A fuzzy rule-based approach to modeling affective user satisfaction towards office chair design

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International Journal of Industrial Ergonomics 34 (2004) 31–47

A fuzzy rule-based approach to modeling affective user satisfaction towards office chair design Jungchul Park, Sung H. Han* Division of Mechanical and Industrial Engineering, Pohang University of Science and Technology, San 31, Hyoja Dong, 790-784 Pohang, South Korea Received 30 October 2003; received in revised form 19 December 2003; accepted 9 January 2004

Abstract Affective user satisfaction is considered one of the most important factors in designing consumer products. Researchers have attempted to build models explaining the relationship between design variables of consumer products and affective user satisfaction using statistical multivariate analysis techniques such as linear regression and quantification theory. These techniques, however, have limitations due to the inability of capturing non-linearity of human feelings. This paper proposes a fuzzy rule-based approach to building models relating product design variables to affective user satisfaction. Affective user satisfaction such as luxuriousness, balance, and attractiveness were modeled for office chair designs. Regression models were also built on the same data to compare model performance. The results showed that fuzzy rule-based models were better than regression models in terms of prediction performance and the number of variables included in the model. Methods for interpreting the fuzzy rules are discussed for practical applications in designing office chairs. Relevance to industry This study proposes a fuzzy rule-based method for analyzing and interpreting affective user satisfaction of consumer products, which can help designers and developers to identify important design variables, and to estimate the responses of various user groups for a new product design. r 2004 Elsevier B.V. All rights reserved. Keywords: Affective user satisfaction; Fuzzy rule-based models; Subtractive clustering algorithm; Office chair design

1. Introduction Affective user satisfaction is one of the most important factors for a product to be successful in the market. Companies spend a significant amount of efforts designing an affective product. For *Corresponding author. Tel.: +82-54-279-2203; fax: +8254-279-2870. E-mail address: [email protected] (S.H. Han).

consumer products, affective user satisfaction is considered as important as product functionality. Often, affective user satisfaction is closely related to the appearance of a product as well as its functional performance (Dandavate et al., 1996; Yang et al., 1999). Although faithful in utilitarian needs, a bad looking product cannot appeal to consumers. In contrast, a nice looking product not only appeals to consumers, but also improves corporate image.

0169-8141/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ergon.2004.01.006

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Interestingly however, it is difficult to find research studies regarding the effects of image or style of a product on affective user satisfaction (Chuang and Ma, 2001). Although subjective satisfaction is included in the original usability concept (Shackel, 1984), most usability studies have focused on objective performances (Nielsen and Levy, 1994) rather than subjective satisfaction. Only recently, Kansei engineering (Nagamachi, 1995) introduced a concept that emphasized the importance of incorporating consumer’s feelings into product design. Nagamachi (1995) proposed a method for translating consumer’s feelings and emotion into design features. A variety of mathematical techniques, such as factor analysis, multiple linear regression, or artificial neural network, were used in analyzing the relationship between affective user satisfaction and product design. A similar study, but from a different viewpoint, was reported by Han and his colleagues (Han et al., 2000). They proposed a new concept of usability that expanded the traditional usability by emphasizing affective user satisfaction as important as user’s task performance. Accordingly, they developed a variety of usability dimensions including both subjective and objective aspects, and attempted to evaluate product usability based on empirical models explaining functional relationships between usability dimensions and product design features. Multiple regression techniques (Myers, 1990) were the major tool for building the models. These two approaches, although their main focuses are different (the former is for designing, and the latter is for evaluating product design in terms of affective user satisfaction), share an important aspect in common. Both assumed the cause-and-effect relationship between design features and affective user satisfaction, and employed mathematical models to describe the relationship. This mathematical representation enjoys several advantages. First, it can be used to predict the level of affective user satisfaction of a product, and provide evaluation criteria for various design alternatives. For example, the functional relationships developed by Han et al. (2000), described significant design features for a certain satisfaction dimension, which could serve

as evaluation criteria for determining whether a product provided a high (or low) level of affective user satisfaction. Second, an optimal design can be obtained by using such optimization techniques as steepest decent (Hong et al., 2002) and genetic algorithm (Mitchell, 1996). Finally, parameters (e.g., regression coefficients) in the model enable us to substantiate expert knowledge, and obtain insights into the relationship between product design and affective user satisfaction. To maximize these advantages, the models should represent the true responses of consumers in a simple and understandable form. However, there is a trade-off between model complexity and understandability. Simple models cannot provide sufficient information necessary to understand the true relationship. Too complex models, on the other hand, are not easy to interpret. It is important to select an efficient model structure appropriate to the nature of a problem. Unfortunately however, little attention has been given to this issue in the literature. Most modeling efforts in this field were made using multiple linear regression models (Jindo and Hirasago, 1997; Nakada, 1997; Tanoue et al., 1997; Han et al., 2000). This approach is easy and simple to apply but has limitations. First, too many variables (or regressors) are usually included in a model, and the variables are often meaningless or difficult to interpret. Note that Han and Hong (2003) reported that dummy variables included in a model were difficult to interpret although including them resulted in a good model in terms of such model performances as p-values and prediction sum of squares (PRESS). Second, many variables in the regression approach may stem from a linearity assumption of the model. Linear modeling techniques assume that the effect of an independent variable is constant throughout the entire range of the problem space. This means that the same model is applied to all products without considering the characteristics of each. Under this assumption, more and more variables are included in the model to fit a wide range of products. To avoid or at least minimize the non-linearity, second-order terms, such as pure quadratic and linear-by-linear

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interactions, were included in the model (Han et al., 2000). This approach, however, is not a fundamental solution, since it also increases the number of variables in the model. Worse yet, the resulting model is often difficult to interpret when there are many interactions and pure quadratic effects. This drawback was reported by Shimizu and Jindo (1995) with a different viewpoint. They argued that the non-linearity of human feelings could hardly be treated in a multiple regression analysis framework. They applied a fuzzy regression technique instead of traditional statistical regression in order to account for fuzziness of human feelings. However, it is still controversial whether fuzzy regression is better than multiple regression in treating the non-linearity of human responses. It is difficult to find studies in the literature comparing performance of the two approaches. Furthermore, Kim et al. (1996) reported that there is no proof that fuzzy regression is superior to its statistical prototype (regression) in handling the non-linearity. It is interesting to note that the original name of the fuzzy regression is ‘‘fuzzy linear regression.’’ A variety of non-linear modeling techniques are available as an alternative to model the nonlinearity. Examples include artificial neural networks and many statistical learning algorithms. An attractive alternative to a global non-linear model is to model the nonlinear structure with a combination, or mixture, of local linear submodels (Tipping and Bishop, 1999). This motivates the ‘mixture of experts’ technique for regression (Jordan and Jacobs, 1994). This study proposes fuzzy rule-based models, which are also a mixture of local linear models, as a means to build the relationship between affective user satisfaction and design features (or variables) of consumer products. The proposed models not only take into account the fuzziness of human responses, but also have an advantage in interpretation. Affective user satisfaction of office chairs is modeled to demonstrate the effectiveness of the approach proposed in this study. In addition, multiple linear regression models are also developed, and compared to examine performance of the two approaches.

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2. Fuzzy rule-based model A fuzzy rule-based model uses the fuzzy set theory proposed by Zadeh (1965). A fuzzy set is a set with a smooth boundary, which allows a partial membership (Yen and Langari, 1998). The notion of a membership in a fuzzy set is thus a degree, which is expressed as a number between 0 and 1. For example, the degree that we can say the weather is ‘‘cool’’ varies with the temperature. Fig. 1 shows how the concept of ‘‘cool weather’’ can be represented with a fuzzy set. A fuzzy rule-based model consists of fuzzy if– then rules. Each fuzzy if–then rule associates a condition of input data with a specific conclusion of output. The ‘‘if–part’’ of a fuzzy rule is in charge of a specific region of an input space, and the ‘‘then–part’’ has a local model that fits best to the data in the corresponding region. The term, ‘‘fuzzy,’’ means that regions in an input space are fuzzy sets with smooth boundaries. Therefore, the regions allow partial memberships and can even overlap with each other. From a knowledge representation viewpoint, a fuzzy if–then rule can be viewed as a scheme for obtaining knowledge (especially human knowledge). The knowledgerelevant feature enables us to interpret the model easily. The notion of fuzzy rule-based inference can be understood by using a metaphor of drawing a conclusion with a ‘‘panel of experts’’ (Yen and Langari, 1998). Let us assume that you are to make a decision on an issue, and there is a group of experts from different fields you can consult. You will get various opinions from the experts,

Membership 1

5

10

20

25

T (°C)

Fig. 1. Fuzzy set representation of ‘‘cool weather’’.

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and some of them would fit the current problem better than others. Therefore, you need to evaluate each opinion on the basis of its relevance to the current problem. A final conclusion can be effectively drawn summing up the opinions with different weights. Likewise, if input data come into a fuzzy rule-based model, each rule, acting like an expert, gives an answer using its own local submodel. Meanwhile, the degree to which the current input matches the condition of each rule is computed. The matching degree is measured by the distance between the input data point and the center of each local region, which is considered as a confidence level of the suggested answer. The model obtains a final output after giving a weight to each answer according to its confidence score, and averaging them. In this study, fuzzy rule-based models were developed in two stages. In the first stage, local sub-regions are determined by analyzing the pattern of input data. The regions can be determined intuitively, which requires too many trial and errors (Yen and Langari, 1998). Here, clustering techniques are used to find the subsets of an input space that characterize possible occurrences of data. Each cluster is then associated with a fuzzy rule. A variety of clustering techniques are available to obtain the subsets. A fuzzy C-means algorithm (Bezdek, 1981), a self-organizing map (Kohonen, 1990), and a subtract clustering algorithm (Chiu, 1997) are well-known examples. It is known that the subtractive clustering algorithm is efficient and easy to use (Chiu, 1997) for the following reasons. First, it provides a proper number of clusters automatically. Second, it is very stable because each data point is considered a potential cluster center. In the second stage, a local model is built for each cluster. Mamdani Model (Mamdani and Assilian, 1975), Takagi–Sugeno–Kang (TSK) Model (Takagi and Sugeno, 1985; Sugeno and Kang, 1988), and Standard Additive Model (Kosko, 1997) can be applied in this step. In this study, TSK Model was chosen because it is known to be able to solve a complex and high-dimensional problem with a small number of rules. The local models based on TSK Model are multiple linear regression models. Therefore, the overall

model is a mixture of rules each of which has the form IF xi ACk ;

THEN y ¼ a0 þ

M X

aj xij ;

j¼1

where xij is the jth input of the ith data point xi, M is the dimension of input, which equals to the number of input variables, y is the output variable, a0 and ai are the regression parameters, and Ck represents the kth cluster. The degree that an input data point belongs to a cluster is expressed as a number between 0 and 1. An input near a cluster center has a higher membership to the cluster. The membership mapping is represented in a membership function, which is normally Gaussian or trapezoidal. Since the Ck was determined for each rule in the first step, the model parameters a0 and ai can be easily solved using a linear optimization technique. Fuzzy rule-based models were implemented using subclust and genfis2 function (Chiu, 1994) included in the Matlab Fuzzy logic toolbox. The number of rules and the parameters of ‘‘if– part’’ membership functions were determined by the subtract clustering algorithm. A linear leastsquares estimation technique was used to determine each rule’s ‘‘then–part’’ regression parameters. The genfis2 function utilizes an AND (conjunction) type connective and Max operator in combining multiple input conditions, and a center of area (COA) defuzzification method in converting the final combined fuzzy conclusion into a crisp number (Yen and Langari, 1998).

3. Data collection 3.1. Product design variables An existing data set was used to model the relationship. Yun et al. (2001) reported a study that used expert opinions to select design variables for office chairs. Using a framework developed by Han et al. (2000), they decomposed a typical office chair into a total of 48 design variables (Table 1). A total of 50 chairs were collected and measured. All the chairs were office chairs primarily sold for

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Table 1 Design variables of office chairs (modified from Yun et al., 2001) Component

Design variables

Backrest

Tilt of backrest Color of backrest Brightness of backrest color Width of backrest Length of backrest Thickness of backrest Height of backrest Width–height ratio of backrest

Material of backrest Degree of backrest material finish Degree of spinal curvature support Degree of lumbar support Shape of backrest Low back support Headrest

Seat pan

Seat pan adjustment Color of seat pan Brightness of seat pan color Length of seat pan Width of seat pan Thickness of seat pan

Range of seat pan height Material of seat pan Degree of seat pan material finish Sliding level of hips Degree of seat pan curvature Degree of weight distribution

Armrest

Color of armrest Material of armrest Degree of lower arm support

Shape of armrest

Base

Shape of base Wheels

Degree of leg comfort Degree of base movement

Whole body

Number of colors used Use of decoration Use of pattern Use of cushion Use of curved lines Size of whole body

Width–height ratio of whole body Areal ratio of seat pan and backrest Number of materials used Degree of surface material cleanness Number of controls Access and ease of adjust controls

office use as opposed to the home use chairs. The price range of the collected chairs was $100 to $2000. Fig. 2 presents examples of the office chairs used in the data collection. Three different types of scales were used to measure the design variables: rating (experimenters rate a product based on rating scales), measurement (a physical dimension is measured using an equipment), and category (a proper category is selected by experimenters). A measurement checklist was developed to measure the products systematically. 3.2. Affective user satisfaction data Yun et al. (2001) reported that affective user satisfaction towards office chairs could be classified into 13 specific dimensions as shown in

Fig. 2. Examples of office chairs used in the data collection.

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Table 2 Image/impression dimensions of office chairs (modified from Yun et al., 2001) Dimension

Definition

Luxuriousness Balance

How luxurious a product looks How balanced the shape, layout and size of a product look How simple the design or image of a product looks How attractive a product is How voluminous a product is How attractive the color of a product looks How comfortable a product looks How attractive the texture of a product is (visually or tactually) How harmonious a product looks How rigid and stable a product looks How clear and neat the appearance of a product looks How elegant or graceful a product looks How satisfactory a product is

Simplicity Attractiveness Volume Color Comfort Texture Harmoniousness Ruggedness Neatness Elegance Overall satisfaction

Table 2. The dimensions shown in Table 2 are images/impressions that the users could feel towards office chairs. A total of 60 subjects voluntarily participated in an evaluation experiment. An equal number of male and female subjects participated in the evaluation. To investigate age and gender effects, the participants were divided into four groups: (1) males in 20s–30s (average of 28.7), (2) males in 40s–50s (average of 44.9), (3) females in 20s–30s (average of 27.3), and (4) females in 40s–50s (average of 44.7). A within-subjects design was used in the evaluation experiment. In other words, each participant evaluated every product for every user satisfaction dimension. In the instruction session, affective user satisfaction dimensions were explained and the participants performed practice trials to get familiar with the experimental task. In the main experiment, they evaluated each product using a rating scale between 0 (absolutely disagree) and 100 (absolutely agree) for the affective dimensions. The order of products and dimensions was randomized to avoid any systematic effects. They were allowed to see, touch, sit on and adjust the chairs for

evaluation. It took a subject about 2.5 h to evaluate 50 chairs on 13 dimensions. One of the primary purposes of this study is to compare performance between fuzzy rulebased and regression-based models. However, comparing all 13 models would be time consuming and require a large amount of efforts. In addition, it is not necessary to compare all the models to get insights into performance differences. Thus, this study selected a part of the dimensions: luxuriousness, balance, and attractiveness for comparison.

4. Developing fuzzy rule-based models Fuzzy rule-based models were developed in four steps: (1) variable screening in which irrelevant input variables were eliminated, (2) model validation and selection in which the best set of input variables was selected for modeling, (3) final model building in which fuzzy rule-based models were developed, and (4) model interpretation in which the models are translated back to the designer’s terms. The following four sections describe in detail each of the steps. 4.1. Variable screening Selecting appropriate input variables is important in a modeling procedure. Irrelevant variables should be screened out before building models, because a model with a large number of input variables is difficult to handle, and may lead to misleading interpretations. Since the variables listed in Table 1 are an entire set for all 13 affective dimensions, it was necessary to select only variables for the three dimensions of interest. A reduced set of variables were determined by expert opinions and brainstorming. For a dimension, each variable was evaluated and rated as one of four categories (strongly relevant, relevant, weakly relevant, or irrelevant). Weakly relevant and irrelevant variables were eliminated. Table 3 shows the variables remained after the screening. Note that only continuous variables were used to build fuzzy rule-based models because categorical variables are known to be difficult to handle in fuzzy rule-based models (Yen and Langari, 1998).

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Table 3 Design variables remained after screening Satisfaction dimension

Number of variables

Continuous variable

Categorical variable

Luxuriousness

11 (11a)

Tilt of backrest Width of backrest Height of backrest Height of whole body Areal ratio of seat pan and backrest Number of controls Brightness of backrest color Use of decoration Use of pattern Use of cushion Size of whole body

Wheels Low back support Headrest Shape of backrest Material of backrest Color of backrest Material of seat pan Color of seat pan Shape of armrest Material of armrest Shape of base

Balance

3 (1a)

Width—height ratio of backrest Width—height ratio of whole body Areal ratio of seat pan and backrest

Shape of backrest

Attractiveness

5 (6a)

Width—height ratio of backrest Number of colors used Brightness of backrest color Use of decoration Use of curved lines

Shape of backrest Material of backrest Color of backrest Color of seat pan Color of armrest Shape of base

a

Number of categorical variables.

4.2. Model validation and selection Although irrelevant variables were already eliminated, the number of remaining variables is still too large. For example, the luxuriousness dimension had a total of 11 variables that survived from the variable screening process. Including all of them in a model is not only inefficient but also undesirable for model performance, since models with too many variables are unlikely to perform well on new data (Duda et al., 2001). One way of avoiding this problem is to examine model performance of various variable subsets, and choose the best one. This is called the best subset procedure. This procedure finds the best subset of r variables where r is given a priori (Draper and Smith, 1981). It examines all possible combinations of r variables in terms of a specific performance criterion. In this study, since the proper number of variables (r) is not known, the best subset procedure was applied for different subset sizes. To consider both model fitness and generalization

ability, sum of training and checking mean squared errors (MSE) was used as the performance criterion. A 10-fold cross validation was used (Stone, 1974). That is, fifty product data were randomly divided into 10 sub-data sets. A model was built based on nine of them (45 data points), and checked by the remaining one (5 data points). This process was repeated ten times with different combinations of training and checking data sets, and the averages of training and checking MSE were calculated, respectively. Fig. 3 shows performance of the best subset models for luxuriousness. In all the four user group models, both training and checking MSEs decrease initially, but at a certain point, checking MSEs start to increase while training MSEs remain decreasing or stable. This means that beyond a certain number of variables, the model tends to overfit the data. An overfitted model explains the training data almost completely, however it cannot be generalized to explain new and untrained data (Duda et al., 2001). Note that

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Fig. 3. Performance of the best subset models for luxuriousness (by user group with different subset sizes). (a) Models for males in 20s– 30s; (b) Models for males in 40s–50s; (c) Models for females in 20s–30s; (d) Models for females in 40s–50s.

the models for the other dimensions showed similar patterns. The best subset model providing the least sum of training and checking MSE was selected as the final model for each affective user dimension. Note that the number of variables in the final models ranged from one to four. 4.3. Final model building Final models were developed using the variables selected in the previous step, which utilized all the 50 products data. It was not necessary to separate a checking data set in developing the models because the previous step confirmed the best set of input variables for modeling performance. A total of 12 fuzzy rule-based models were developed for luxuriousness, balance, and attractiveness dimensions of four different user groups. The entire set of modeling results is presented in Appendix A. An attractiveness model for office chairs (female users in 20s–30s) is presented in Table 4 as an

example. The model consists of three fuzzy rules, each of which explains attractiveness of an office chair in terms of its use of decoration and curved lines (i.e., roundness). The if–part of a rule shows the center and the radius of an input cluster, and the then–part presents a local linear model for the cluster. For example, Rule 1 in Table 4 shows that near the center point of Cluster 1 (x30 ; x35 )= (1.096, 0.284), attractiveness of a chair can be estimated by the polynomial 5:065x30  1:131x35 þ 55:63; where x30 is the use of decoration and x35 is the use of curved lines. 4.4. Model interpretation Proper model interpretation provides useful information about design features and their effects on affective user satisfaction. In addition, the fuzzy rule-based models developed in this study can provide product cluster information. They show how the products are classified according to their design features. The affective user

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Table 4 Fuzzy rule-based model for attractiveness of office chairs (female users in 20s–30s) Rule

If–part (cluster)

Then–part (local model) x35

x30

Rule 1 Rule 2 Rule 3

y

Center

Radius

Center

Radius

Equation

1.096 1.979 0.396

1.009 1.009 1.009

0.284 0.159 1.842

1.021 1.021 1.021

y ¼ þ5:065x30  1:131x35 þ 55:63 y ¼ þ2:367x30 þ 2:138x35 þ 41:3 y ¼ þ3:603x30 þ 4:277x35 þ 53:77

y=attractiveness of a chair (female users in 20s–30s); x30=use of decoration; x35=use of curved lines.

7

High

Cluster 3 6

Medium

5

Roundness

Cluster 2

4

ter 2

3 Cluster 1 2

Low

satisfaction level of each product cluster can also be estimated by entering each cluster center value into the models. For the example shown in the above (i.e., attractiveness model for female users in 20s–30s), each rule’s cluster can be visualized as a circle in a two-dimensional input space as shown in Fig. 4. Products are represented in the graph as small dots. By adding the mean value of each variable (x30 ; x35 )=(2.646, 3.909), three cluster centers (1.096, 0.284), (1.979, 0.159), and (0.396, 1.842) in Table 4 are converted back to the original 7-point rating scale, resulting in (1.577, 3.625), (4.625, 3.750), and (2.250, 5.751), respectively. The three clusters represent products with Low decoration and Medium roundness (Cluster 1), High decoration and Medium roundness (Cluster 2), and Medium–Low decoration and High roundness (Cluster 3). Model outputs of the cluster centers were 50.1, 46.0, and 59.4, respectively. This result implies that the female subjects in 20s–30s evaluated the products near Cluster 1, 2, and 3 as medium, low, and high attractiveness, respectively. In Table 4, the parameters of the then–part equations can be considered as the effects of design variables in the corresponding product cluster. For example, the model of Rule 1 can be interpreted in such a way that for the Cluster 1 products the decoration has a positive effect on the users’ feeling of attractiveness (i.e., x30 has a positive coefficient value of 5.065), while the roundness has a negative effect (i.e., x35 has a negative coefficient value of 1.131). Note that the effect of a design variable differs among different product clusters. The other models can be interpreted in this way.

1 0

0

1

Low

2

3

4

Medium

5

6

7

High

Decoration Fig. 4. Fifty products (dots in the figure) are classified into three fuzzy clusters (circles).

5. Comparison with multiple linear regression models Traditional regression models were built on the same data set and compared with the fuzzy rulebased models. The same procedure proposed by Han et al. (2000) was used to build the regression models. The same variable screening procedure was used as described in Section 4.1. Note that categorical variables were included in building the models because the regression approach is capable of handling them. In addition, second-order terms and two-factor interactions were added to the pool of input variables. This process was necessary

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Table 5 Result of the regression models

Add Square and InteractionTerms for the Continuous Variables.

α =0.05

Stepwise Regression

Satisfaction dimension

User group

Luxuriousness

Males in 20s–30s 10.2 Males in 40s–50s 7.4 Females in 20s–30s 9 Females in 40s–50s 8.6

0.927 0.884 0.833 0.854

Balance

Males in 20s–30s Males in 40s–50s Females in 20s–30s Females in 40s–50s

0.491 0.356 0.459 0.407

Attractiveness

Males in 20s–30s Males in 40s–50s Females in 20s–30s Females in 40s–50s

α = α + 0.05 number of Vars. ≤ 12 Max VIF < 10

NO

YES Save the Model as a Candidate

Max VIF < 2 YES NO

Average Average number of R2 variables

6.8 7.2 6.2 6.2 12 12 10 11

0.799 0.727 0.714 0.711

Delete the Variable with Max VIF and Build a new Model

Select the Best Model

Fig. 5. Procedure for building regression models.

because it would be fair to compare the fuzzy models with the best regression models. Before modeling began, input variables were selected using a stepwise selection procedure (Miller, 1990). Coefficient of determination (R2 ), PRESS, and variance inflation factor (VIF) were considered to select the best subset regression models. Fig. 5 briefly illustrates the regression model building procedure. Like the fuzzy approach, a 10-fold cross validation was used again. Nine sub-data sets were used to build a model, with remaining one for checking. This was repeated five times with random combinations of training and checking data sets, and the average was taken for each performance measure. Table 5 summarizes the result. The two approaches were compared in terms of prediction capability, model interpretation, and the number of variables in the models. 5.1. Prediction capability Fig. 6 presents training and checking errors between the two approaches. The training errors,

shown in Figs. 6(a), (c), and (e), represent the goodness of fit. Both models showed a good fit and there was little difference between them. The checking errors indicating prediction performance are presented in Figs. 6(b), (d), and (f). Note that the fuzzy models have smaller checking errors (average RMSE of the fuzzy models (4.32) was 45.7% less than that of the regression models (7.96)), which imply better prediction performance. 5.2. Number of variables The fuzzy models generally had a smaller number of variables than the regression models. The average number of variables included in the models is presented in Fig. 7. The average was taken over the four user groups. Note that the fuzzy models included only 2–3 independent variables, while the regression models included from 3 to 15, and 8.88 on the average. The average number of parameters in the models is shown in Fig. 8. Although the fuzzy models have a much smaller number of variables than the regression models, the average number of parameters in the fuzzy models is only slightly smaller than that in the regression models. It is because the fuzzy models have multiple rules, each

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J. Park, S.H. Han / International Journal of Industrial Ergonomics 34 (2004) 31–47

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Males Females Females 40s-50s 20s-30s 40s-50s

Fuzzy rule-based model

Regression model Fig. 6. Training and checking errors. (a) Luxuriousness-Training error; (b) Luxuriousness-Checking error; (c) Balance-Training error; (d) Balance Checking error; (e) Attractiveness-Training error; (f) Attractiveness-Checking error.

of which has its own parameters for the variables, while the regression models have only one for each variable. The difference in the number of variables is attributable to the difference in the number of initial input variables. The fuzzy models excluded categorical variables, while the regression models considered not only categorical, but also twofactor interactions and second-order variables as input candidates. Note that including more and more variables in a fuzzy model tends to overfit the data as shown in Fig. 3. On the other hand, reducing the number of variables in the regression

approach would lead to an underfit or poor performance in prediction. Therefore, it is concluded that the difference in the number of variables comes from inherent characteristics of the two approaches. The multiple local modeling strategy of the fuzzy rule-based model makes it possible to use a small number of input variables by applying multiple parameters for each. A smaller number of variables makes model interpretation simple and understandable. Nevertheless, it should be noted that the models may provide incomplete information on potential design variables.

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5.3. Model interpretation As explained earlier, the fuzzy rule-based models provide information about product

The number of variables

12 10 8 6 4 2 0 Luxuriousness

Balance

Attractiveness

Fuzzy rule-based models Regression models

Fig. 7. Average number of variables included in the model.

The number of parameters

12 10 8 6

clusters. They classify products into several clusters by product characteristics related to affective user satisfaction. The affective user satisfaction level of each product cluster can be identified as well. The rules can be interpreted to describe the influence of design variables in each cluster. It is assumed that the effect of a design variable varies from cluster to cluster. However, care should be taken when interpreting each local model. According to a recent report, individual fuzzy rules can show an erratic local behavior, while a global model generates a good behavior (Yen and Gillespie, 1995). In the regression models, global effects of design variables are easily understood. One difficulty is however, to interpret second-order terms and interactions. These terms were needed because the regression models attempted to describe the global non-linear behavior with one linear equation. These terms are not easy to understand unless prior information is available. As a result, from the perspective of interpretation, these two modeling approaches are complementary to each other. The fuzzy rule-based models classify products by their characteristics and give local information for each cluster, while the regression models describe the global effects of design variables. 5.4. Summary of comparison

4 2 0 Luxuriousness

Balance

Attractiveness

Fuzzy rule-based models Regression models

Fig. 8. Average number of parameters included in the model.

The two modeling approaches are compared in Table 6. A fuzzy rule-based model consists of multiple local linear models, while a regression model is a single global model. A fuzzy model cannot handle categorical variables, while a regression model can. A fuzzy model predicts more accurately than a regression model with a smaller number of variables.

Table 6 Comparison of two modeling approaches Comparison item

Fuzzy rule-based model

Regression model

Model characteristic Input variable types

Multiple local linear models Rating type Measurement type

Number of variables Predictive capability Model interpretation

Small (2–4 variables) Better Product classification Local effects of design variables

A global linear model Rating type Measurement type Category type Large (3–15 variables) Worse Global effects of design variables

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A regression model can give information about the global influence of each design variable, which is hardly provided by a fuzzy model.

6. Conclusion Fuzzy rule-based models were examined to explain the relationship between affective user satisfaction and product design variables. The proposed technique was applied to modeling luxuriousness, balance, and attractiveness of office chairs for various user groups. A total of 12 models were developed, and one of them was interpreted as an example. To verify performance of the proposed approach, traditional regression models were built using the same data, and compared. Fuzzy rule-based models had a benefit in terms of the number of variables. They also turned out to be adequate for predicting affective user satisfaction levels of a new product. Fuzzy models provide information on product classes and their satisfaction levels, while regression models describe the global effect of design variables. With time and cost limitations, product designers or developers can choose any of the two

modeling approaches depending upon his/her main purpose. A fuzzy model is recommended when prediction accuracy is critical, or it is necessary to classify products into groups based on design features. It is also preferred when only a few design variables are available, or of interest. On the other hand, a regression model would be better if simple expression of the model is need, or overall effects of design variables are of interest. When there are no limitations on time and budget, both models can be developed so that information from the two models are combined together. This would provide more fruitful information on affective user satisfaction. In conclusion, a fuzzy rule-based model can be used in place of, or at least complementary to a regression model to investigate the relationship between affective user satisfaction and product design. It considers both non-linearity and fuzziness of psychological responses of human users. Relevant to this point is Nagamachi’s remark (1991): ‘‘Psychological feeling of product image is a fuzzy concept.’’ Proposed models can help product designers to get insights into important design variables, and to estimate responses of various user groups for a new product design.

Appendix A. Twelve fuzzy rule-based models developed in this study Model for luxuriousness (male users in 20s–30s) Rule

If–part (cluster)

Then–part (local mode) x20

x3

Center

x32

Center

Radius

Radius

Rule 1

5.334

12.13

1.373

1.324

Rule 2

5.966

12.13

1.503

Center

x33

y

Radius

Center

Radius

Equation

0.129

1.244

0.366

1.157

1.324

0.004

1.244

0.259

1.157

y ¼ þ0:2948x3  3:204x20  8:536x32 þ 8:689x33 þ 75:81 y ¼ þ1:04x3  7:257x20 þ 1:814x32 þ 9:244x33 þ 51:27 y ¼ þ1:247x3  4:811x20 þ 1:26x32 þ 5:293x33 þ 22:25 y ¼ 1:602x3 þ 15:12x20 þ 3:862x32  9:259x33  14:31

Rule 3

24.67

12.13

1.828

1.324

0.554

1.244

2.309

1.157

Rule 4

9.834

12.13

2.623

1.324

2.346

1.244

0.816

1.157

y=Luxuriousness of a chair (male users in 20s–30s). x3=Height of backrest. x20=Brightness of backrest color. x32=Use of cushion. x33=Size of whole body.

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44

Model for luxuriousness (male users in 40s–50s) Rule

If–part (cluster) x31

Rule 1 Rule 2 Rule 3

Then–part (local model) x33

y

Center

Radius

Center

Radius

Equation

0.096 2.03 1.721

1.337 1.337 1.337

0.491 0.991 2.159

1.157 1.157 1.157

y ¼ þ1:386x31 þ 4:118x33 þ 58:57 y ¼ 1:719x31 þ 13:06x33 þ 60:91 y ¼ 6:122x31 þ 2:361x33 þ 56:51

y=Luxuriousness of a chair (male users in 40s–50s). x31=Use of pattern. x33=Size of whole body. Model for luxuriousness (female users in 20s–30s) Rule

If–part (cluster) x16

Rule 1 Rule 2 Rule 3

Then–part (local model) x30

x33

y

Center

Radius

Center

Radius

Center

Radius

Equation

0.54 1.46 1.46

1.98 1.98 1.98

0.396 0.896 2.479

1.009 1.009 1.009

0.441 0.759 2.309

1.157 1.157 1.157

y ¼ 2:606x16  2:28x30 þ 3:296x33 þ 33:2 y ¼ 6:266x16 þ 14:48x30  5:772x33 þ 97:74 y ¼ 5:16x16 þ 3:042x30 þ 8:501x33 þ 54:13

y=Luxuriousness of a chair (female users in 20s–30s). x16=Number of controls. x30=Use of decoration. x33=Size of whole body. Model for luxuriousness (female users in 40s–50s) Rule

If–part (cluster) x1

Then–part (local model) x30

x32

x33

y

Center

Radius

Center

Radius

Center

Radius

Center

Radius

Equation

Rule 1

0.84

10.39

0.771

1.009

0.946

1.244

0.378

1.157

Rule 2

3.84

10.39

0.104

1.009

0.629

1.244

0.916

1.157

Rule 3

7.16

10.39

1.146

1.009

0.754

1.244

0.834

1.157

Rule 4

0.84

10.39

2.104

1.009

0.129

1.244

1.509

1.157

y ¼ þ0:3225x1  6:411x30 þ 5:394x32 þ 10:03x33 þ 63:66 y ¼ 0:4287x1 þ 4:537x30  0:2512x32 þ 5:066x33 þ 50:51 y ¼ 0:2572x1 þ 13:47x30 þ 3:439x32  1:273x33 þ 78:9 y ¼ þ0:1195x1 þ 9:419x30  4:622x32 þ 4:203x33 þ 48:63

y=Luxuriousness of a chair (female users in 40s–50s). x1=Tilt of backrest. x30=Use of decoration. x32=Use of cushion. x33=Size of whole body.

ARTICLE IN PRESS J. Park, S.H. Han / International Journal of Industrial Ergonomics 34 (2004) 31–47 Model for balance (male users in 20s–30s) Rule

If–part (cluster) x13

Rule 1 Rule 2 Rule 3

Then–part (local model) x14

y

Center

Radius

Center

Radius

Equation

0.071 0.293 0.088

0.235 0.235 0.235

0 0.599 0.386

0.266 0.266 0.266

y ¼ þ17:57x13 þ 55:13x14 þ 55:09 y ¼ þ10:21x13 þ 35:55x14 þ 49:95 y ¼ 43:28x13 þ 109:2x14 þ 105:7

y=Balance of a chair (male users in 20s–30s). x13=Width–height ratio of whole body. x14=Areal ratio of seat pan and backrest. Model for balance (male users in 40s–50s) Rule

Rule 1

If–part (cluster)

Then–part (local model)

x14

y

Center

Radius

0.011

0.266

Equation y ¼ þ10:1x14 þ 63:77

y=Balance of a chair (male users in 40s–50s). x14=Areal ratio of seat pan and backrest. Model for balance (female users in 20s–30s) Rule

If–part (cluster) x13

Rule 1 Rule 3

Then–part (local model) x14

y

Center

Radius

Center

Radius

Equation

0.107 0.195

0.235 0.235

0.074 0.375

0.266 0.266

y ¼ 27:68x13 þ 18:6x14 þ 56:92 y ¼ 16:93x13 þ 13:6x14 þ 68:74

y=Balance of a chair (female users in 20s–30s). x13=Width–height ratio of whole body. x14=Areal ratio of seat pan and backrest. Model for balance (female users in 40s–50s) Rule

Rule 1 Rule 2

If–part (cluster)

Then–part (local model)

x14

y

Center

Radius

0.1 0.325

0.266 0.266

y=Balance of a chair (female users in 40s–50s). x14=Areal ratio of seat pan and backrest.

Equation y ¼ þ3:615x14 þ 61:28 y ¼ þ9:571x14 þ 70:43

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Model for attractiveness (male users in 20s–30s) Rule

If–part (cluster) x6

Rule 1

Then–part (local model) x35

Center

Radius

Center

0.018

0.2646

0.217

y Radius

Equation

1.021

y ¼ 9:016x6 þ 1:045x35 þ 59:6

y=Attractiveness of a chair (male users in 20s–30s). x6=Width–height ratio of backrest. x35=Use of curved lines. Model for attractiveness (male users in 40s–50s) Rule

If–part (cluster)

Then–part (local model)

x6

y

Center Rule 1 Rule 2

Radius

0.1 0.48

Equation y ¼ þ0:9181x6 þ 58:89 y ¼ 6:713x6 þ 56:83

0.2646 0.2646

y=Attractiveness of a chair (male users in 40s–50s). x6=Width–height ratio of backrest. Model for attractiveness (female users in 20s–30s) Rule

If–part (cluster) x30

Rule 1 Rule 2 Rule 3

Then–part (local model) x35

y

Center

Radius

Center

Radius

Equation

1.096 1.979 0.396

1.009 1.009 1.009

0.284 0.159 1.842

1.021 1.021 1.021

y ¼ þ5:065x30  1:131x35 þ 55:63 y ¼ þ2:367x30 þ 2:138x35 þ 41:3 y ¼ þ3:603x30 þ 4:277x35 þ 53:77

y=Attractiveness of a chair (female users in 20s–30s). x30=Use of decoration. x35=Use of curved lines. Model for attractiveness (female users in 40s–50s) Rule

If–part (cluster) x6 Center

Rule 1 Rule 2 Rule 3

0.087 0.231 0.041

Then–part (local model) x20

Radius

Center

0.2646 1.373 0.2646 1.753 0.2646 0.878

x35

y

Radius

Center

Radius

Equation

1.324 1.324 1.324

0.467 0.284 1.892

1.021 1.021 1.021

y ¼ 4:087x6  4:918x20  0:1528x35 þ 70:6 y ¼ 14:38x6  1:447x20 þ 1:111x35 þ 59:53 y ¼ 37:02x6 þ 3:121x20 þ 12:17x35 þ 52:82

y=Attractiveness of a chair (female users in 40s–50s). x6=Width–height ratio of backrest. x20=Brightness of backrest color. x35=Use of curved lines.

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