantages and significant importance in evaluating students’ ability to create landscape bridges. In terms of advantages, the general analytic hierarchy process relies more on determined values and subjective judgments, whereas the interval reliability analytic hierarchy process introduces the concept of interval numbers, which can better cope with complex fuzzy information, such as vague aesthetic standards and uncertain environmental impacts in landscape bridge creation, making the evaluation results more realistic. At the same time, it can also calculate the reliability interval and effectively evaluate potential risks, such as bridge structure safety and durability, which is lacking in general methods. In terms of significance, this method provides a more scientific and comprehensive perspective for evaluating students’ ability to create landscape bridges. The results can provide a strong basis for the selection and optimization of design schemes, help decision-makers consider both artistic beauty and functional implementation as well as risk factors such as structural reliability, thereby promoting the development of landscape bridge design toward higher quality, safety, and innovation and enhancing the overall creative level.

8. Conclusion

This study applies output - oriented interval reliability theory to evaluate the landscape bridge design ability of Chinese students in bridge aesthetics courses. In line with sustainable development, it also considers ecological and environmental factors during the evaluation. It aims to overcome the limitations of traditional evaluation methods and more accurately measure students' performance in complex and uncertain landscape bridge design contexts. Traditional evaluation methods often overlook fuzzy factors in the design process, while this study's theoretical application provides a new way to comprehensively and scientifically evaluate students' abilities including their integration of sustainable concepts. This ensures the results better reflect their true level and guide teaching improvement and student development.The conclusions drawn from the practical application of the four landscape bridge creation cases are as follows.

(1) Interval reliability theory effectively addresses uncertainty problems by considering the interval range of parameters. This study, used output orientation to focus on the quality and reliability of student design outcomes. Output orientation emphasizes the final design output as the evaluation core, combined with interval reliability theory, which can quantitatively evaluate multiple aspects, including the structural safety, aesthetic value, and functional implementation of landscape bridges designed by students. For example, the indicator of structural safety is no longer a simple judgment of whether it is qualified or not but rather an analysis of safety under different environmental conditions based on reliability intervals, making the evaluation align more closely with actual design needs.

(2) In the case application of Chinese students, we collected landscape bridge design works from multiple groups of students. This theory is applied to evaluate multiple dimensions. In the aesthetic dimension, the interval reliability of the design's line fluency, color matching harmony, and other aspects were analyzed. In terms of functionality, the reliable range considers factors such as traffic capacity and integration with the surrounding environment. For example, a student's design has high reliability in color matching and good aesthetic literacy but has low reliability in terms of functional integration with the surrounding landscape, indicating insufficient consideration of environmental factors in the design. This detailed evaluation provides a targeted analysis of each student's design ability.

(3) Through in-depth analysis of the evaluation results, several interesting phenomena were discovered. On the one hand, some students have outstanding abilities in aesthetic performance, but there are shortcomings in combining aesthetics with structural reliability, reflecting a lack of knowledge integration ability. On the other hand, some students excessively pursue functional implementation in their designs while neglecting the reliable range of aesthetic values, resulting in an overall design imbalance. Moreover, from the overall data perspective, students generally perform poorly in considering the reliability of multiple factors when dealing with complex design requirements. These findings provide an important basis for adjusting curriculum teaching content and methods and suggest that teachers need to strengthen the cultivation of students' comprehensive design ability and multifactor balancing ability.

The results of this study have important implications for the teaching of bridge aesthetics courses. Teachers should pay attention to cultivating students' ability to combine aesthetics with reliability theory in the teaching process. Through various methods, such as case analysis and practical projects, students should be guided to comprehensively consider the interval reliability of various factors when designing. In the future, the evaluation index system can be further optimized to make it more refined and accurate. Moreover, this evaluation method can be extended to more related courses, laying the foundation for comprehensively improving students' landscape bridge design abilities, cultivating high-quality professional talent, and promoting the development and improvement of bridge aesthetics education.