Modeling affective responses for product form design based on consumer
segmentation and information fusion
Fang-Chen Hsu, Meng-Dar Shieh
Department of Industrial Design, National Cheng Kung University, Tainan, Taiwan
70101
Chih-Chieh Yang
Department of Multimedia and Entertainment Science, Southern Taiwan University,
Tainan County, Taiwan 71005
Abstract
In the product design field, modeling consumer’s affective responses (ARs) for
product form design is very helpful for developing successful products. However, the
heterogeneous nature of consumer preference patterns is often neglected in most
researches thus the resulting prediction model is of less value for the real-world
applications. In the present paper, a Kansei engineering (KE) method is proposed to
construct the consensus prediction model of consumer’s ARs based on the concepts of
consumer segmentation (CS) and information fusion (IF). First, a fuzzy c-means
(FCM) clustering is applied to separate the consumers with heterogeneous preference
patterns into homogenous groups. In every consumer group, the relative importance
of each consumer and the interaction between pairs of consumers can be determined
according to the results of the FCM clustering. Secondly, a state-of-the-art machine
learning approach known as “support vector regression (SVR)” is used to construct
the individual AR prediction model for each consumer. These individual models have
out-performing predictive ability of the ARs for each consumer due to the good
generalization performance of the SVR algorithm. Finally, a fuzzy integral
aggregation operator, namely the 2-additive Choquet integral, is used to combine the
SVR models and also taking into account the relative importance and interaction of
consumers in the consumer group. A case study of mobile phone design is also given
to demonstrate the effectiveness of the proposed method.
Keywords: Product form design; Kansei engineering; Fuzzy c-means clustering;
Support vector regression; 2-additive Choquet integral.
1. Introduction
In today’s highly competitive market, the benefits provided by products must
meet the consumer’s needs to ensure the success of enterprises. The degree of
consumer’s affective responses (ARs), as a critical criterion to measure if a product
meets the needs of a consumer, is very important for choosing attractive product
design to consumers. Aim at capturing consumer’s preference and relates it into the
products, the problem of modeling ARs can be found in many disciplines. For
example, consumer preferences related to product attributes has been studied
intensively in the field of consumer research. In food industry, the research of
hedonics emphasizes to analyze the characteristics of food, such as outward
appearance and the chemometrics data, and examine their effects on the consumer’s
feelings (MacKay, 2006). The study of emotional responses in product design
explores how to design products triggering ‘happiness’ in consumer’s mind and find
out which product attributes help in communication of positive emotions (Demirbilek
& Sener, 2003). The purpose of these research is try to connect consumer’ ARs to the
target products regardless that they are described with different domain-specific
product attributes.
Product differentiation as a marketing strategy assumes that providing diversity
or variations of products according to consumer’s demand is helpful to obtain a
horizontal share of a broad market (Smith, 1956). However, for mature products
which have similar functionality and specification, such as consumer electronics, it is
difficult to design a product effectively and make it fit the consumer’s need well.
Since the way a product looks is one of the most important factors affecting a
consumer’s purchasing decision, modeling consumer’s ARs based on product form
design is very useful lead to success product design. Traditionally, the success of a
product’s design depended on the designers’ artistic sensibilities, which quite often
did not meet with great acceptance in the marketplace. Therefore, many systematic
product design studies have been carried out to get a better insight into consumers’
subjective perceptions. The most notable research is Kansei engineering (KE)
originated from Japan (Nagasawa, 2004). The basic assumption of KE is that there
exists a cause-and-effect relationship between consumers’ ARs and product form
features (PFFs). The prediction model can be constructed by consumers’ evaluation
data gathered from questionnaire investigation and the PFFs of the evaluated product
samples. Using the prediction model, the relationship between ARs and product form
design can be analyzed and a specially designed product form for specific target
consumer groups can be produced more objectively and efficiently.
In the literatures of KE, it hasn’t be pointed out explicitly that the complexity for
modeling ARs is mainly due to its multiple-consumer versus multiple-product nature.
The construction of the prediction model is often involved with large amounts of
consumers with heterogeneous needs and a wide variety of products. Two different
schemes
including
single-consumer/multiple-product
and
multiple-consumer/single-product can be identified to clarify this modeling problem.
On the one hand, the single-consumer/multiple-product scheme can be regarded as a
kind of personal preference profiles concerning with various product alternatives.
Similar ideas can be found in the research of online recommendation system or
e-commerce applications. In such an open-selection environment which consumer can
freely to choose their preference products, the preferred products of consumers are
usually different. Instead of providing personal recommendation for individual
customer only, unified suggestion for certain target group of consumer, called
collaborative recommendation, is often of greater interest (Cheung, Kwok, Law, &
Tsui,
2003).
However,
the
potential
to
combine
individual
single-consumer/multiple-product models into one unified suggestion model is
seldom to be mentioned in the product design field. On the other hand, the
multiple-consumer/single-product scheme, which is frequently used in KE research,
deals with the consumer’s data by averaging individual consumer evaluation data for
the same product. The problem of data averaging of consumer evaluation data is that
using the averaged data can only capture the most manifest trends in consumer
satisfaction patterns. Since the consumer’s ARs are usually heterogeneous in nature,
averaged consumer data may fail to represent any individual opinion (Lee & Pope,
2003). Another strategy to handle the consumer data called “mean centering”, in
which the variance for individual consumer is taken into consideration, suffers the
same shortcoming (Westad, Hersleth, & Lea, 2004).
This study proposed a KE method to construct the consumer’s AR model of
product form design based on the concepts borrowed from consumer segmentation
(CS) and information fusion (IF). In the proposed method, a fuzzy c-means (FCM)
clustering is applied to separate the consumers with heterogeneous opinions into
homogenous groups of consumers with similar preferences. For segmentation purpose,
the preference data of consumers evaluated on the representative product samples is
used as segmentation variable. In every homogenous cluster obtained by FCM
clustering, the relative importance of each consumer can be determined by the
membership grades while the interaction between pairs of consumers determined by
their distance in a multidimensional scaling space. Individual prediction model of ARs
for each consumer is constructed using support vector regression (SVR). The PFFs
used as input data and the evaluated AR scores gathered from the questionnaire as
output values are used to construct the prediction model. In order to deriving a unified
consensus model for each homogenous group and combine the prediction model of
each consumer in the group, a fuzzy integral method, namely the 2-additive Choquet
integral, is used to aggregate the output AR value of individual consumer prediction
model considering the importance and interaction of consumers within the group.
The reminder of the paper is organized as follows. Section 2 reviews the
background of AR modeling, CS, and IF. Section 3 presents the outline of the
proposed KE method for modeling ARs of product form design. The detailed
implementation procedure of the proposed KE method is given in Section 4. Section 5
demonstrates the results of the proposed method using mobile phone designs as an
example. Finally, Section 6 presents some brief conclusions.
2. Background review
2.1. Prediction model of affective responses
One of the frequently encountered problems for modeling ARs is how to deal
with the nonlinear relationship between the PFFs and the ARs of consumer. There
exist various methods which can be used to construct the prediction model regarding
it as a regression/function estimation problem. The mostly adopted techniques in the
product design field such as multiple linear regression (MLR) (Han, Kim, Yun, &
Hong, 2004) and partial least squares regression (PLSR) (MacKay, 2006) heavily
dependent on the assumption of linearity hence can not deal with the nonlinear
relationship effectively. In addition, prior to establish the prediction model, data
simplification or variable screening is often needed to obtain better results. In order to
deal with the nonlinearity, “black-box” methods including neural networks (NN) and
SVR are good candidates for building the prediction model. Also, endowed with
numerous highly-evolving techniques developed in machine learning, NN and SVR
have great potential to construct real-world applications instead of in-lab research. For
example, equipped with reliable techniques for model/parameter selection, such as
cross-validation (CV), ensemble learning, and Bayesian inference, one can obtain best
generalization performance and reduce the overfitting problem. The capability to
integrate with fuzzy set and rough set is beneficial for processing the analytical data in
the format of imprecise and vague information in product design. It is a common
situation for modeling ARs to involve with large amounts of consumers and product
samples. Therefore, the technique of “mixture of expert”, which is often used as a
divide-and-conquer scheme in pattern recognition, is also very suitable to reduce the
complexity for modeling prediction model. These ideas are yet be explored widely in
the product design field.
2.2. Consumer segmentation
Since Smith (1956) presented the concept of CS, it has become an important
marketing strategy. It is known that the need of consumer is often diverse and
heterogeneous. By distinguishing different homogeneous groups, more precise
adjustment of product alternatives to these consumer groups can be made. In order to
recognize the consumer heterogeneity effectively, the choice of relevant segmentation
variables and the methods used to construct segments are two critical factors.
Different consumer characteristics such as demographics, lifestyle, socio-economic
factors, purchase behavior, attitudes/preference toward product alternatives etc., can
be used as segmentation variables to construct segments. For example, Bock &
Uncles (2002) had identified five distinct types of CS according these segmentation
variables. In this study, the AR is regarded as a kind of consumers’ needs. Thus, the
segmentation variables should be capable to reflect their preferences toward product
design. The variables such as demographics, lifestyle and other factors which are
frequently used in marketing research do not directly connected to the product itself
thus not suitable for CS in product design. On the contrary, the preference data of
consumers evaluated on the representative product samples is more suitable to be used
as segmentation variable for AR research in product design.
The construction of CS had commonly applied cluster analysis. The purpose of
cluster analysis is to construct homogenous groups with respect to the segmentation
variables. Various methods including K-means clustering, self-organizing maps, FCM
clustering, and support vector clustering had been used for CS. Among these methods,
FCM clustering is the most robust method compared to other non-fuzzy clustering for
CS (Shin & Sohn, 2004). FCM clustering is known as being capable to deal with the
overlapping clusters and is stable even in the presence of outliers. The main reason of
its superiority is due to the production of the fuzzy partition in which each data point
is associated with a set of membership grades indicating the degrees this point
belongs to the different clusters. The distances between data points in the clustering
results also provide useful information to understand their mutual relation. In a
consequence, FCM clustering is very suitable for the application of CS.
2.3. Information fusion
IF has drawn considerable interests in the field of multicriteria decision making
(MCDM) and pattern recognition in recent years. It involves with merging different
information sources to obtain the consensual opinion. Hence, it is very suitable to
combine preference information consists of subjective description of a group of
people. The simplest way to perform IF is via the use of aggregation operator. A
complete review of the existing aggregation operators can be found in the paper of Xu
& Da (2002). The crux of IF problem is to choose a suitable aggregation operator and
then different pieces of information can be combined to obtain a unified consensus.
However, due to the inherent interaction among diverse information sources, classical
operators such as average, minimum, maximum even for more generalization in the
additive form do not work well in the real world problems. Moreover, it has been
mentioned in Dubois & Prade (2004) that, although averaging operators are natural
candidates for merging preference data, they are not suitable for data expressed in
bipolar scales which were appeared frequently in the study of consumer preferences.
Another crucial issue of IF is to determine the relative importance of different
information sources, or more generally, to express the inherent interaction among
various information sources. For resolving the interaction between information
sources, the fuzzy integral is superior to other classical aggregation operators by
providing a more intuitive and effect manner with the aid of nonadditive set function
on the power set of all information sources. The Choquet integral can be regarded as
the generalized weighted mean operator and the Sugeno integral as the generalized
weighted maximum and weighted minimum operators. These two variants of the
fuzzy integral have also been proven to be valuable tools to deal with the IF problem
(Labreuche & Grabisch, 2003). It is also possible to integrate domain knowledge for
determining the importance and interaction of information sources automatically. For
example, to obtain membership grade of image pixel from the grey-level property
(Zhu, Bentabet, Dupuis, Kaftandjian, Babot, & Rombaut, 2002), incorporate with
spatial information into the decision making problem (Makropoulos & Butler, 2006),
or generate the weight distributions of aggregation operators based on probability
density functions (Sadig & Tesfamariam, 2007) etc. Inspired by these ideas, the
density and the distribution of the information sources obtained from the results of CS
based on fuzzy clustering can be used to aggregate the ARs of consumers.
3. Outline of the proposed affective response model for product form design
A typical prediction model of consumer’s ARs in KE is shown in Fig. 1. This
kind of model does not take into account the diversity and heterogeneity of
consumer’s ARs. More specifically, the prediction model only capture the most
manifest trends by aggregating the AR data y1 ,..., yn of n consumers using certain
aggregation operator Ag , such as the arithmetic average operator or the mean
centering technique. In fact, even the effects of different aggregator operators have
not been studied extensively in the field of KE. Moreover, considering the
performance of the methods used to construct the model, e.g. MLR and PLSR, can
only deal with the linear relationship between the PFFs x1 ,..., xm and the aggregated
consumer’s AR y Ag of all consumers. The resulting prediction model is of less value
to construct the real-world applications.
This study proposes to overcome the shortcomings of the typical prediction
model based on the concepts of CS and IF. The proposed AR model is consists of
three parts including construction of consumer groups, construction of individual AR
model for consumer and construction of the consensus prediction model. An overview
of the proposed model is shown in Fig. 2. First, with the aid of FCM clustering using
the consumer’s preference data evaluated on the representative product samples, all
consumers are grouped into different clusters. Consumers S1 ,..., Sn within each
consumer group are regarded as information sources with similar preferences. Two
characteristics of information sources including the relative importance w of the
consumers and the interaction I between pairs of consumers are considered. The
importance w of consumers S1 ,..., Sn are calculated according to their membership
grade 1 ,..., n belongs to the consumer group. The interaction I i , j between all
pairs of consumer Si and S j are calculated according to the distance d i , j in a
multidimensional scaling space. Secondly, a series of SVR prediction models
SVR1 ,..., SVRn are then constructed for consumers S1 ,..., Sn in the consumer group.
The product samples are decomposing into PFFs x1 ,..., xm using morphological
analysis. Training of these prediction models can be done by taking x1 ,..., xm as input
data while the individual AR y1 ,..., yn toward every product samples as output
values. By choosing suitable parameters of the training model, these individual
models will have out-performing predictive ability of the ARs for each consumer due
to the good generalization performance of the SVR algorithm. Finally, the 2-additve
Choquet integral aggregation operator Ag CI is used to combine the individual AR
y1 ,..., yn of the SVR models SVR1 ,..., SVRn and obtain an aggregated AR y Ag for
each consumer group. The aggregation operator Ag CI not only integrates the
individual AR y1 ,..., yn but is also capable to handle the relative importance w of
each consumer and the interaction I between pairs of consumers. In a consequence,
a unified consensus prediction model for each consumer group can be derived.
Consequently, the proposed method is very suitable for modeling the ARs of
consumers which exhibit with heterogeneous preference patterns while maintain high
predictive performance for product samples with unknown ARs. The complete
implementation procedures of the proposed model are detailed in the following
section.
<Insert Fig. 1 about here>
<Insert Fig. 2 about here>
4. Implementation procedures
4.1. Construction of consumer groups
4.1.1. Preference evaluation using representative products
A total of 69 mobile phones of different design were first collected from the
Taiwan marketplace. Three product designers each with at least 5 years experiences
were then asked to choose the most representative products according to their PFFs.
The resulting products picked up by the three designers were discussed and finally
condensed to 15 products for preference evaluation. In order to collect the preference
data of these representative products, 30 subjects (15 of each sex) were asked to
evaluate these products using a score from -1 (dislike) to +1 (like) in an interval of 0.1.
The preference data of consumers evaluated on the representative product samples is
used as segmentation variables for FCM clustering.
4.1.2. Fuzzy c-means clustering for consumer segmentation
FCM clustering is adapted to reveal the hidden structure of consumer preference
data by organizing the consumers into clusters such that consumers within a cluster
have similar preference toward product samples than other consumers belonging to
different clusters. Using FCM requires the setting two parameters including the
number of clusters c and the fuzzification parameter m . Tuning the parameter m
can adjust the influence of noise for clustering. In addition, for m  1 , FCM
becomes hard and finally reduced to the typical K-means clustering. In this study, the
parameter m was adjusted from 1.05 to 2 while the number of clusters c was
varied from 2 to 7 to examine the effect of clustering. In order to check the
significance of the structure of preference data imposed by the clustering algorithm
and determine the optimal clustering parameters, how to assess the validity of the
clustering results is an important issue. Various validity measures have been reported
in the literatures (Xie & Beni, 1991) to identify the quality of clustering including
partition coefficient, classification entropy, partition index, separation index and
Xie-Beni index etc. However, the consumer preference data is often high-dimensional,
these validity measures which only provide a single numerical value might be difficult
to analyze and interpret. Low dimensional graphical representation of the clustering
results could be more informative than a single value. Principal component analysis
(PCA) and Sammon mapping are the two frequently used techniques for the
visualization of the clustering results. In this study, the FUZZSAMM algorithm (Feil,
Balasko, & Abonyi, 2007), which is a modified version of Sammon mapping, is
adapted. Compared to the Sammon mapping which only taking the distance between
data samples and the cluster centers into account, FUZZSAMM introduced the
membership values obtained from fuzzy clustering as additional weighted augment
and is more suitable for human inspection compared to other visualization techniques
(Feil, Balasko, & Abonyi, 2007). Consequently, the clustering results on the consumer
preference data will be used to calculate the importance and interaction of consumers
in each cluster in order to construct the consensus prediction model.
4.2. Construction of individual affective response model for consumers
4.2.1. Product form representation using morphological analysis
In this study, morphological analysis is used to represent the product form design.
Compared to other product form representations such as object-oriented
representation and level-of-detail representation, morphological analysis allows the
PFFs to be represented in a simple and intuitive manner. The mixture of continuous
and discrete attributes is also allowed. This method begins with decomposing the
product into several main components then examining every possible attribute for
each component. For this study, a mobile phone was decomposed into body, function
button, number button and panel. Continuous attributes such as length and volume are
recorded directly. Discrete attributes such as type of body, style of button etc. were
represented as categorical choices. Twelve PFFs of the mobile phone designs,
including four continuous attributes and eight discrete attributes, were used. Notice
that the color and texture information of the product samples were ignored and
emphasis was placed on the PFFs only. The PFFs of collected product samples were
used as input data fed into the SVR model. A complete list of all PFFs is shown in
Table 1.
<Insert Table 1 about here>
4.2.2. Determination of representative adjectives
Prior to conducting the AR evaluation experiment, the number of adjectives
needs to be reduced by screening out redundant or similar adjectives. In this study,
twenty-two bipolar adjectives were adopted from the research of Hsu, Chuang, &
Chang (2000), as shown in Table 2. Factor analysis as a feature extraction method was
used to merge similar adjectives from the original 22 dimensions and construct new
dimensions by choosing a suitable number of factors. The adjective with the highest
factor loading in each factor was chosen as the most representative. Although there is
no straightforward method to determine the number of factors, we followed the
suggestion of Miller (1956) that the number of adjectives used to conduct semantic
differential evaluations should be about 5 to 7. The number of factors was varied from
3 to 7 and examines the percentage of variances explained for each extracted factor.
The factor loading using three factors is shown in Table 3. The extracted three factors
account for 50.1%, 23.4% and 14.3% of explained-variance respectively. Notice that
factor 1 accounts for more than half of the percentages of variance. The total
cumulative percentage of variances is 87.8% indicating that the results of factor
analysis using three factors is quite acceptable. The increase in the factor number can
increase the total cumulative percentage. However, the variance of factor 1 remains
around 50% and the variance of the other factors would become too small (lower than
10%). As a consequence, representative adjectives were extracted using three factors
and the resulting adjectives were traditional-modern, rational-emotional and
heavy-handy. These three adjective-sets were used to conduct semantic differential
evaluations using a questionnaire.
<Insert Table 2 about here>
<Insert Table 3 about here>
4.2.3. Semantic differential evaluation for affective responses
Three bipolar adjectives including traditional-modern, rational-emotional and
heavy-handy were extracted using factor analysis. However, in order to simplifier the
aggregation process of the fuzzy integral and better investigate the property of the
aggregated results, only a unipolar half of the three adjectives, namely modern,
emotion and handy, is used for semantic differential evaluations (Osgood, Suci, &
Tannenbaum, 1957) to measure the ARs of consumers. For the task of collecting the
evaluation data for mobile phone design, 30 subjects were asked to evaluate each
product sample using a score in the unipolar scale between [0,1]. In this manner, they
can express their ARs toward every product sample using these three adjectives. It
should be mentioned that if consumers are asked to evaluate the whole set of product
samples at the same time, the experimental results will inevitably induce more errors.
As a consequence, each consumer was asked to evaluate only one-third product
samples of the total (23/69) randomly picked from all the samples. The product
samples were presented to consumers in the format of questionnaires by asking them
the semantic differential scores of most relevant adjectives. A user-friendly interface
for the questionnaire was also provided to collect the evaluation data in a more
effective way. The evaluation data of each consumer can be recorded directly, thus
simplifying the data post-processing time. The presentation order of the product
samples were randomized to avoid any systematic effects. Each consumer’s
evaluation scores toward every product samples were used as the output values in the
SVR model.
4.2.4. Construction of SVR training model
The SVR training model for each consumer is constructed based on the collected
product samples. The PFFs of these product samples were treated as input vectors
while the evaluation AR scores toward every product samples were used as output
values in the SVR model. Since SVR can only deal with one output value at a time,
three prediction models for each consumer were constructed according to different
adjectives. The training scheme of a single prediction model based on SVR is
depicted in Fig. 3. First, product samples consist of a series of input vectors are fed
into the training model. These input vectors are mapped into feature space by a map
function  . The mapping  is usually nonlinear and unknown. Instead of
calculating  , the kernel function K is used to compute the inner product of two
vectors
xi
and
xj
in
the
feature
space
 ( xi )
and
(x j ) ,
that
is,
K ( xi , x j )   ( xi )   ( x j ) . SVR is also known as its elegance in solving the nonlinear
problem with the kernel functions that automatically doe a nonlinear mapping to a
feature space. Any function satisfying Mercer’s condition can be used as the kernel
function (Vapnik, 1995). Of the commonly used kernel functions, the Gaussian kernel
is favored for many applications due to its good features (Wang, Xu, & Lu, 2003); and
thus was adapted as follows:
Gaussian kernel: K ( xi , x j )  exp( xi  x j
2
/ 2 2 ) ,
where  is the spread parameter determining the influence of squared distance
between xi and x j to the kernel value. Using Gaussian kernel, dot products are
computed with the output values of the training samples under the map  . The
weights in the SVR represent the knowledge acquired from the product samples.
Finally, the dot products are added up using the weights 1 ,...,  m . This, plus a
constant term b yields the final predictive output value as follows:
m
y    i K ( x, xi )  b .
i 1
For detailed derivations of the SVR algorithm, the authors recommend the textbook of
Vapnik (1995).
<Insert Fig. 3 about here>
4.2.5. Choosing optimal parameters of SVR model
The performance of the SVR model is heavily dependent on the regularization
parameter C , the parameter  of the  -insensitive loss function, and the spread
parameter  of Gaussian kernel. Therefore, choosing these parameters is crucial for
constructing SVR model. In this study, CV (Hsu, Chang, & Lin, 2003), as a simple
but reliable technique, is adopted to obtain the optimal training parameters of SVR in
a systematic manner to obtain the best generalization performance and reduce the
overfitting problem. The whole training set is divided into five subsets of equal size
(5-fold CV) to avoid the danger of overfitting. Since the process of CV is very
time-consuming, a two-step strategy is taken to find the optimal parameters. In the
first step, a coarse grid search is taken using the following sets of values:






C  105 ,104 ,...,105 ,   105 ,104 ,...,105 ,  2  105 ,104 ,...,105 . Thus 11×11×11
＝1331 combinations of parameters are tried in this step. An optimal (C0 ,  0 , 02 ) is
selected from the coarse grid search. In the second step, a fine grid search is
conducted around (C0 ,  0 , 02 ) , where
C  0.2C0 ,0.4C0 ,...,0.8C0 , C0 ,2C0 ,4C0 ,...,8C0  ,
  0.2 0 ,0.4 0 ,...,0.8 0 ,  0 ,2 0 ,4 0 ,...,8 0  , and

 2  0.2 02 ,0.4 02 ,...,0.8 02 , 02 , 2 02 , 4 02 ,...,8 02

A total of 9×9×9＝729 combinations are tried in this step. The final optimal
parameters are selected from this finer search. The root mean squared error (RMSE)
was used to evaluate the performance of training models on different parameters. The
RMSE is defined as following:
RMSE 
1 l
( yi  di ) 2
l i 1

where yi and d i denote the predicted output and the measured value respectively
of l product samples. The best combination of parameters of each SVR model is
chosen to build the prediction model of individual consumer using all product
samples.
4.3. Construction of consensus affective response prediction model
4.3.1. Fuzzy integral for fusing individual affective response models
In the application of product design, the consumer evaluation data can be either
expressed in numerical or qualitative format. Consumers can assign a numerical score
to each product sample or compare the product samples in an ordinal ranking
according to their subjective perception. For choosing suitable fuzzy integral method
for IF, it is known that the Choquet integral is more suitable for numerical data and
the Sugeno integral is suitable for qualitative data. Since our purpose is to construct
the unified consensus model which is capable to predict future product samples with
unknown ARs, the Choquet integral is adapted to aggregate consumer’s AR data in a
numerical scale. Based on the same rationale underlying the proposed methodology,
the Sugeno integral can also be used to combine ordinal models to suggest specific
product sample with highest degree of ARs. Moreover, depending on the considered
evaluation scale belongs to unipolar or bipolar, the adopted fuzzy integral needs to be
taken with special care. The traditional (asymmetric) Choquet integral is only capable
to deal with unipolar evaluation data. As for bipolar data, the Sipos integral
(symmetric Choquet integral) (Grabisch & Labreuche, 2002) or generalized Choquet
integral (Grabisch & Labreuche, 2005) based on the concept of bi-capacity have also
been proposed recently. However, in order to investigate the property of the
aggregated consensus model, only the unipolar evaluation data with traditional
Choquet integral is considered in this study.
In order to aggregate the unified output value from the output value set y1 ,..., yn
of an AR dimension obtained from n individual SVR model, the aggregation
operator Ag CI using the Choquet integral can be expressed as follows (Cliville,
Berrah, & Mauris, 2004):
n
AgCI ( y1 ,..., yn )   yi ( wi 
i 1
1
 Iij )  I0 min( yi , y j ) Iij  I0 max( yi , y j ) Iij ,
2 j i
ij
ij
where wi denotes the relative importance parameter of consumer Si and I ij
denotes the interaction parameter between pairs of consumers Si and S j . Note that
the above formulation is the 2-additive Choquet integral which only considers the
2-order interaction between couples of consumers. Although higher order of
interaction up to n -tuples can be defined, it is suffice to consider the 2-additive fuzzy
measures in most real world applications (Angilella, Greco, Lamantia, & Matarazzo,
2004).
4.3.2. Characterization of the importance and interaction parameters
The consensual consumer’s AR aggregated by the Choquet integral is largely
depends on the relative importance parameter wi and the interaction parameter I ij .
In order to explain the usage of the parameters wi and I ij , the interaction parameter
I ij is ignored and it can be seen that the Choquet integral reduces to the weighted
average operator. In other words, the aggregated result only appears as a sum of the
weighted AR data yi  wi . Furthermore, the interaction between pairs of consumers
can be adjusted by tuning the parameter I ij in the interval [ 1, 1] . A positive I ij
indicates the relation between pairs of consumers is complementary, that is, the
importance of Si and S j is significant greater than the importance of Si and S j
alone. On the contrary, a negative I ij indicates the relation between pairs of
consumers is redundant, that is, the importance of Si and S j is almost the same as
importance of Si and S j alone. Consumers can be regarded as independent
information sources without interaction if the value of I ij equals to zero.
4.3.3. Calculation of the importance parameters
In the proposed method, the importance and interaction of consumers grouped into
the same homogeneous clusters are calculated according to the result of FCM
clustering. The relative importance of each consumer is calculated according to the
membership grade of each consumer indicated the degree he/she belongs to certain
cluster. A technique similar to the one proposed by Hsu & Chen (1996) is adopted
which was originally used to determine the relative weight of a group of experts. The
procedure for calculating the relative importance of consumer from the results of
FCM clustering is described as follows:
(1) Determine a suitable threshold to screen out the less important consumers with
relative small membership grades and preserve n consumers near the center of
cluster.
(2) Select the most important consumer in the designated cluster with the largest
membership grade max . This consumer is assigned a weight value rmax  1 .
(3) Compare other remaining consumers with the most important consumer and
assign them a relative weight ri , i  1,..., n  1 according to the proportion of
membership grade to max . In such a way, these weights satisfy the conditions
that max{r1 ,..., rn }  1 and min{r1 ,..., rn }  0 .
(4) Normalize the value of ri and obtain the relative weight value
n
wi  ri /  ri , i  1,..., n to satisfy the condition
i 1
n
w
i 1
i
 1 . Note that if the
importance of each consumer is equal then w1  ...  wn  1/ n .
4.3.4. Calculation of the interaction parameters
The interaction between pairs of consumers is determined according to their
distance in the multidimensional scaling space, which is constructed by the
FUZZSAMM algorithm (Feil, Balasko, & Abonyi, 2007). Recall that FUZZSAMM is
already used for the visualization of CS. The distances between consumers in the
constructed low-dimensional space (2 dimension in this study) also provide an
intuitive measure of the interaction between consumers. A neutral distance D of
independent relation is then defined. A distance dij  D between consumers Ci and
C j represents the interaction parameter I ij  0 . If the distance dij  D then a
negative value will be assigned to I ij . This indicates that the preference of consumers
Ci and C j is very close and the importance of these two consumers is almost the
same as each consumer alone. The extreme case of negative d ij appears when the
position of the two consumers is overlapped and I ij  1 . For the case that dij  D ,
a positive value will be assigned to I ij .
5. Results and discussions
5.1. Results of segmented consumer groups
For judging the results of segmented consumer groups, two parameters and five
validity measures are used to look over the effect of FCM. Thought there are different
scalar validity measures been proposed in the literature, none of them is perfect by
oneself. Through the methods used in this research, the researchers can settle the
value of groups according to their requirement by the visualized way.
The fuzzification parameter m adjusts the softness of clustering so
that m=2 could have the optimal effect of fuzziness. Fig. 4 illustrates the segmented
consumer groups contrast with different values of c. While the number of cluster c is
greater than 3, some of the groups would be overlapping and appear to be one group
only. Take c=5 for example, there are three groups are overlapping so that the number
of cluster is 3 actually, and the suitable value of the clusters for this case would be 3.
Fig. 5 exhibits five indexes of different number of cluster c. Partition Coefficient
(PC) measures the amount of overlapping between cluster, and the optimal number of
cluster is at the maximum value. Classification Entropy (CE) measures the fuzziness
of the cluster partition, which is similar to PC. Partition Index (SC) is the ratio of the
sum of compactness and separation of the clusters. It is a sum of individual cluster
validity measures normalized through division by the fuzzy cardinality of each cluster.
A lower value of SC indicates a better partition. On the contrary of SC, Separation
Index (S) uses a minimum-distance separation for partition validity, therefore, the
larger value of S corresponds to better clusters. Xie-Beni Index (XB) aims to quantify
the ratio of the total variation within clusters and the separation of clusters. The
optimal number of clusters should minimize the value of XB. To coordinate these
indexes, the number of cluster c could be 3 or 4. By putting Fig. 4 and Fig. 5
together, the optimal number of clusters in this study is 3, and the consumers would
be segmented into 3 groups.
Fig. 4 shows the results of segmented consumer groups obtained by FCM clustering.
Fig. 5 shows the validity measure values of different number of clusters.
<Insert Fig. 4 about here>
<Insert Fig. 5 about here>
5.2. Analysis of the importance of consumers
The importance of consumers which is calculated based on the membership
grade indicates their relative weights of the groups. Consumers are segmented into
three groups, and their membership grades and importance values are showing in Fig.
6. Each consumer belongs to three clusters at the same time by having different
membership grades. When the influence is small enough, it could be ignored because
the consumer is far away each center of the clusters and have no intention of the
clusters. When the influence is great than some value, consumers could be a follower
of one or more clusters with the significant influence. With this case, the threshold of
membership grade is 0.4.
After passing over the less important consumers, the preserved consumers are
assigned a weight value to the cluster. The weight value of the most important
consumer in the specified cluster is set to be 1, and the weight values of the other
consumers are calculated according to the largest weight value. Then the weight
values are normalized to be the relative weight values with the specification for the
total amount of them being 1
Fig. 6 shows the membership grades of three clusters and the calculated importance
values of consumers.
<Insert Fig. 6 about here>
5.3. Analysis of the interaction between consumers
5.4. Performance of individual affective response models
The individual SVR prediction models, using 5-fold CV and two-step grid search
to obtain the optimal parameters, have quiet small error rates. The average RMSE of
these models is 0.459, and the average correlation coefficient between the consumers’
original response and predictive value is 98.99%. Moreover, the optimal parameter
values of all consumers are close to each other. The range of C and  2 is 0.1 to
1.1, and the values of  are almost small than 0.01. The values of these parameters
tend to be small than 1 and would be used to construct the SVR model.
Fig. 7 shows the predictive ability of consumer’s AR of the SVR models.
Table 4 shows the optimized parameters and the performance of all the SVR
prediction models constructed from 15 consumers.
<Insert Fig. 7 about here>
<Insert Table 4 about here>
5.5. Analysis of the consensus prediction model
6. Conclusions
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Fig. 1. A typical prediction model in KE.
individual
satisfaction
y1
Product
samples
Ag
y2
...
Input
form
feautures
x1 ,..., xm
yn 1
yn
Aggregation
operator
averaging,
mean centering,
...
Prediction
model
( MLR,
PLRS ,
NN ,
SVR...)
Single
satisfaction
y Ag
Fig. 2. Overview of the proposed AR model for product form design.
SVR1
SVR-consumer S n
2
yn 1
yn
Product samples
d 2,n 1
importance of
consumers
w
Aggregated
response
y Ag
representative
products
n 1
preference
evaluation
d1,n
Sn
n
d1,n 1
d n , n 1
S n 1
oup
SVRn
d 2,n
1
other gr
SVR-consumer Sn 1
d1,2
p
ou
SVRn 1
morphological
analysis
S2
Fuzzy
integral
...
Input
form
feautures
x1 ,..., xm
y2
gr
SVR-consumer S 2
interaction between
consumers
Consumer
I
AgCI
group
S1
er
SVR2
Fuzzy clustering
h
ot
SVR-consumer S1
individual
response
y1
Fig. 3. Training scheme of the SVR model.
Input
vectors
Mapped
vectors
Kernel
function
Weights
x1
 ( x1 )
K ( x, x1 )
x2
 ( x2 )
K ( x, x2 )
1
2
y
 ( xm )
...
...
...
xm
K ( x, xm )
m
predictive
output
Fig. 4. The results of segmented consumer groups projected by FUZZSAMM ( c varied from 2 to 7).
(a) c = 2
(b) c = 3
(c) c = 4
(d) c = 5
(e) c = 6
(f) c = 7
Fig. 5. Validity measure values of different number of clusters.
(a)
(b)
(c)
(d)
(e)
Fig. 6. Membership grades of clusters ( c = 3) and the calculated importance values of
consumers.
(a)
(b)
Fig. 7. The predictive ability of consumer’s AR of the SVR models evaluated on the adjective “modern”.
(a) Consumer 1
(b) Consumer 2
(c) Consumer 3
(d) Consumer 4
(e) Consumer 5
(f) Consumer 6
(g) Consumer 7
(h) Consumer 8
(i) Consumer 9
(j) Consumer 10
(k) Consumer 11
(l) Consumer 12
(m) Consumer 13
(n) Consumer 14
(o) Consumer 15
Table 1. Complete list of PFFs of mobile phone design.
Form features
Type
Attributes
Length
Continuous
None
Continuous
None
Continuous
None
Continuous
None
( X1 )
Width
( X2 )
Body
Thickness
( X3 )
Volume
( X4 )
Type
Discrete
( X5 )
Type
Block body
Flip body
Slide body
( X 51 )
( X 52 )
( X 53 )
Full-
Partial-
Regular-
separated
separated
separated
( X 61 )
( X 62 )
( X 63 )
Round
Square
Bar
( X 71 )
( X 72 )
( X 73 )
Circular
Regular
Asymmetric
( X 81 )
( X 82 )
( X 83 )
Square
Vertical
Horizontal
( X 91 )
( X 92 )
( X 93 )
Discrete
Function button
( X6 )
Style
Discrete
( X7 )
Shape
Discrete
Number button
( X8 )
Arrangement
Discrete
( X9 )
Detail treatment
Discrete
( X 10 )
Regular seam
Seamless
Vertical seam
Horizontal
( X 101 )
( X 102 )
( X 103 )
seam
( X 104 )
Position
Discrete
Panel
( X 11 )
Shape
Middle
Upper
Lower
Full
( X 111 )
( X 112 )
( X 113 )
( X 114 )
Square
Fillet
Shield
Round
( X 121 )
( X 122 )
( X 123 )
( X 123 )
Discrete
( X 12 )
Table 2. Bipolar adjectives adopted from Hsu, Chuang, & Chang (2000).
1 Traditional-modern
2 Hard-soft
3 Old-new
7 Coarse-delicate
8 Masculine-feminine
9 Rational-emotional
4 Heavy-handy
5 Obedient-rebellious
6 Nostalgic-futuristic
10 Hand made-hi tech
11 Childish-mature
12 Unoriginal-creative
13 Simple-complicated
14 Conservative-avant grade
15 Standard-outstanding
19 Inert-active
20 Personal-professional
21 Obtuse-brilliant
16 Common-particular
17 Plain-gaudy
18 Decorative-practical
22 Discordant-harmonious
Table 3. The factor loadings of the 22 bipolar adjectives by factor analysis.
Adjectives
Factor 1
Factor 2
1 Traditional-modern
0.9604
0.1081
0.1455
6 Nostalgic-futuristic
0.9578
0.0377
0.1745
3 Old-new
0.9569
0.1597
0.1359
21 Obtuse-brilliant
0.9428
－0.1315
0.1398
16 Common-particular
0.9298
0.1543
0.2995
0.9074
0.1778
0.1439
15 Standard-outstanding
0.9043
0.1817
0.3262
12 Unoriginal-creative
0.9031
0.2072
0.2348
14 Conservative-avant grade
0.8643
0.1568
0.4557
17 Plain-gaudy
0.8061
0.1189
0.5247
10 Hand made-hi tech
0.7617
－0.3816
0.0575
22 Discordant-harmonious
0.6652
0.1797
－0.2190
11 Childish-mature
0.6225
－0.5119
0.3132
9 Rational-emotional
－0.0020
0.9847
－0.0366
8 Masculine-feminine
0.0442
0.9272
－0.2402
2 Hard-soft
0.1522
0.9112
－0.1429
－0.4663
－0.8183
－0.1881
19 Inert-active
0.5607
0.7684
0.0497
20 Personal-professional
0.5576
－0.7044
0.3799
4 Heavy-handy
0.0265
0.1958
－0.8656
5 Obedient-rebellious
0.3139
－0.1468
0.7682
13 Simple-complicated
0.5253
－0.0711
0.7463
Eigenvalue
12.3
5.4
1.7
Percentage of variance
50.1
23.4
14.3
Cumulative percentage
50.1
73.5
87.8
7 Coarse-delicate
18 Decorative-practical
Factor 3
Final statistics
The bold underlined numbers indicate the groups of adjectives associates with
factors 1-3.
Table 4. The optimized parameters, the performance (RMSE) and correlation coefficient (CC) of the SVR prediction models.
Consumer
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
C
0.83176
0.83176
0.83176
0.83176
0.83176
0.83176
0.83176
1.0471
0.83176
0.83176
0.83176
0.83176
0.83176
0.83176
0.83176

0.000871
0.00012
0.000851
0.000331
0.000331
0.000631
0.000525
0.00055
0.000195
0.011482
0.001259
0.001023
0.0002
0.00631
0.00011
0.34674
0.16218
0.91201
0.16218
0.33884
0.91201
0.20417
0.91201
0.16218
0.20417
0.34674
0.91201
0.16218
0.19498
0.91201
0.0475
0.0494
0.0477
0.0439
0.0497
0.0484
0.0461
0.049
0.0374
0.0413
0.0476
0.0482
0.044
0.0422
0.0454
0.9952
0.9882
0.975
0.9846
0.987
0.9913
0.9884
0.9947
0.9855
0.9981
0.9974
0.9941
0.9954
0.9911
0.9819
2
RMSE
CC