Evaluation and Decision of a Seat Color Design Scheme for a High-Speed Train Based on the Practical Color Coordinate System and Hybrid Kansei Engineering

Abstract

Color is an important visual element of high-speed train seats, which has a significant impact on passenger travel experience. In order to solve the problem that color design relies on the subjective experience of designers, this study aims to establish an effective evaluation and decision method for seat color design in a high-speed train based on the Practical Color Coordinate System (PCCS) and hybrid Kansei Engineering. Firstly, we created a series of design schemes based on the typical colors in the PCCS. Secondly, a new hybrid Kansei Engineering system was constructed; in this system, forward Kansei Engineering was constructed with Factor Analysis (FA) and Multidimensional Scaling Analysis (MDS) to analyze the cognitive feature of color sample. The Analytic Hierarchy Process (AHP) and Independent Weight Coefficient Method (IW) were used to calculate comprehensive weights, and backward Kansei Engineering was constructed with the TOPSIS to optimize and evaluate color design schemes. Finally, the design and evaluation methods were illustrated with a case. The results showed that (1) the three main influencing factors of seat color design for high-speed trains included function, aesthetics and experience, and comfort and harmony; two other potential factors included calmness and relaxation. (2) In the PCCS, warm colors have a better esthetic, while cool colors are calmer. Tones with medium brightness and saturation such as It- and Sf-tones are the optimal choice, while the V-tone is not suitable for seat color design. The effectiveness of this method is verified by a case study, which provides a reference for seat color design evaluation and optimization of high-speed trains.

1. Introduction

With the rapid development of high-speed train technology, emotionalization and humanization have become a significant trend in train interior design [1]. In this context, research on the visual effect design of high-speed train interiors has been increasingly gaining attention [2]. Color is an important visual element for the high-speed train interior environment; creating a comfortable and reasonable color environment is one of the most important tasks in high-speed train interior design [3]. Color design can improve passengers’ emotional experience, reduce passengers’ visual fatigue, and enhance the design’s esthetic effect [4]. Seats are one of the essential facilities in high-speed train interiors; their color design is an important part of the high-speed train interior environment’s visual effect. Examples of various high-speed train seat colors collected from the web are shown in Figure 1.

Color has always been one of the hot research topics in the industrial design research field. It involves different factors such as function, esthetics, culture, etc. In the past, the research method of color design was mainly based on the description of subjective experience. With the development of color science research, various color analysis systems have provided new techniques for the quantitative research of color [5]. At present, the Ostwald color system [6], the Munsell color system [7], the Natural Color System (NCS) [8], and the Practical Color Coordinate System (PCCS) [9] are widely used in color research.

The PCCS integrates the respective advantages of the Ostwald system, Monsell system, and NCS; it combines the brightness and saturation of colors to establish a tone map, which makes color perception more intuitive.

Kansei Engineering is one of the most important methods of emotion research for product design, and it is a combination of qualitative and quantitative methods used to analyze the psychological cognition of users and the emotional features of products [10]. This method was first introduced by Mitsuo Nagamachi in the 1970s [11], and it is widely used in the research field of product style design. Kansei Engineering can be divided into forward Kansei Engineering and backward Kansei Engineering [12]. Forward Kansei Engineering transforms the emotional responses of users into design elements [13], and backward Kansei Engineering obtains the emotional responses of users by analyzing the product’s design features [14]. Hybrid Kansei Engineering combines the two methods to analyze the relationship between users’ emotional responses and product design features [15].

Traditional Kansei Engineering is usually used for emotional cognition research on product color in one dimension, while hybrid Kansei Engineering is used for analyzing the emotional level of products and users from multiple dimensions, which can make up for the shortcomings of traditional Kansei Engineering research.

In summary, high-speed train seat color design is a combination of emotion and function. It is closely related to the users’ emotional cognition, which has a significant impact on passengers’ psychological feelings. However, how to evaluate and decide the color design scheme objectively is one of the problems that needs to be solved in the field of high-speed train industrial design. In order to solve this problem, this study combines the PCCS with hybrid Kansei Engineering to establish evaluation and optimization method for color design.

In this study, the PCCS is used for the quantitative analysis of colors, and a hybrid Kansei Engineering system is established to analyze the emotional features of different colors, so as to provide references for designers to evaluate and optimize the design scheme.

The framework of this research is shown in Figure 2. The main structure of this research is as follows: In Section 2, the relevant literature on seat color design and hybrid Kansei Engineering was reviewed to identify the shortcomings of the current research, providing a basis for our method design. In Section 3, through the theoretical analysis of the PCCS and hybrid Kansei Engineering, an evaluation and decision model is constructed. In Section 4, the method is illustrated through a study case. In Section 5, the results are analyzed and discussed, and Section 6 provides the summary and prospect of the full research.

2. Literature Review

Color is one of the most intuitive visual elements for product appearance [16]. Various colors will make users experience different emotional cognition. This has been a concern in the fields of vehicle design, interior architecture, and product style design. Wagner, AS et al. [17], by comparing different types of automotive interior color design, obtained preferences of color design and proposed that reasonable colors and patterns can improve the lightweight and spacious sense of automotive interiors. Stoykov, D [18] used VR technology to study the color design of camper van interiors. Chen, YH et al. [19] used fuzzy-set theory and Kansei Engineering to study the color matching design of aircraft cockpits and obtained emotional evaluation results for different color schemes. Gunes, Elif et al. [20] studied the emotional responses to different buildings’ indoor colors and obtained the emotional reactions to various colors. Manav, B [21] obtained emotional keywords by studying the emotion associations of color matching in the built environment. Park, BH et al. [22] studied different interior styles using the data-driven method to provide references for the collocation of interior colors and materials. Yu, LW et al. [23] studied the impact mechanism of consumers’ purchase decisions by analyzing color association.

The PCCS was proposed by the Japan Color Research Institute in 1964 [24]. It combines the advantages of the Ostwald color system and Munsell color system [25], and it is intuitive and easy to operate; as such, it is widely used in research into clothing, products, architecture, and other fields. Yu-En Yeh [26] combined an artificial neural network and genetic algorithm to construct a product color optimization method based on the PCCS. Zhang B C et al. [27] proposed an APP color evaluation method suitable for children with autism spectrum disorder based on the PCCS and AHP-TOPSIS; this study suggested that the PCCS is an intuitive method for obtaining color features. Chen T Y et al. [28] combined the PCCS and Grey Relational Analysis to propose a product color design method for color scheme creation. Chen W W et al. [29] took eight representative styles of clothing in different colors as the research object and used the PCCS to obtain the relationship between color attributes and style descriptions. Kim, SeongJin [30] used the PCCS to analyze the distribution feature and image feature of shop sign colors. Gao S et al. [31] combined the PCCS with the Grey Clustering Method to evaluate and study the color matching of a user interface for the elderly. Bai G T et al. [32] obtained typical colors through the PCCS to create a design scheme for elderly-oriented furniture and, through combination with the fuzzy comprehensive evaluation method, provided a reference for design creation.

Based on the above research, the PCCS is a frequently used analytical tool in color research, which has strong practicability, and this color system can help to analyze the color characteristics accurately.

Kansei Engineering is a method focused on the users’ emotional demands and product features. It can transform emotional elements into concrete design elements. Kansei Engineering is divided into forward Kansei Engineering (where users’ emotional needs infer product features) and backward Kansei Engineering (where product features infer users’ emotional responses). Hybrid Kansei Engineering combines forward Kansei Engineering and backward Kansei Engineering. It was first proposed by Matsubara, Y and Nagamachi, M in 1995 [33]. It is a bidirectional Kansei Engineering system, which can not only obtain the user’s emotional response but can also extract the emotional characteristics of the product. It provides a effective reference for product scheme optimization and decision-making.

Kansei Engineering is mainly used for studying emotional data based on various mathematical models. Some scholars obtain the relationship between landscape color and Kansei words through the semantic difference method (SD) [34]. Multidimensional Scaling Analysis (MDS) is usually used to analyze and classify the color features [35]. Some scholars use Factor Analysis (FA) to obtain the key semantic features of product emotion design [36]. Some scholars evaluate the emotional features of products through the Analytic Hierarchy Process (AHP) [37] and fuzzy comprehensive evaluation (FCE) [38].

Hybrid Kansei Engineering has advantages as it can extract users’ emotional responses and perform cognitive analysis of products’ emotional features. It is continuously used in the research field of product color, shape, ergonomics, and other factors. Xue L [39] used hybrid Kansei Engineering to study the image system of high-speed train seats and established a decision system for image design and evaluation. Liu X [40] used hybrid Kansei Engineering to study the ergonomics of the interior environment of an aircraft cabin, providing a reference for the ergonomic design of the aircraft cabin. Zhao L [41] used hybrid Kansei Engineering to study the styling design of laptop computers. Wu T Y et al. [42] proposed a product color design method based on hybrid Kansei Engineering. In the related research on hybrid Kansei Engineering, Factor Analysis, the AHP, the TOPSIS, and other methods are widely used. Quan HF et al. [43] established a product evaluation method by integrating Factor Analysis, the AHP, the entropy weight method, GRA, and the TOPSIS. Liu DS et al. [44] evaluated the product design scheme by integrating the triangular fuzzy method, Kansei Engineering, GRA, and the TOPSIS. Li M et al. [45] combined Factor Analysis, the AHP, and the TOPSIS to provide an objective method for the theme selection of handicraft designs, and explained the method using design cases. Deng L et al. [46] combined Kansei Engineering and the TOPSIS to establish an esthetic evaluation method for Human–Machine Interaction Interface layout.

As seen in relevant studies, hybrid Kansei Engineering is a combination of various methods such as Factor Analysis, the AHP, the TOPSIS, and others. Factor Analysis can reduce the dimensions of data, while MDS can be used to analyze object similarity. AHP methods are often combined with other weight calculation methods to avoid relying too much on the subjective experience of experts. The TOPSIS is a common evaluation and optimization method.

In recent years, the interior color design of high-speed trains has gradually attracted attention. Zhi J y [47] used Kansei Engineering to study the visual perception of high-speed train seats’ color. Xu X f et al. [48] established an interior color design method for high-speed trains based on the NCS. Xie Xh [49] proposed a subway train interior design method based on the NCS and Kansei Engineering. Qiao C et al. [50] analyzed the esthetic elements of color design for subway train interiors and proposed that harmony and balance were the key elements needed for the esthetic design of train interiors.

To sum up, the PCCS is a intuitional and practical color analysis tool. Hybrid Kansei Engineering is one of the most efficient methods for the emotional analysis of users and products. The combination of the PCCS and hybrid Kansei Engineering can provide guidance for the evaluation and optimization of seat color design for high-speed trains.

Based on the above related research, this study constructs a comprehensive color optimization and evaluation method. Firstly, this study uses the PCCS to analyze the typical color features of different types of seats. Secondly, Factor Analysis is combined with Multidimensional Scaling Analysis to explore the potential influencing factors of color perception. Thirdly, a comprehensive weight calculation method is constructed to avoid the shortcomings of the AHP, and it is combined with the TOPSIS to optimize and evaluate the color design scheme.

3. Materials and Methods

3.1. Evaluation and Decision Model Based on the PCCS and Hybrid Kansei Engineering System

In this study, the evaluation and decision model for high-speed train seat color design is established mainly from two dimensions: the PCCS and hybrid Kansei Engineering.

Firstly, based on the analysis of the seat color design of high-speed trains, typical colors were extracted from the color wheel and tone map in the PCCS.

Secondly, a hybrid Kansei Engineering model was constructed using color emotional cognition and color scheme evaluation. The model uses Factor Analysis (FA) and Multidimensional Scaling Analysis (MDS) to analyze the cognitive characteristics of different color design schemes. Then, the AHP method and Independent Weight Coefficient Method (IW) were combined to calculate the comprehensive weight of color as an influencing factor. The TOPSIS method was used to optimize and analyze the design scheme.

For the hybrid Kansei Engineering, a forward Kansei Engineering system was established using FA and an MDS to obtain the cognitive characteristics of different colors. The AHP-IW and TOPSIS were used to construct a backward Kansei Engineering system, which was used to evaluate and optimize different color design schemes.

Finally, we analyzed the color selection and evaluation results in the PCCS. This study provides a color scheme reference and effective design suggestions for the seat color design of high-speed trains.

The research route and methods are shown in Figure 3.

3.2. Practical Color Coordinate System

The PCCS is a practical color analysis system, which has the advantages of both the Ostwald color system and Munsell color system. The PCCS color wheel has 24 hues in total and is based on the psychological primary colors of red, yellow, blue, and green. It can be divided into 4 parts: 1–8 are warm colors, 9–12 are slightly cold colors, 13–19 are cool colors, and 20–24 are slightly warm colors [51]. The 24-hue color wheel analysis is shown in Figure 4 [52].

In the PCCS, the brightness values are divided into 17 levels, from 1.5 to 9.5, and the brightness is determined from a low level to a high level; each 0.5 increment is a level. The saturation value is divided into 9 levels, from 1 s to 9 s, and the saturation is determined from a low level to a high level; each increment of 1 is a level [53,54]. Brightness is shown on the vertical axis, and saturation is on the horizontal axis, as shown in Figure 5.

The PCCS integrates colors from the dimensions of tone, brightness, and saturation and displays the brightness and saturation of color in the plane from the perspective of tone. The user can obtain the color feature description of the brightness and saturation by analyzing the position in the tone map.

In the PCCS tone map, the color saturation (0 s–9 s) increases from left to right in the horizontal direction. The brightness (1.5–9.5) of the color increases from the bottom to the top in the vertical direction. The upper left is the high-brightness, high-saturation area. The lower left is the low-brightness, low-saturation area. The upper right is the high-brightness, low-saturation area. The lower right is the low-brightness, high-saturation area. Based on the above analysis, the PCCS tone map can be divided into 4 areas (chroma is not included), including the light tone area, pure tone area, dark tone area, and medium tone area [55]. The analysis of the PCCS hue diagram is shown in Figure 6 [56].

3.3. Hybrid Kansei Engineering System

Kansei Engineering is a technology for measuring and obtaining users’ emotional responses [57], which is commonly used with the semantic difference method (SD method). The SD method uses a Likert scale to obtain the user’s emotional response by scoring the Kansei words [58], as shown in Figure 7.

In this study, the emotion measurement method is mainly based on the statistical analysis results of the questionnaire survey.

Hybrid Kansei Engineering is a bidirectional emotion measurement system. In forward Kansei Engineering, users’ emotional responses are transformed into design elements by measuring Kansei words. In backward Kansei Engineering, the Kansei word description of the emotional features of the product style is obtained by analyzing the emotional elements of the product. The principle of hybrid Kansei Engineering is shown in Figure 8.

Forward Kansei Engineering is used to obtain the user’s emotional cognition result. The user’s emotional cognition for typical color samples is measured using the SD method based on Kansei words. Key semantic features and emotional cognitive dimensions of the color samples are obtained using Factor Analysis (FA) and Multidimensional Scaling Analysis (MDS).

Backward Kansei Engineering is used to evaluate the emotional features of color schemes. The AHP and the Independent Weight Coefficient Method (IW) are combined to constitute the comprehensive weight. The comprehensive weight was combined with the TOPSIS to optimize and evaluate the schemes, and then the ranking and emotional characteristics of each design scheme were obtained. The construction process of the hybrid Kansei Engineering system is shown in Figure 9.

3.3.1. Factor Analysis

Factor Analysis (FA) is a multivariate statistical method used to extract the correlation between multiple variables [59]. It is a multivariate statistical analysis method that summarizes variables with complex information relationships into a few unrelated factors. This method can use relatively few independent factors to explain the majority of the original data. The FA principle is shown in Equation (1) [60].

(1)$$\begin{gathered} y_1=l_{11}{F}_1+l_{11}{F}_2+\dots +l_{1m}{F}_m+{\epsilon }_1 \\ {y}_2=l_{21}{F}_1+l_{21}{F}_2+\dots +l_{2m}{F}_m+{\epsilon }_2 \\ \dots \\ {y}_p=l_{p1}{F}_1+l_{p1}{F}_2+\dots +l_{pm}{F}_m+{\epsilon }_p \end{gathered}$$

where y₁, y₂, …, y_p represent random vectors of the original variable p, and the coefficient l_ij is the loading of the j variable on the k factor, which reflects the interpretation of the variable by the factor. F = (F₁, F₂, …, F_m) are the common factors, ε = (ε₁, ε₂, …, ε_p) are special factors, and F and ε are unobservable (m < p).

3.3.2. Multidimensional Scaling Analysis

Multidimensional Scaling Analysis (MDS) is a dimensionality reduction method that can be used to identify similarities between study objects [61]. It can be used to display the relationships between multiple study objects in a lower-dimensional space (usually a two-dimensional space) and reflect the similarities.

Euclidean distance is often used as the similarity measure of MDS, in which d_ij is the Euclidean distance between the i and j objects, and y₁, y₂, …, y_n represent data points after dimensionality reduction. Methods such as Basic SMACOF can be used to optimize. The objective function is shown in Equation (2) [62].

(2)$f(ij)=\min {{\displaystyle \sum _{i<j}\left(\left|y_i-\right.\left.y_j\right|-d_{ij}\right)}}^2$

In MDS, the stress coefficient is used to calculate fitness [63], as shown in Equation (3).

(3)$Stress=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1,j=1,i\ne j}^n(d_{ij}-{\widehat{d}}_{\mathrm{ij}}{)}^2}}{{\displaystyle \sum _{i=1,j=1,i\ne j}^n{d_{ij}}^2}}}}$

3.3.3. Comprehensive Weight by AHP-IW

• (1).. The subjective weight is calculated by the AHP

The Analytic Hierarchy Process (AHP) is a multidimensional criteria analysis methodology proposed by T.L. Saaty in the 1970s [64]. The method treats the multi-objective decision problem as a system and decomposes the objective system into different indicators. It compares the influence degree of each indicator based on the subjective experience of experts, and then calculates the weight ranking of each indicator [65], as shown in Figure 10. Table 1 describes the importance and scores between the two indicators.

The main calculation process of the AHP is shown in Equations (4)–(10).

The judgment matrix A is constructed through pairwise comparison and scoring between the evaluation indicators by experts.

(4)$A={\left(a_{ij}\right)}_{nm}=\left[\begin{array}{llll}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ a_{n1}& a_{n2}& \cdots & a_{nn}\end{array}\right]$

The geometric average method is employed to determine the weight value of each index. To calculate the product Ai for each row value in the judgment matrix, the following equation is used:

(5)$A_i={\displaystyle \prod _{j=1}^n{a}_{ij}\left(i=1,2,\cdots ,n\right)}$

To calculate the geometric mean of A_i, the following equation is used:

(6)$\overline{W_{s,i}}=\sqrt[n]{A_i}(i=1,2,\cdots ,n)$

The relative weight Wsi is obtained after normalization using the following equation:

(7)$W_{s,i}={\displaystyle \frac{\overline{W_i}}{{\displaystyle \sum _{i=1}^n{\overline{W}}_i}}}\left(i=1,2,\cdots ,n\right)$

The largest eigenvalue is calculated using the following equation:

(8)${\mathsf{\lambda }}_{\max }={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\frac{{\left(A·W\right)}_i}{n{W}_i}}$

The consistency index calculation for a consistency test is as follows:

(9)$CI={\displaystyle \frac{{\mathsf{\lambda }}_{\max }-n}{n-1}}$

Finally, the consistency ratio (CR) is calculated according to a random consistency coefficient value (RI, as shown in Table 2). When CR < 0.1, it indicates that the consistency of the matrix is acceptable; if this is not the case, the matrix needs to be adjusted again [66].

(10)$CR={\displaystyle \frac{CI}{RI}}$

• (2).. The objective weight is calculated by IW

The Independent Weight Coefficient (IW) method is an objective method to obtain weights. It uses multiple regression analysis to calculate the multiple correlation coefficient between indicators and then obtains the indicator weight. In this method [67], a larger multiple correlation coefficient represents more repetitive information, illustrating that the indicator is more easily replaced by other indicators, so its weight should be smaller [68].

Firstly, according to the questionnaire, the evaluation matrix B of m subjects for n indicators is established, as shown in Equation (11).

(11)$B=\left(b_{ih}\right)=\left[\begin{array}{llll}{b}_{11}& b_{12}& \cdots & b_{1m}\\ b_{21}& b_{22}& \cdots & b_{2m}\\ \cdots & \cdots & \cdots & \cdots \\ b_{n1}& b_{n2}& \cdots & b_{nm}\end{array}\right]$

where b_ih is the score value of the h subject on the i index, h = 1, 2, ⋯, m.

The multiple correlation coefficient (ρ_i) between an indicator and other indicators is obtained through linear regression analysis. The independence weight coefficient is calculated by Equation (12):

(12)$W_{o,i}={\displaystyle \frac{{\rho }_i^{-1}}{{\displaystyle \sum _{i=1}^n{\rho }_i^{-1}}}}$

• (3).. Comprehensive weight calculation

Based on the subjective weights calculated by the AHP and the objective weights calculated by the IW, the product method can be used to calculate comprehensive weight [69], as shown in Equation (13):

(13)$W_{C,i}={\displaystyle \frac{W_{s,i}·W_{o,i}}{{\displaystyle \sum W_{s,i}·W_{o,i}}}}$

3.3.4. TOPSIS Method

The TOPSIS method is an evaluation method for multi-attribute problems, which was proposed by C.L. Hwang and K. Yoon in 1981 [70]. This method is a evaluation and decision-making method used to sort finite evaluation objects according to the distance between the best solution and the worst solution [71]. The principle of this method is as follows.

The evaluation matrix X is constructed by m evaluation objects and n evaluation indicators.

(14)$X=\left[\begin{array}{llll}{\mathrm{x}}_{11}& {\mathrm{x}}_{12}& \cdots & {\mathrm{x}}_{1m}\\ {\mathrm{x}}_{11}& {\mathrm{x}}_{12}& \cdots & {\mathrm{x}}_{2m}\\ \cdots & \cdots & \cdots & \cdots \\ {\mathrm{x}}_{n1}& {\mathrm{x}}_{n2}& \cdots & {\mathrm{x}}_{nm}\end{array}\right]$

The evaluation matrix X is standardized. In this study, the sum of squares normalization (SSN) method is used to normalize the data [72]. The calculation formula is shown in Equation (15).

(15)$z_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{{\displaystyle \sum _{i=1}^n{x}_{ij}^2}}}}$

The weighted evaluation matrix Z’ is obtained by weighting the normalized data, as shown in Equation (16).

(16)$Z^{\prime }=Z·W=\left[\begin{array}{llll}{z^{\prime }}_{11}& {z^{\prime }}_{12}& \cdots & {z^{\prime }}_{1m}\\ {z^{\prime }}_{21}& {z^{\prime }}_{22}& \cdots & {z^{\prime }}_{2m}\\ \cdots & \cdots & \cdots & \cdots \\ {z^{\prime }}_{n1}& {z^{\prime }}_{n2}& \cdots & {z^{\prime }}_{nm}\end{array}\right]$

Based on matrix Z’, the positive and negative ideal solutions can be determined, as shown in Equations (17) and (18).

(17)$C^{+}=\{\max \left(c_{i1}\right),\max \left(c_{i2}\right),\cdots \max \left(c_{in}\right)\}i=1,2,\cdots ,m$

(18)$C^{-}=\{\min \left(c_{i1}\right),\min \left(c_{i2}\right),\cdots \min \left(c_{in}\right)\}i=1,2,\cdots ,m$

The Euclidean distance between each object to be evaluated and the positive and negative ideal solutions are calculated according to Equations (10) and (11), respectively.

In Equation (19), d_i⁺ is the Euclidean distance between the i th object to be evaluated and the optimal solution.

In Equation (20), d_i⁻ is the Euclidean distance between the i th object to be evaluated and the worst solution.

(19)$d_i^{+}=\sqrt{{{\displaystyle \sum _{j=1}^n\left(c_{ij}-c_j^{+}\right)}}^2}$

(20)$d_i^{-}=\sqrt{{{\displaystyle \sum _{j=1}^n\left(c_{ij}-{\mathrm{c}}_{ij}^{-}\right)}}^2}$

Finally, the score value E_i of the evaluation object is obtained, as shown in Equation (21).

(21)$E_i^{+}={\displaystyle \frac{d_i^{-}}{d_i^{+}+d_i^{-}}}$

4. Case Study

4.1. Typical Color Acquisition and Scheme Creation Based on PCCS

In order to obtain the uniformity of color sample distribution and reflect the actual train seat color design case, in this study, four typical hues were selected from the four regions (warm, slightly warm, cold, and slightly cold) of the color wheel. Then, five typical tones (two from the medium tone) were selected from the four areas of the PCCS tone map (light tone area, pure tone area, dark tone area, and medium tone area). The PCCS numbers and HSB numbers of 20 typical color samples are shown in Table 3.

On this basis, 20 seat color design schemes (K1-K20) of high-speed trains were generated. All color design effects were rendered in blender 4.0 software and the image size is 1920 × 1080 pixels, as shown in Figure 11.

4.2. Color Emotional Cognitive Characteristics Analysis Based on Forward Kansei Engineering

Forward Kansei Engineering was used to obtain the emotional cognitive characteristics of color, and the methods included FA and MDS.

Firstly, through the collection of comments on color from the relevant literature about color design (Web of Science, CNKI, etc.) [73,74,75], relevant adjectives were selected as emotion evaluation vocabulary. The adjectives with strong typicality and no ambiguity were selected as Kansei words to constitute the positive and negative adjective groups, and finally, 10 groups of typical Kansei words were obtained, as shown in Table 4.

Combined with typical Kansei words, the SD method (−3 to 3) is used to measure the emotional degree of color design schemes, and the questionnaire example is shown in Table 5.

Secondly, the emotional features of 20 color design schemes were surveyed by an emotional cognition questionnaire. A total of 40 adults (the subjects had normal vision, no color blindness, or color weakness) were invited to participate in the questionnaire survey. The subjects were scored according to the effect of 20 color design schemes (Figure 11). The questionnaire indicators and scores were input into SPSS 22 software to calculate average values, as shown in Table 6.

The questionnaire results were input into SPSS 22 software for FA. The KMO was 0.518 and the Bartlett’s test of sphericity was 0.000 (<1%), indicating that the questionnaire data can be factor-analyzed. The total explained variance is presented in Table 7.

The first three factors explain 82.693% of the variable information, so the number of extracted factors was set to three. The factors were rotated with the maximum variance method. Factor classification of the Kansei words was performed according to the absolute value of the rotated component matrix, and the smaller absolute value was removed to avoid visual interference. The rotated component matrix is shown in Table 8.

Factor 1, named the function factor, consists of S2 (Lively–Dull), S3 (Elegant–Vulgar), S6 (Light–Heavy), S7 (Soft–Stiff), and S8 (Wide–Narrow) and mainly reflects the function feature of color design.

Factor 2, named the convenience factor, consists of S1 (Amiable–Aloof), S5 (Romantic–Rational), and S10 (Calm–Excited) and mainly reflects the esthetic feature of color design.

Factor 3, named the experience factor, consists of S4 (Upscale–Cheap) and S9 (Innovative–Conservative) and mainly reflects the sense of experience of color design.

The component score coefficient calculated according to SPSS 22 software, and the scoring formulas of each factor are shown in Equations (22)–(24).

F₁ = −0.201 × S₁ + 0.174 × S₂ + 0.308 × S₃ + 0.146 × S₄ + 0.293 × S₅ + 0.277 × S₆ + 0.087 × S₇ + 0.262 × S₈ − 0.076 × S₉ + 0.122 × S₁₀(22)

F₂ = 0.441 × S₁ − 0.061 × S₂ − 0.026 × S₃ − 0.021 × S₄ + 0.152 × S₅ − 0.103 × S₆ + 0.209 × S₇ − 0.132 × S₈ − 0.075 × S₉ − 0.438 × S₁₀(23)

F₃ = 0.299 × S₁ + 0.099 × S₂ − 0.173 × S₃ − 0.488 × S₄ − 0.393 × S₅ − 0.053 × S₆ + 0.068 × S₇ + 0.008 × S₈ + 0.372 × S₉ + 0.034 × S₁₀(24)

The rankings of the factor 1 scores for the 20 schemes are shown in Figure 12. The scores from low to high indicate the functionality of the color from good to poor.

The ranking of the factor 1 scores shows that medium/high-brightness and -saturation colors are more suitable for the basic functional needs of human vision. The functionality of low-brightness and -saturation colors is poor.

The rankings of the factor 2 scores for the 20 schemes are shown in Figure 13. The scores from low to high indicate the esthetic of a color from good to poor. It shows that the esthetic of warm colors is better than cool colors.

The rankings of the factor 3 scores for the 20 schemes are shown in Figure 14. The scores from low to high indicate the experience of a color from good to poor. The ranking of factor 3 scores shows that high-saturation colors create a sense of experience more easily.

Thirdly, in order to obtain the similarity and potential influencing factors among the 20 design schemes, the data were analyzed by MDS using SPSS 22 software. In SPSS 22 software, stress was 0.11971 and RSQ was 0.91730; this shows that the fitting of the data is good. The stimulus coordinates diagram of the analysis results is shown in Figure 15.

According to the MDS results, in the horizontal direction, from left to right, the brightness of the colors varies from low to high, reflecting a move from solemnity to relaxation. In the vertical direction, from the bottom to the top, the colors vary from cool to warm, reflecting a move from enthusiasm to indifference.

The right side of the color map can be used as a color design preference. The top right is relaxation–calm, and the bottom right is relaxation–enthusiasm. The color cluster distribution map is shown in Figure 16.

4.3. Evaluation of Color Design Scheme Based on Backward Kansei Engineering

Backward Kansei Engineering is used to evaluate and optimize design schemes, and the main methods include AHP-IW and TOPSIS.

Firstly, an evaluation index of seat color design for high-speed trains was established using FA results and the AHP model. In the overall color evaluation framework, the main factors include functional level, esthetic level, and experience level; each level is divided into three aspects, as shown in Table 9.

Based on the color evaluation indicators (Table 9), this study invited 10 experts from industrial design and high-speed train interior design research to compare and score each indicator. Then, the AHP (Equations (4)–(10)) was used to calculate the weight of each index. The results are shown in Table 10, Table 11, Table 12 and Table 13.

The calculation results satisfy the criterion CR < 0.1 in Table 12, Table 13, Table 14 and Table 15. This indicates that the consistency of the judgment matrix passes the test. The overall weight can be obtained by multiplying the first-level index weight and the second-level index weight. The weight analysis of evaluation indicators of color design is shown in Table 14.

Secondly, the objective weight is calculated using the Independent Weight Coefficient Method (IW) based on the questionnaire. A 5-level rating scale (1–5) was used for scoring: a higher score indicates a higher degree of importance. A total of 40 individuals rated the importance of nine indicators. According to Equations (11) and (12), the objective weights were calculated, as shown in Table 15.

On the basis of the obtained subjective weights and objective weights, the product method (Equation (13)) was used to calculate the comprehensive weights, and the results are shown in Table 16.

Thirdly, the TOPSIS was used to evaluate and optimize the design scheme. A total of 40 individuals rated 20 color design schemes based on nine indicators (Table 1). The score scale is from 1 to 10, indicating very poor (0 <~≤ 3), poor (3 <~≤ 5), general (5 <~≤ 6), good (6 <~≤ 8), and excellent (8 <~≤ 10). Then, the TOPSIS method was used to evaluate and rank the schemes.

By calculating the arithmetic mean of the score data, the matrix Z after normalization according to Equation (15) was as follows:

$Z=\left[\begin{array}{l}2.7502.9252.6253.5003.3005.0755.3753.8503.850\\ 5.2254.9253.6253.3252.9005.2503.3752.3251.850\\ 6.0504.7753.6753.3752.9505.4003.4752.4751.950\\ 5.0754.7254.4753.7253.2005.5505.1505.9505.325\\ 6.2256.1756.0506.0505.1755.9005.4756.6005.300\\ 6.5506.2256.2006.1505.5006.1005.7756.7005.350\\ 6.7006.4506.3506.2255.6756.2255.8506.6505.425\\ 6.3006.3756.3006.3505.7506.3006.3256.8005.750\\ 4.3004.3505.6255.3503.9506.3004.3254.8004.100\\ 6.1756.2756.0755.4504.8506.4004.4004.7254.250\\ 6.2506.2006.1755.4754.8756.4254.4254.7504.875\\ 5.4755.2755.0756.4505.8506.2756.0506.1506.050\\ 4.1503.3503.6254.3502.9505.1753.2503.6753.050\\ 6.4005.8756.0255.3004.8506.4254.3754.7004.200\\ 6.5504.8506.0505.2504.8755.6504.3754.6004.225\\ 5.5504.7755.8505.6754.9755.9005.8256.0755.450\\ 5.5254.6254.8503.9753.8504.5004.1254.4253.900\\ 6.6503.6755.2254.2503.8253.9753.3753.6253.425\\ 6.6754.7005.0504.8504.7005.6003.5753.7753.600\\ 4.5504.6755.0755.3755.0255.4504.4505.6004.150\end{array}\right]$

The normalized matrix Z was multiplied by the corresponding weights (Table 16) to obtain the weighted matrix Z’.

$Z^{\prime }=\left[\begin{array}{l}0.2500.5623.0820.0840.1781.3450.0860.1310.254\\ 0.4750.9464.2560.0800.1571.3910.0540.0790.122\\ 0.5510.9174.3140.0810.1591.4310.0560.0840.129\\ 0.4620.9075.2540.0890.1731.4710.0820.2020.351\\ 0.5661.1867.1030.1450.2791.5640.0880.2240.350\\ 0.5961.1957.2790.1480.2971.6170.0920.2280.353\\ 0.6101.2387.4550.1490.3061.6500.0940.2260.358\\ 0.5731.2247.3960.1520.3111.6700.1010.2310.380\\ 0.3910.8356.6040.1280.2131.6700.0690.1630.271\\ 0.5621.2057.1320.1310.2621.6960.0700.1610.281\\ 0.5691.1907.2490.1310.2631.7030.0710.1620.322\\ 0.4981.0135.9580.1550.3161.6630.0970.2090.399\\ 0.3780.6434.2560.1040.1591.3710.0520.1250.201\\ 0.5821.1287.0730.1270.2621.7030.0700.1600.277\\ 0.5960.9317.1030.1260.2631.4970.0700.1560.279\\ 0.5050.9176.8680.1360.2691.5640.0930.2070.360\\ 0.5030.8885.6940.0950.2081.1930.0660.1500.257\\ 0.6050.7066.1340.1020.2071.0530.0540.1230.226\\ 0.6070.9025.9290.1160.2541.4840.0570.1280.238\\ 0.4140.8985.9580.1290.2711.4440.0710.1900.274\end{array}\right]$

Then, the ideal solutions of all indicators were obtained through Equations (17) and (18), as shown in Table 17.

The Euclidean distance between the positive ideal solution and the negative ideal solution was calculated using Equations (19) and (20). The closeness coefficient (E⁺) to the positive ideal solution was calculated using Equation (21) calculate. The final calculation results are shown in Table 18.

The analysis results of 20 color design schemes’ relative posting progress are shown in Figure 17.

5. Results and Discussion

The color preference analysis performed by the forward Kansei Engineering system, based on the results of FA and MDS, is shown in Figure 18. The influencing factors of color emotional cognition mainly include functional factors, esthetic factors, and experience factors by FA. The influence of color emotional cognition includes two main potential factors: sense of calm and sense of relaxation. These two influencing factors have significant correlation with color temperature (warm or cold) and color brightness, respectively. According to the PCCS tone map, the Sf-tone has better functionality while the It-tone has better experience.

The influencing factors for color design in the backward Kansei Engineering system, according to the subjective weight calculation results of the AHP and the objective weight calculation results of the IW, are analyzed, as shown in Figure 19. In the two weight calculation methods, A3 and B3 are the most important. This shows that the comfort of a color’s visual effect and the harmony of color aesthetics have the greatest impact on the seat color design of high-speed trains. The importance of A2, A3, and B3 is consistent in the two methods; this indicates that the width, comfort, and harmony of a color has a significant impact on color perception.

On the basis of TOPSIS analysis results, in order to research the relationship between brightness, saturation, and design scheme ranking, the relationship between brightness and saturation ranking of 20 design schemes was analyzed, as shown in Figure 20.

As can be seen from Figure 20, the colors with medium/high brightness and medium/low saturation rank higher, which is more suitable for the color design of high-speed train seats.

The first six designs are K7, K8, K6, K11, K10, and K5. These color design schemes are mainly in the cool color range and have high brightness, as shown in Figure 21.

According to the PCCS tone map, the design scheme with the highest scores are mainly It-tones and Sf-tones. This shows that the design scheme with high-brightness colors has better satisfaction. The design schemes with the lowest scores are mainly V-tones in the PCCS. This shows that the design scheme with high-chroma colors has poor satisfaction. The analysis is shown in Figure 20.

In the forward Kansei Engineering, the esthetic of slightly warm colors is more attractive. The It- and Sf-tones have better functionality and experience. In backward Kansei Engineering, the It- and Sf-tones rank high, and the design scheme using the V-tone ranks low.

To sum up, the higher the brightness of the color, the lighter and wider it feels. The higher the saturation of the color, the more novel it feels, but these colors should not be used as the first choice for high-speed train seat color design. In the PCCS, It, Sf, and other medium-saturation, high-brightness tones should be the first choice for high-speed train seat color design, as shown in Figure 22.

The relationship between color and emotional description was explored through correlation analysis of 10 Kansei words. The results are shown in Figure 23. S6 and S8, S2 and S9, and S2 and S8 have a strong positive correlation. This indicates that the brighter the color, the stronger the feeling of innovation and the wider the seat appears. The lighter the shade of a color, the wider the seat appears. S1 and S10, S4 and S8, and S5 and S10 have a strong negative correlation, indicating that the feeling of color amiability and romance is strong, while the feeling of calm is weaker.

Based on the correlation analysis of the Kansei words, the relationship between each factor and brightness and saturation is discussed, and the results are shown in Figure 24. The analysis results show that the samples with low saturation and high brightness appear more frequently, and the scores of the color factors are better.

6. Conclusions

This study combines the PCCS and hybrid Kansei Engineering to propose a color optimization and evaluation method for high-speed train seat color design and provides a reference for color design scheme decision-making. Within this framework, three main influencing factors and two potential factors affecting color design are identified through forward Kansei Engineering using a combination of FA and MDS. Then, a comprehensive weight calculation method is constructed using the AHP and IW methods. This comprehensive weight calculation method avoids the subjective deviation of single-weight calculation, improves the objectivity, and evaluates the color design scheme with the TOPSIS to obtain rankings of the design scheme. Finally, the optimal tones were obtained in the PCCS. On the basis of this, the key Kansei words affecting color emotional cognition were analyzed, and the influence of brightness and saturation on color emotional cognition was explored.

The principal contributions and limitations of this study are as follows:

• (1).. The combination of the PCCS and hybrid Kansei Engineering is an effective method for color design optimization and evaluation. The PCCS can easily obtain typical color samples, and hybrid Kansei Engineering can effectively obtain the emotional cognitive characteristics of each tone. This method can avoid the creation of a color design scheme that is too dependent on the subjective experience of the designer.

• (2).. In forward Kansei Engineering, the combination of FA and MDS can effectively obtain the main influencing factors of color design effects and explore the emotional cognitive characteristics of different color schemes. The combination of the two methods can not only objectively obtain the main influencing factors of color but can also establish the relationship between the color attributes (hue, brightness, saturation, etc.) and the emotional features.

• (3).. In backward Kansei Engineering, a comprehensive weight calculation method based on the AHP and IW is constructed. Compared with the traditional AHP, the combination of the AHP and IW can reflect the weight of influencing factors more objectively. This method can avoid relying too much on experts’ experience. On this basis, the TOPSIS is used to optimize and evaluate the design schemes and can effectively obtain a ranking of the design schemes’ satisfaction.

• (4).. This study also has some limitations. The design of the high-speed train seats is a single color, and color matching designs with different colors are not considered. Materials and finishings are closely related to color perception, which is also a limitation of this study. In addition, the emotional measurement method analyzes the results of the questionnaire survey using a statistical method. Psychological experiment equipment was not used to obtain the emotional cognitive features. Future studies can be carried out using color matching designs with different colors, and experimental equipment such as eye trackers can be used to study the psychological cognition of color, so as to provide more references for design creation.

Author Contributions

Conceptualization, methodology, X.-H.X.; formal analysis, Y.X.; visualization, S.G.; data curation, H.Z.; writing—review and editing, H.Y.; writing—review and editing, design, validation, X.-H.X. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The datasets used during the current study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. High-speed train seat color examples.

Figure 2. General research framework.

Figure 3. Diagram of research routes and methods.

Figure 4. PCCS color wheel.

Figure 5. Color brightness and saturation in PCCS.

Figure 6. (a) PCCS tone map; (b) area analysis in the PCCS tone map.

Figure 7. The principle diagram of SD method.

Figure 8. Principle diagram of hybrid Kansei Engineering system.

Figure 9. The hybrid Kansei Engineering system in this study.

Figure 10. Example of AHP model.

Figure 11. Seat color design schemes.

Figure 12. Factor 1 scores for 20 schemes.

Figure 13. Factor 2 scores for 20 schemes.

Figure 14. Factor 3 scores for 20 schemes.

Figure 15. Stimulus coordinates diagram.

Figure 16. Color feature distribution diagram.

Figure 17. Relative posting progress of 20 color design schemes.

Figure 18. (a) Preferred range of esthetic; (b) preferred range of function and experience.

Figure 19. Comparison of calculation results of subjective weight and objective weight.

Figure 20. Brightness and saturation analysis of color design scheme.

Figure 21. (a) The first six design schemes; (b) preferred and non-preferred tones.

Figure 22. (a) Emotional characteristics of warm and cold colors; (b) emotional characteristics of different brightness and saturation; (c) color design preference tone.

Figure 23. Correlation analysis of the Kansei words.

Figure 24. (a) Correlation analysis of factor 1 score and brightness/saturation; (b) correlation analysis of factor 2 score and brightness/saturation; (c) correlation analysis of factor 3 score and brightness/saturation.

Table 1

Value and meaning of 1–9 scale.

Scale	Significance	Meaning
1	Equally important	Both indicators are equally important
3	Slightly important	The indicator i is slightly more important than indicator j
5	Moderately important	The indicator i is moderately more important than indicator j
7	Strongly importance	The indicator i is strongly more important than indicator j
9	Absolutely important	The indicator i is absolutely more important than indicator j
2, 4, 6, 8	Midpoint	Indicates the median of the above two elements

Table 2

RI value.

n	1	2	3	4	5	6	7	8	9	10	11
RI	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46	1.49	1.52

Table 3

Typical color sample.

Number	Tone	Tone Number	PCCS Number	H	S	B
1	V	v6	YO-7.0-9 s	37	100	95
2		v12	G-5.5-9 s	153	100	60
3		v18	B-3.5-9 s	207	100	61
4		v24	RP-4.0-9 s	332	78	67
5	It	It6	YO-8.5-5 s	32	47	100
6		It12	G-8.0-5 s	147	33	83
7		It18	B-6.5-5 s	213	35	76
8		It24	RP-7.0-5 s	340	31	85
9	sf	sf6	YO-7.0-5 s	32	54	84
10		sf12	G-6.5-5 s	149	40	66
11		sf18	B-5.0-5 s	212	43	60
12		sf24	RP-5.5-5 s	339	36	68
13	d	d6	YO-5.5-5 s	32	63	66
14		d12	G-5.0-5 s	150	50	51
15		d18	B-3.5-5 s	210	55	45
16		d24	RP-4.0-5 s	339	43	52
17	dp	dp6	YO-5.0-8 s	36	100	67
18		dp12	G-4.0-8 s	154	100	44
19		dp18	B-2.5-8 s	207	100	46
20		dp24	RP-3.0-8 s	332	76	51

Table 4

Collection of Kansei words.

Number	Kansei Words	Number	Kansei Words
S1	Amiable–Aloof	S6	Light–Heavy
S2	Lively–Dull	S7	Soft–Stiff
S3	Elegant–Vulgar	S8	Wide–Narrow
S4	Upscale–Cheap	S9	Innovative–Conservative
S5	Romantic–Rational	S10	Calm–Excited

Table 5

Color emotional cognition questionnaire example.

Kansei Words	−3	−2	−1	0	1	2	3	Kansei Words
	Extremely	Quite	Slightly	Neutral	Slightly	Quite	Extremely
S1 Amiable	[Image omitted. Please see PDF.]							Aloof
S2 Lively								Dull
S3 Elegant								Vulgar
S4 Upscale								Cheap
S5 Romantic								Rational
S6 Light								Heavy
S7 Soft								Stiff
S8 Wide								Narrow
S9 Innovative								Conservative
S10 Calm								Excited

Table 6

The average score of the emotional feature for 20 design schemes.

	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10
K1	−2.725	−2.825	−0.425	−2.225	−1.175	−0.575	−2.225	−1.050	−2.850	2.525
K2	2.325	−2.525	−0.375	−1.200	2.250	1.875	−2.175	−0.850	−2.825	−2.300
K3	2.625	−2.350	−0.325	−1.625	2.225	1.900	0.625	−0.300	−2.525	−2.425
K4	−2.150	−2.675	−2.850	−2.725	−2.575	2.100	−1.450	0.600	−2.775	2.225
K5	−2.675	−2.550	−2.200	1.300	−2.350	−2.625	−2.725	−2.625	−2.650	1.450
K6	−2.425	−2.375	−2.325	1.425	2.025	−2.425	−2.425	−2.750	−2.425	−2.700
K7	−2.225	−2.400	−2.650	1.325	2.150	−2.475	−2.275	−2.825	−2.325	−2.850
K8	−2.325	−2.125	−2.850	−2.375	−2.550	−2.225	−2.225	−2.650	−2.525	−2.375
K9	−2.550	−1.825	−1.725	−1.775	−2.325	−2.275	−2.525	−2.300	1.325	1.725
K10	2.025	−1.925	−1.225	−1.350	2.150	−2.350	−2.250	−2.425	1.325	−2.625
K11	2.225	−1.725	−2.525	−2.350	−2.625	−2.150	−2.375	−2.525	1.425	−2.650
K12	1.425	−1.825	−2.375	−2.425	−2.650	−2.225	−2.375	−2.250	1.575	1.675
K13	−2.325	2.325	0.575	−2.025	2.275	1.375	−1.825	0.950	2.075	1.875
K14	2.475	2.200	0.725	−2.150	2.175	1.525	1.925	0.375	2.175	−2.125
K15	2.625	2.150	0.100	−2.200	2.325	1.450	1.975	0.725	2.075	−2.550
K16	−2.250	2.625	0.075	−2.575	−2.825	1.550	−1.625	0.775	2.275	2.125
K17	−1.925	2.425	0.825	−2.425	2.275	2.350	−1.525	1.050	2.475	1.625
K18	2.700	2.325	0.050	−2.275	2.450	2.150	1.550	1.500	2.325	−2.325
K19	2.850	2.200	0.300	−2.450	2.550	2.450	2.225	1.550	2.250	−2.425
K20	−1.075	2.725	−2.475	−2.675	−2.525	2.550	−1.250	1.725	2.425	2.750

Table 7

Total explained variance.

Components	Initial Eigenvalue			Extract the Sum of Squares of Loads			The Sum of the Squares of Rotating Loads
	Total	Percentage of Variance	Accumulate %	Total	Percentage of Variance	Accumulate %	Total	Percentage of Variance	Accumulate %
1	4.952	49.519	49.519	4.952	49.519	49.519	3.700	36.998	36.998
2	2.284	22.839	72.357	2.284	22.839	72.357	2.343	23.427	60.426
3	1.034	10.336	82.693	1.034	10.336	82.693	2.227	22.268	82.693
4	0.790	7.897	90.590
5	0.416	4.159	94.749
6	0.207	2.070	96.819
7	0.194	1.938	98.756
8	0.100	0.997	99.753
9	0.016	0.165	99.918
10	0.008	0.082	100.000

Table 8

Rotated component matrix.

	Main Ingredients
	Factor 1	Factor 2	Factor 3	Factor Meaning
S2	0.746			Function factor
S3	0.842
S6	0.845
S7	0.622
S8	0.861
S1		0.859		Esthetic factor
S5		0.611
S10		−0.913
S4			−0.858	Experience factor
S9			0.711

Table 9

Evaluation indicators and definitions.

First-Level Indicators	Second-Level Indicators	Meaning
Function (A)	Placid (A1)	The psychological calm of the seat color design
	Wide (A2)	The extent of the visual field of the seat color design
	Comfort (A3)	Visual comfort of the seat color design
Esthetics (B)	Novelty (B1)	The uniqueness of the seat color design
	Rhythm (B2)	Dynamic sense of seat color design
	Harmony (B3)	Coordination and unity between the seat color design and the train interior
Experience (C)	Glamorous (C1)	The color design gives a fascinating experience
	Fashion (C2)	The seat color design effect reflects the trends of the times
	Delicate (C3)	The exquisite and delicate sense of the seat color design of the train

Table 10

Judgment matrix and weight value of the A level.

A	A 1	A 2	A 3	ω (A)	λmax	CI	CR
A 1	1	0.355	0.166	0.09322	3.077	0.039	0.074
A 2	2.814	1	0.205	0.19849
A 3	6.025	4.887	1	0.70829

Table 11

Judgment matrix and weight value of the B level.

B	B 1	B 2	B 3	ω (B)	λmax	CI	CR
B 1	1	0.361	0.145	0.0846	3.086	0.043	0.083
B 2	2.766	1	0.169	0.1750
B 3	6.893	5.933	1	0.7404

Table 12

Judgment matrix and weight value of the C level.

C	C 1	C 2	C 3	ω (C)	λmax	CI	CR
C 1	1	0.388	0.278	0.1350	3.037	0.018	0.035
C 2	2.578	1	0.404	0.2861
C 3	3.599	2.475	1	0.5789

Table 13

Judgment matrix and weight value of the first level.

	A	B	C	ω (T)	λmax	CI	CR
A	1	5.092	6.382	0.7127	3.099	0.049	0.095
B	0.196	1	3.178	0.2007
C	0.157	0.315	1	0.0865

Table 14

Subjective weight result.

First-Level Indicators	Weight (Ws1)	Sorting	Second-Level Indicators	Weights (Ws2)	Sorting	Overall Weights (Ws3)	Sorting
A	0.7127	1	A1	0.0932	3	0.0664	4
			A2	0.1985	2	0.1415	3
			A3	0.7083	1	0.5048	1
B	0.2007	2	B1	0.0846	3	0.0170	8
			B2	0.1750	2	0.0351	6
			B4	0.7404	1	0.1486	2
C	0.0865	3	C1	0.1350	3	0.0117	9
			C2	0.2861	2	0.0247	7
			C3	0.5789	1	0.0501	5

Table 15

Objective weight result.

Second-Level Indicators	Multiple Correlation Coefficient (ρi )	Weights (Wo)	Sorting
A1	0.923	9.92%	5
A2	0.930	9.84%	6
A3	0.546	16.76%	1
B1	0.881	10.39%	4
B2	0.817	11.20%	3
B4	0.708	12.93%	2
C1	0.946	9.67%	8
C2	0.933	9.81%	7
C3	0.966	9.47%	9

Table 16

Comprehensive weight result.

Indicators	Score	Sorting
A1	0.0476	4
A2	0.1006	3
A3	0.6116	1
B1	0.0128	8
B2	0.0284	6
B3	0.1389	2
C1	0.0082	9
C2	0.0176	7
C4	0.0343	5

Table 17

Positive and negative rational solutions.

Sample	C +	C −
A1	0.610	0.250
A2	1.238	0.561
A3	7.455	3.082
B1	0.158	0.081
B2	0.319	0.158
B3	1.705	1.055
C1	0.099	0.051
C2	0.228	0.078
C2	0.399	0.122

Table 18

TOPSIS calculation results.

Sample	d +	d −	E +	Sorting
K1	3.430	0.112	0.032	20
K2	2.507	0.936	0.272	18
K3	2.461	0.983	0.285	17
K4	1.727	1.710	0.498	16
K5	0.281	3.158	0.918	6
K6	0.142	3.296	0.959	3
K7	0.021	3.435	0.994	1
K8	0.049	3.390	0.986	2
K9	0.680	2.766	0.803	10
K10	0.254	3.184	0.926	5
K11	0.163	3.275	0.953	4
K12	1.173	2.267	0.659	12
K13	2.513	0.927	0.269	19
K14	0.302	3.137	0.912	7
K15	0.303	3.152	0.912	8
K16	0.474	2.970	0.862	9
K17	1.395	2.047	0.595	15
K18	1.075	2.389	0.690	11
K19	1.202	2.236	0.650	14
K20	1.181	2.257	0.657	13

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