Hybrid Kansei engineering

KE was founded by M. Nagamachi in Japan in the early 1970s. It is widely used in product color emotional design due to its accessibility and practicality [14,15]. The term “kansei” is Japanese for “feeling and image”, encompassing a compound of human psychological processes influenced by societal development, fashion trends, and lifestyle concepts [14,16,17]. Via qualitative reasoning and quantitative analysis, KE practically captures users’ psychological feelings and needs regarding products, enhancing experiences and services by integrating these insights into product design.

Among the six updated KE types—category classification, KE system (KES), HKES, KE modelling, virtual KE, and collaborative KE designing [16,18,19]—HKES was noteworthy as a particularly powerful design tool. HKES comprises FKES and BKES. Specifically, FKES translates users’ potential needs into specific design elements, aligning designs more closely with user desires; while BKES evaluates and optimizes based on users’ emotional needs [18,20]. By incorporating multidisciplinary theories and technologies in design element collection and scheme evaluation, HKES facilitates the creation of product designs that align with market demands.

To address real-world multi-objective optimization, Yang [21] integrated a multi-objective genetic algorithm (MOGA) into FKES to generate product alternatives and support vector regression (SVR) for predicting emotional responses. This was demonstrated with a mobile phone design case. Shieh et al. [22] advanced this methodology by incorporating a multi-objective evolutionary algorithm (MOEA) into FKES. Among the tested MOEAs, the non-dominated sorting genetic algorithm-II (NSGA-II) and the strength Pareto evolutionary algorithm-2 (SPEA2) excelled in convergence and diversity, respectively, as shown in a vase design case study. Wang [23] also adopted SVR within BKES, whereas he incorporated GST into FKES to accurately estimate the influence weighting of high-price machine tool shape parameters. In the high-speed train seat color study by Xie et al. [24], typical color schemes were generated via the practical color coordinate system. Within FKES, factor analysis and multidimensional scaling translated users’ emotional characteristics, while the analytic hierarchy process (AHP) and the independent weight coefficient method were employed for weighting. In BKES, the technique for order of preference by similarity to ideal solution (TOPSIS) optimized the color schemes, indicating that tones with medium brightness and saturation—light and soft—are preferable choices.

HKES features bi-directional translation, making it suitable for designing products that meet users’ emotional needs or preferences. In both FKES and BKES, the methodology applies consistent standards when selecting analytical tools and techniques. Specifically, the quantitative analysis of design factors in FKES should be based on users’ primary needs, and vice versa for the emotional or affective evaluation of design schemes in BKES [17,18,20]. This ensures that the selected designs closely match the users’ real-world contexts.

Pleasure-arousal-dominance model

When people interact with product colors, visual and neural processing can subconsciously trigger emotional fluctuations and value judgments. These reactions occur through relevant emotional representations in the brain. At the same time, emotional signals that align with aesthetic preferences are generated. This reflects the brain’s integrated response to color perception [25,26]. Color functions both as a visual attribute and as an emotional medium. It is closely connected to environmental factors, cultural norms, and human behaviors. The way color is presented, and the emotional or affective responses it elicits, are strongly dependent on context [27,28].

Understanding how color’s emotional representation forms is essential for accurately assessing color experiences. Over time, many psychological measurement frameworks have been developed to analyze and categorize emotional responses in different contexts. These range from the James–Lange Theory of Emotion in the 1880s to the Constructed Emotion Theory in the 2000s [29, 30]. The PAD model, introduced by A. Mehrabian and J. Russell in the 1970s, scaled emotional states through three dimensions: pleasure-displeasure (P), arousal-nonarousal (A), and dominance-submissiveness (D) [30,31]. This model views human emotions as multidimensional psychological phenomena and has been widely used in emotional designs and related KE processes [32].

The PAD emotional scale is practical for evaluation and data processing. It is minimally influenced by external factors such as the environment and equipment. For this reason, it has been adopted in diverse fields including architecture, interior design, fashion, consumer goods, and electronics. Using the PAD scale and related theory, Tantanatewin et al. [33] and Divers [34] examined emotional responses to interior color in restaurant and therapeutic settings, respectively. Tantanatewin et al. found that pleasure was the strongest predictor of whether people would enter a restaurant, with bright and warm colors enhancing this feeling. Divers highlighted the nuanced effects of color value and chroma—beyond just hue—on emotions, advocating for an evidence-based approach to creating inviting environments. In rural accommodation lighting, Wei et al. [35] discovered that colored lighting combinations influenced arousal but had limited effects on pleasure and dominance. Warm white light combined with blue-yellow or green-yellow hues prominently boosted visual comfort and alleviated anxiety, while blue-red light increased attraction. Moreover, cool white light combinations could lessen the sensation of warmth.

Particularly, the Institute of Psychology at the Chinese Academy of Sciences developed a localized PAD scale to aid Chinese users. Using this scale, Gao et al. [36] and Zhao et al. [37] analyzed users’ emotional responses in Chinese Weibo texts and mobile library interfaces, respectively, confirming its applicability across various themes. Notably, Li et al. [31] reported that the Chinese version demonstrated reasonable reliability and validity in the P and D dimensions, but showed limitations in the A dimension.

Fuzzy grey relation analysis

The targeted evaluation of design prototypes or schemes is essential in the user preference assessment phase. This step is also a key part of the BKES process. Current evaluation methods mainly rely on users’ emotion scales or custom Likert-scale questionnaires [38,39]. Users’ emotional responses to product features often involve randomness and uncertainty. Grey System Theory (GST), developed by Deng in the 1980s, was designed to analyze systems with uncertain or incomplete information. It is therefore a suitable mathematical approach for this context. In particular, Grey Relational Analysis—a widely used GST model—is commonly employed in emotional experiences and related KE processes [40,41]. It assesses the correlation between emotional responses and product features, refining designs by prioritizing features that evoke desired emotions.

Applying fuzzy weighting to grey relational degrees enhances the emotional preference assessment process. This combined method allows more nuanced decision-making in uncertain contexts. It also clarifies relationships between competing objectives. Researchers have extended this approach by combining GRA and fuzzy logic with other decision-making tools such as the Analytic Hierarchy Process (AHP), the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and Quality Function Deployment (QFD).

Yadav et al. [42] introduced an integrative approach combining GRA, fuzzy AHP, and Taguchi methods to upgrade aesthetic quality in car profile design. By quantifying customer emotions and designer insights, they identified five key aesthetic attributes: originality, family-feeling, masculine, elegant, and modern. This approach effectively handled vague data, theoretically raising customer satisfaction and market competitiveness. Wang et al. successively conducted two studies using GRA and fuzzy logic to explore product evolution and user emotional experiences. Their GRA-fuzzy TOPSIS approach [43] captured consumer emotions and prioritized design alternatives, bridging cognitive gaps between consumers and designers, as demonstrated with smart capsule coffee machines. Additionally, their GRA-fuzzy QFD approach [44] mapped emotional needs to design parameters in wickerwork lamps, improving customer satisfaction and product distinction in competitive markets. Via combining fuzzy GRA and fuzzy AHP, Olabanji et al. [45] amended the conceptual design of pipe bending machines. This method evaluated feature weights and sub-features, comparing designs to an ideal benchmark, successfully identifying optimal solutions. Xue et al. [46] (Xue et al. 2019) and Zhou et al. [47] used a Kansei Engineering framework that incorporated fuzzy GRA to match the design elements of train seats and electric recliner chairs with user perceptions. Through 3D modeling and real-time evaluation based on relevant quantified design element matrix, both studies effectively predicted visualized product prototypes to match consumer imagery.

In summary, subjective evaluations in emotional design often contain ambiguity. Combining GRA with fuzzy sets helps to transform multi-objective evaluation metrics into manageable single-objective problems [45,47]. Specifically, GRA quantifies the similarity between referenced and evaluated emotional states, identifying emotional preferences and corresponding design features. Fuzzy sets offer a nuanced representation of users’ emotional preferences by effectively handling the vagueness inherent in their emotional responses. This synergy fosters more flexible and accurate evaluations, leading to more rational decision-making and raising the reliability of outcomes in complex environments.

Application of eye-tracking technology in color analysis

Eye-tracking experiments capture a series of eye movement behaviors, such as fixations and saccades, which are elicited by visual perceptual stimuli and reflect changes in observers’ perceptual and cognitive demands. Eye-tracking technology records these ocular movements and provides quantitative physiological data that can be used to infer underlying cognitive processes and predict psychomotor performance. Owing to its ability to objectively reveal users’ perceptual and attentional patterns, eye-tracking has been widely applied in research on product appearance design [48], interface design [49], and landscape design [50].

Color variation is a critical visual stimulus that significantly influences eye movement behavior and visual attention allocation. Consequently, eye-tracking methods have been increasingly adopted in color-related design studies. For example, Lee et al. [51] employed eye-tracking technology to investigate the effects of different graphic designs on participants’ cognition, emotion, and perception, with particular emphasis on the role of color in emotional responses and coffee flavor perception. Pradhan et al. [52] explored the complex relationship between color psychology and consumer preferences in coffee packaging design. Yu et al. [53] combined eye-tracking data with subjective evaluations to examine preferences for rosewood and wenge wood under different hue and lightness conditions. Hu et al. [54] integrated eye-tracking techniques with questionnaire surveys to analyze the relationships between color and visual perception in historical museum exhibition environments, focusing on hue, saturation, and brightness.

Overall, these studies demonstrate that eye-tracking technology provides a powerful and objective means for analyzing color perception and visual attention. In this study, eye-tracking is therefore adopted as an independent validation approach to support the analysis of color emotional evaluation results.

Preliminary stage: extraction of product color schemes

Before conducting the formal Kansei Engineering analysis, it is necessary to first extract product colors and construct representative color schemes, which serve as the basis for subsequent evaluation and measurement. In this study, an initial screening of product color schemes was performed by combining k-means clustering with expert visual assessment. The overall procedure is illustrated in Fig 2.

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Fig 2. Process and methods for extracting initial product color schemes.

https://doi.org/10.1371/journal.pone.0341895.g002

The process begins with the extraction of representative colors from existing product images. After removing background elements and mitigating illumination interference, the k-means clustering algorithm is independently applied to each product image to identify visually dominant color components. To ensure mathematical rigor in the color extraction process, the k-means clustering method adopted in this study aims to minimize the within-cluster sum of squared errors, which can be expressed as follows [55]:

(1)

Here, x denotes a pixel in the product image represented as a vector in the color space; C_i represents the i-th cluster; μ_i is the centroid color of cluster C_i; and k is the number of clusters. The k-means algorithm partitions image pixels into multiple regions by iteratively minimizing intra-cluster variance, grouping pixels with similar color attributes together. Each cluster is represented by a centroid, which can be regarded as a representative single color reflecting a major component of the product’s appearance.

Considering the characteristics of product color composition and to reduce the influence of highlights and shadows, the number of clusters was set to 5 during the color extraction stage. In practice, the k-means clustering was implemented in a Python environment using standard clustering functions to process pixel-level image data. Upon convergence, the algorithm outputs the centroid colors of each cluster along with their corresponding pixel proportions. These centroid colors are treated as representative single colors for subsequent screening and color scheme construction.

For each product, the extracted colors are ranked according to their pixel proportions, and the top-ranked colors are retained as primary single-color candidates. Subsequently, all extracted single colors from different products are matched to the closest Pantone color references to form a unified single-color library. Based on this color library, a group of experts with backgrounds in product design and color design were invited to combine the extracted single colors into feasible two-color and three-color schemes, following criteria of color harmony and suitability for the product. Through expert discussion and evaluation, a set of representative color schemes was finally selected and used as the base schemes for subsequent PAD-based evaluation and analysis.

Stage 1: color emotional design

This stage primarily involved creating the PAD emotional scale and measuring, analyzing, and screening color-matching prototypes based on the scale. Each dimension—P, A, D—contained four pairs of opposite adjectives, listing from V₁ to V₁₂, as displayed in Table 1. These pairs applied a nine-point scale from −4 to +4 to describe users’ emotional responses [56]. Through scaling these responses along the adjective axes, each emotion is mapped to a specific PAD coordinate. For color design, this three-dimensional description visualizes how different colors evoke emotions, helping identify those that elicit positive responses [30]. By inserting measurement results into Equation system (2), the actual PAD coordinate (P, A, D) for a test prototype’s emotional response is obtained.

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Table 1. PAD emotion scale with 12 pairs of opposite adjectives.

https://doi.org/10.1371/journal.pone.0341895.t001

(2)

Furthermore, ten distinct color-perception-linked emotional characteristics—five positives and five negatives—were selected from previous studies [20,34,56,57]. As exhibited in Table 2, these emotional states and their PAD coordinates served as reference points for assessing PAD-coordinated emotional responses and corresponding color schemes. As is known, emotional discrepancy refers to the absolute distance between the participates’ actual emotional response and the reference emotion in the PAD dimensions. The minimal distance, calculated using Equation (3), indicates how closely the participates’ emotional state aligns with the reference, revealing the specific emotional characteristic evoked by a color-matching prototype [20,56,57].

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Table 2. 10 adopted emotion characteristic references and their PAD coordinates.

https://doi.org/10.1371/journal.pone.0341895.t002

(3)

Here, L_mn represents the emotional discrepancy between an actual emotional response and each emotional characteristic (No. n) for each color-matching prototype (No. m). The variables m and n refer to the specific color-matching prototype and emotion characteristic reference, respectively. Meanwhile, (P_m, A_m, D_m) and (p_n, a_n, d_n) denote the PAD coordinates for the corresponding prototype’s emotional response and the specific reference, respectively.

The minimum value, L_mn-min, within the result set [L_mn] reveals the emotional characteristic of the prototype. After identifying and eliminating prototypes likely to evoke negative emotions, the remaining color-matching schemes were prepared for further optimization. To empirically validate this stage, participants were recruited to evaluate the color-matching prototypes. Measurements were collected from 216 participants during the recruitment period from 10/10/2024–25/11/2024.

Stage 2: user preference assessment

Stage 2 primarily focused on the targeted assessment and optimization of the emotional preferences associated with the remaining color-matching schemes. Additionally, to upgrade qualitative analysis, an extra dimension—user satisfaction (S)—was introduced into the PAD coordinate system. For four-dimensional PADS emotional responses, the fuzzy GRA calculation and assessment process can be divided into the following steps [45,56,58]:

1. 1). Establishing comparison “emotion” matrix and reference sequence, normalizing original “emotion” data.
2. 2). Computing fuzzy membership degrees, determining absolute differences between normalized “emotion” values and grey relational coefficients.
3. 3). Calculating fuzzy grey relational degrees.

In the first step, all remaining schemes’ PADS-coordinated emotional responses were integrated into a comparison matrix X, as displayed below:

(4)

Due to the vagueness in emotions and their evaluations, min-max normalization ensured all evaluation data fell within the [0,1] range, enhancing computability. As shown in Equation (5) and (6), x_u’(i), X were normalized from x_u(i), X, respectively.

(5)

(6)

In the second step, a fuzzy similarity matrix was constructed based on X’ using the cosine angle method, followed by the calculation of fuzzy membership degrees [45,58]:

(7)

Here, r_u represented the fuzzy membership degree for each remaining scheme, x’_umax referred to the optimal emotional response within x_u(i) in each emotional dimension.

Next, the absolute differences of x_u’(i) were calculated as follows:

(8)

(9)

The maximum absolute difference, Δx’_max, and the minimum, Δx’_min, among ΔX’ were used in Equation (10) to work the grey relational coefficient out. To strengthen the distinction between obtained coefficients, the resolution coefficient, ρ, was typically set to 0.5 [58,59].

(10)

Since grey relational coefficients were based on absolute differences between comparison and reference sequences, they were fairly dispersed, complicating overall comparison. Therefore, when calculating the relational degree, these coefficients were averaged into a single value.

(11)

With the fuzzy grey relational degree, Ru, obtained using Equation (11), color-matching schemes could be ranked and screened according to their fuzzy grey relational degrees.

Verification stage: eye-tracking experiment

To validate the rationality and accuracy of the proposed HKES approach in color scheme evaluation, an eye-tracking experiment was conducted to objectively examine the consistency between the model-based ranking results and users’ actual visual behavior. The verification procedure included experimental design, eye-tracker calibration, and eye-tracking data collection and analysis.

Attention heatmaps were used to visualize the spatial distribution of visual attention across different color schemes, providing an intuitive indication of their relative visual attractiveness. [60] However, as heatmaps primarily reflect overall attention patterns and are limited in quantitative comparison, total fixation duration was further adopted as a key eye-tracking metric. This indicator represents the cumulative time participants fixated on a given stimulus and is widely associated with visual interest and preference [61].

By combining attention heatmaps and total fixation duration, the visual attention characteristics of different color schemes were analyzed and compared with the rankings obtained from the HKES model. The consistency between eye-tracking results and model-based evaluations provides additional evidence supporting the effectiveness and cognitive plausibility of the proposed HKES approach.

The experiment was conducted according to the guidelines of the Declaration of Helsinki and approved by the Institutional Ethics Committee of Anhui University (protocol code: BECAHU-2024–014).

Color scheme extraction and participants recruitment

In this case study, a typical household hair dryer with diverse color designs was selected as the research object. Product images were collected from online retail platforms, brand official websites, and live-streaming channels. A total of 36 representative product images were selected as samples for color extraction. Following the color extraction procedure established in Section 3.1, k-means clustering was applied to process the color information of the product images. Each product image was analyzed independently to extract its primary visual color components, and the extracted results were subsequently aggregated and screened. As a result, an initial set of 36 × Top 2 = 72 single-color candidates was obtained.

Subsequently, these candidate colors were standardized and matched to Pantone color references. Single colors with highly similar color attributes were merged, resulting in a unified single-color library consisting of 25 representative colors. This color library effectively reflects the mainstream color characteristics commonly observed in household hair dryer products.

Based on the constructed single-color library, six experts with backgrounds in product design and color design were invited to participate in the color scheme construction through offline group discussions. Guided by principles of color harmony and the practical application characteristics of household hair dryers, the experts combined the single colors to generate initial two-color and three-color schemes. During the scheme construction process, minor adjustments to individual colors were permitted based on conventional color-matching guidelines, such as warm-cool color balance and the coordination of lightness and saturation, in order to enhance overall visual harmony and product suitability. Through multiple rounds of visual evaluation and group discussion, schemes that did not align with the product’s aesthetic characteristics or practical applicability were gradually eliminated. Ultimately, 20 representative product color schemes were selected as the input for subsequent PAD-based emotional dimension evaluation, enabling analysis of the effects of different color combinations on users’ emotional experiences.

The 20 suitable color schemes were categorized into dual-color and tri-color combinations. In the dual-color schemes, each design consisted of a primary and a secondary color. The tri-color schemes included a primary, secondary, and accent color. As depicted in Fig 3, cases C-01 to C-10 are dual-color, and C-11 to C-20 are tri-color. Each category contained 10 samples covering cool, warm, and neutral tones, presented on visual test boards for subjective evaluation.

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Fig 3. 10 dual- and 10 tri-color test cases applied to color-matching prototypes during Stage 1.

https://doi.org/10.1371/journal.pone.0341895.g003

To ensure the validity of the color PAD emotional experience test, participants needed familiarity with hair dryer selection and usage, as well as color perception and cognition. Participants were selected based on three criteria: 50% male and female distribution, ages 21–50 and generally healthy with normal corrected vision, free from color blindness or other ocular conditions. Ultimately, 216 participants were chosen, equally split by gender.

Emotional experience of color-matching case

Based on the case sample set and the Chinese version of the PAD emotional experience scale, we developed a Likert scale questionnaire to assess participants’ emotional responses to the hair dryer color-matching samples. The complete questionnaire is provided in S1 File. The questionnaire was conducted via an online survey. Participants remotely rated standardized color-matching stimuli (dual-color and tri-color schemes) using Likert scales displayed on the questionnaire interface. Participants were recruited during the period from 10/10/2024–25/11/2024. A total of 216 individuals completed the survey. After removing 8 incomplete questionnaires with missing or incorrect selections, the effective response rate was 96.296%, resulting in valid measurement data of 208 × 20 × 12, totaling 49,920 data points.

After importing the data into SPSS 23.0 for reliability testing, a Cronbach’s alpha of 0.796 was revealed, indicating satisfactory reliability for further analysis. We then calculated the PAD mean values for each of the 20 cases (as shown in Table 3). These mean values were substituted into Equation (2) to obtain the actual PAD measurements for each case. One-way ANOVA was conducted on the PAD emotional ratings obtained from the survey to examine whether different color schemes elicited statistically significant differences in emotional responses. The results showed significant main effects of color scheme on pleasure (P: p = 0.017 < 0.05), arousal (A: p = 0.048 < 0.05), and dominance (D: p = 0.031 < 0.05), indicating that the proposed color combinations produced distinguishable emotional experiences across these three dimensions. By comparing these measurements with the PAD benchmark coordinates in Table 2 using Equation (3), we determined the proximity of each sample’s emotional response to the reference emotional characteristics, as presented in Table 4. The data marked with an asterisk in Table 4 indicate the PAD emotional characteristics of the 20 color schemes.

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Table 3. Mean statistics from PAD scaling measurements of color-matching case samples during Stage 1.

https://doi.org/10.1371/journal.pone.0341895.t003

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Table 4. PAD-coordinated values and emotional characteristics closeness of color-matching prototypes.

https://doi.org/10.1371/journal.pone.0341895.t004

The results indicated that both dual-color and tri-color schemes could evoke positive and negative emotions, suggesting no conspicuous difference in emotional preference based on the number of colors. However, dual-color schemes were more likely to evoke positive emotions in 6 cases, compared to 4 for tri-color schemes, indicating a user preference for dual-color designs. Overall, 50% of the color schemes elicited positive emotions, demonstrating that current market designs align with user preferences but have room for improvement. Specific dual-color cases (C-01, C-04, C-07, C-09) and tri-color cases (C-11, C-13, C-15, C-16, C-18, C-20) were more likely to evoke negative emotions such as boredom, sadness, anxiety, contempt, and disgust. Issues included the use of similar adjacent colors, overly bright or dark tones, and mismatched styles with the product’s function. Adjustments in color choices, particularly avoiding overly monotonous or contrasting schemes, could enhance user satisfaction.

To optimize the emotional design of hair dryer colors, we excluded 10 color schemes that tended to evoke negative emotions. We then conducted a PAD emotional analysis on color schemes that elicited positive emotions. This analysis, informed by design principles and participant feedback, provides insights for designing emotionally appealing products.

For the dual-color schemes, six cases (C-02, C-03, C-05, C-06, C-08, and C-10) were identified as positive designs. Among them, C-02 and C-03 adopted bright tones such as green and yellow, which effectively enhanced user pleasure and attention, though slight reductions in saturation could further balance excitement levels. In contrast, C-05 and C-10 relied on neutral combinations of gray and white, generating feelings of calmness and comfort, with increased brightness expected to improve user interest. Meanwhile, C-06 and C-08 combined magenta with blue to create a more harmonious and balanced appearance, where adjustments in brightness could contribute to a more uplifting overall mood.

For the tri-color schemes, four cases (C-12, C-14, C-17, and C-19) were identified as positive designs. Specifically, C-12 and C-17 employed contrasting colors such as blue and orange, which successfully captured attention and evoked a sense of surprise, though further adjustments in brightness and saturation could help achieve a more balanced emotional response. C-14 combined gray, white, and pink to produce a joyful effect, with an increase in the brightness of gray recommended to avoid visual monotony. In contrast, C-19 applied neutral tones accented with cool colors, generating a soothing and comfortable impression, and enhancing the accent color would likely strengthen its emotional impact. This analysis shows that both dual-color and tri-color schemes can effectively cater to diverse emotional preferences, offering guidance for future color design strategies.

User preference assessment of color-matching schemes

During this stage, we used previous positive emotional color schemes as references, focusing on dual-color and tri-color combinations. Dual-Color Schemes included 6 designs (S-01 to S-06) featuring main colors like yellow and green, with magenta and blue as accents. Each design incorporates varying proportions of neutral tones. Tri-Color Schemes included 4 designs (S-07 to S-10) inspired by “Pop Art” and “Minimalism.” These use ultramarine and black as main colors, with orange-red and purple as accents, and gray and yellow as highlights. Minimalist designs use black, white, and gray with pink and cobalt blue as accents. The color renderings were created using KeyShot software, resulting in 10 color-matching schemes for hair dryers (refer to Fig 4, with all colors using the HSV model [62]). This completes Stage 1 based on the FKES framework.

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Fig 4. Confirmed color-matching schemes for Stage 2.

https://doi.org/10.1371/journal.pone.0341895.g004

The BKES framework was utilized to assess the PAD emotional responses associated with ten hair dryer color design schemes. The evaluation questionnaire encompassed four dimensions: Pleasure (P), Arousal (A), Dominance (D), and Satisfaction (S), each rated on a scale from −4 (“strongly disagree”) to 4 (“strongly agree”). Concurrently, following the PAD emotional experience assessment, participants were asked to provide subjective evaluations of their visual preferences concerning the product’s color design. This evaluation metric, termed Subjective Visual Preferences (V), was consistent with the dimensions employed in the PAD assessment scale. The complete questionnaire is provided in S2 File.

Considering the requirement for collecting a relatively large number of questionnaire responses, the emotional experience evaluation was conducted via an online questionnaire survey. A total of 216 questionnaires were distributed, yielding 212 valid responses and resulting in an effective response rate of 98.148%. This provided a valid dataset comprising 212 × 10 × 4 and 212 × 10, totaling 10,600 data points. The data was imported into SPSS 23.0 for reliability testing, which revealed a Cronbach’s alpha of 0.817, indicating good structural reliability for further analysis. Subsequently, the average scores for each design scheme were calculated (Table 5), and one-way ANOVA was conducted on the PAD emotional ratings obtained from the second questionnaire survey to further examine whether the ten color schemes elicited statistically significant differences in emotional responses. The results revealed significant main effects of color scheme on pleasure (P: p = 0.008 < 0.05), arousal (A: p = 0.017 < 0.05), dominance (D: p = 0.035 < 0.05), and satisfaction (S: p = 0.026 < 0.05). Fuzzy Grey Relational Analysis was conducted using formulas (4) to (10). This analysis determined the fuzzy membership and grey relational degrees for each scheme. These results were applied to formula (11) to compute the fuzzy grey relational degree, facilitating the prioritization of the color design schemes. Additionally, after the fuzzy grey relational analysis, the mean values of subjective visual preference evaluations were normalized to further prioritize the color design schemes based on subjective assessments, as shown in Table 7. The resulting order of preference was S-06, S-05, S-04, S-07, S-01, S-03, S-08, S-10, S-02, S-09.The emotional experience evaluation of hair dryer color design schemes, based on fuzzy grey relational analysis, resulted in the following priority order (Table 7 and Fig 4): S-06, S-05, S-04, S-01, S-07, S-08, S-03, S-10, S-02, S-09.

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Table 5. Mean statistics of PAD-coordinated emotional responses in Stage 2.

https://doi.org/10.1371/journal.pone.0341895.t005

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Table 7. Subjective visual preferences of Mean statistics & Normalized results in Stage 2.

https://doi.org/10.1371/journal.pone.0341895.t007

The top-ranked schemes, S-06, S-05, S-04, S-01, and S-07, emerged as the preferred options from this evaluation. Additionally, the root mean square error (RMSE) was computed between the fuzzy grey relational degrees and the normalized subjective visual preferences for the ten color design schemes in Table 6 and Table 7. An RMSE value of 0.111, which is close to 0, indicates the reliability of both subjective and objective assessment results, affirming the credibility of the scheme prioritization. This concludes Stage 2 of the BKES framework, establishing a research framework for product color emotional design that integrates mixed emotional engineering with PAD emotional measurement and fuzzy grey relational analysis.

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Table 6. Results of fuzzy grey correlation analysis of color-matching schemes in Stage 2.

https://doi.org/10.1371/journal.pone.0341895.t006

Moreover, Fig 5 illustrates the comparison between subjective and objective prioritization results for the ten color-matching schemes in Stage 2. The horizontal axis represents the different schemes (S-01 to S-10), while the vertical axis shows their relative prioritization values. The dark bars correspond to the fuzzy grey relational degrees (objective evaluation), and the light bars represent the normalized results of subjective visual preference assessments. As shown in the figure, both evaluation perspectives reveal a consistent preference order, with schemes S-06, S-05, and S-04 ranking highest, followed by S-01 and S-07. The strong alignment between subjective and objective prioritization further validates the reliability of the proposed evaluation framework, confirming that the integrated PAD–fuzzy GRA approach can accurately capture users’ emotional preferences in color design.

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Fig 5. Subjective and objective prioritization of color-matching schemes in Stage 2.

https://doi.org/10.1371/journal.pone.0341895.g005

Eye-tracking experimental verification

To ensure the objectivity and feasibility of the eye-tracking experiment, a total of 24 participants were recruited for the color imagery cognition experiment, including 12 males and 12 females aged between 21 and 50 years. All participants were in good physical condition, had normal or corrected-to-normal vision, and reported no color blindness, color weakness, or other ocular diseases.

The eye-tracking experiment was conducted using a Tobii Pro X3-120 eye tracker in combination with a desktop computer. The device accurately records participants’ gaze positions and has a sampling rate of 120 Hz. The eye tracker measures 324 mm (12.7 inches) in length, weighs 118 g (4.2 oz.), and can be mounted directly onto computer monitors up to 25 inches using the provided magnetic mounting bracket. The experimental computer was equipped with a Windows 10 (64-bit) operating system, an Intel Core™ i7-14700 CPU, and 32 GB of RAM. The display resolution was set to 1920 × 1080 in full-screen mode.

Prior to stimulus presentation, areas of interest (AOIs) were defined to ensure the validity of the collected eye-tracking data. In the visual test panel, a total of ten AOIs were delineated, each corresponding to one color scheme sample, as shown in Fig 6.

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Fig 6. Areas of interest (AOIs) for experimental samples.

https://doi.org/10.1371/journal.pone.0341895.g006

During the experiment, the 24 participants completed the eye-tracking tasks sequentially following a standardized experimental procedure. The experiment consisted of five stages: an introduction page, a gaze calibration page, an instruction page, a stimulus presentation page, and a concluding page (Fig 7). The instruction presented to participants was: “Please carefully observe the following hair dryer color schemes and determine which color scheme you consider to be the optimal one.”

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Fig 7. Eye-tracking experimental procedure.

https://doi.org/10.1371/journal.pone.0341895.g007

After the experiment, eye-tracking data were exported to generate attention heatmaps (Fig 8). The heatmap results indicate that participants’ visual attention was primarily concentrated on schemes S-06, S-05, and S-04, while relatively less attention was allocated to schemes S-01, S-07, and S-03.

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Fig 8. Attention heatmap results.

https://doi.org/10.1371/journal.pone.0341895.g008

The average fixation duration for each color scheme was calculated. The original fixation duration statistics for color schemes are provided in S3 File. To facilitate comparison with the evaluation results obtained from the HKES model, the eye-tracking metrics were further normalized, and a ranking of the color schemes was derived, as summarized in Table 8.

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Table 8. Fixation duration statistics of color schemes.

https://doi.org/10.1371/journal.pone.0341895.t008

The fixation duration results reveal significant differences in visual attention among the ten color schemes. The final ranking based on eye-tracking data is: S-06, S-05, S-04, S-01, S-07, S-03, S-08, S-10, S-02, and S-09. Among them, scheme S-06 exhibits the longest fixation duration, followed by S-05 and S-04, whereas scheme S-09 consistently receives the lowest level of visual attention.

The ranking obtained from eye-tracking data is highly consistent with the evaluation results derived from the HKES model, indicating strong agreement between model-based assessments and users’ actual visual behavior. This consistency demonstrates that the proposed HKES method effectively captures users’ visual preferences in color scheme evaluation. Therefore, the eye-tracking results provide objective empirical evidence supporting the feasibility and effectiveness of the proposed HKES framework.

Finally, the color scheme S-06, which achieved the best overall evaluation performance, was selected and applied to the overall design of the hair dryer product. Based on this scheme, further optimization was conducted on the product modeling and rendering, including refinements to surface materials and structural details. The final product design rendering is presented in Fig 9.

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Fig 9. Rendering of the product with the optimal color scheme.

https://doi.org/10.1371/journal.pone.0341895.g009