# Affective-Blue Design Methodology for Product Design Based on Integral Kansei Engineering

Authors: Wenwu Lian; Kun-Chieh Wang; Youchang Li; Hong-Yi Chen; Chi-Hsin Yang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Sustainable product designs always draw much attention. However, sustainable or green products are usually costly. This contradiction can be solved via blue design. The concept of blue design originates from the blue economy which is a popular strategy for providing sustainable, healthy, but cheap socioeconomic activities. This study innovatively implements the ideas of sustainability and economy from the blue economy, and the affection (or Kansei in Japanese) from the Kansei engineering into a product design process to become a novel affective-blue design methodology of a product form. The proposed methodology mainly contains three aspects. The first aspect is the merge of a novel Kansei blue model with the traditional Kansei engineering to deal with the semantic space and form decomposition issues encountered in the product form designing process. The second aspect is the adoption of proper data mining schemes to optimally trim and obtain the kernel information from the Kansei evaluation data of products. The third aspect is the usage of appropriate machine learning schemes to establish a precise relationship between product images and design elements from the kernel information. A case study was conducted for the form design of a computer-numerical-control lathe to evaluate the effectiveness of our proposed methodology. The verification results, that all predictive errors are within 4.5% for test samples, show that our blue-affective design methodology is quite satisfying. Through applying this proposed methodology, designers may correctly evaluate and easily catch the essential blue and affective design factors for designing a good industrial product, such as a computer-numerical-control machine tool.


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## Body

## 1. Introduction and Literature Review

The change from product-centric to customer-centric has become one of the most important concerns in product designs. This pushes product designers to work hard on designing attractive products which are customer oriented [1]. However, accompanied by the growth of economy at the cost of industrial pollution, people are aware of the importance of sustainability. The harmful environmental variations excite people to use more green products. Past experiences concerning the economy about green products have shown that most of them are expensive, despite the advantages of sustainable and good to environment [2]. The costly green products seriously retard the aspiration of customers for buying them. Therefore, in 1994, a new economic philosophy the blue economy (BE) was established by G. Pauli [3]. The BE is a popular strategy for providing sustainable, healthy, but cheap socioeconomic activities [4, 5]. Furthermore, BE is a very recent concept recognized as an alternative to the green economy that is very costly [6, 7]. Under this background of BE development, the blue design (BD) appears, which is an engineering design approach that provides products with sustainable, healthy, but cheap economy, capable to offer more with less [8, 9]. So far, it is still challengeable to transform the blue economy rules into practical design strategy. It is the major purpose of this study to dive deeper into BE so as to develop a novel BD strategy for designing attractive products.Although quite a number of past studies had explored affective design methods for products [10–26], scare literature studies were found for studying product designs considering both human’s affective feelings and environment’s sustainable requirements. And, no publication was found thus far in regarding of the methodology of designing affective and blue products. A popular method called the “Kansei engineering (KE),” also known as the affective engineering and firstly proposed in 1980s by a Japanese scholar, Nagamachi [10], is a good way to deal with general product design problems. The KE is a product development method that uses a series of quantitative schemes to transform customer’s affection or Kansei (Japanese word) into design attribute settings. Basically, KE is an ergonomic consumer-oriented translation technology. The KE has been successfully applied in various design problems, such as service designs [11, 12], product form designs [13–15], product packaging designs [16], product function designs [17, 18], and interface designs [19]. The manipulation procedure of KE encompasses four major tasks. First, the customer’s feelings about a predetermined product are collected from the marketplace. Second, a morphological analysis is applied to the selected products. Third, a questionnaire survey of product evaluation is conducted. Fourth, the evaluation results are used to build a proper relationship between customers’ affections and design attributes [10]. One important work in KE procedure is to find proper data manipulation schemes and mathematic models to establish the relationship between customer’s affection and product attributes. Previous studies ever applied many various schemes in KE for data manipulation, such as the analytic hierarchy process (AHP) [20], the grey system theory (GST) [21], the K-means theory [14], and the fuzzy C-means (FCM) [22]. And, for the Kansei model building, there ever appeared the multiple regression scheme [23], deep learning neural network scheme [24], and artificial neural network scheme [25, 26]. Despite KE was a popular method to deal with the design problem of attractive products, a simultaneous consideration of three essential factors: affection, sustainability, and economy in designing a product (or namely, “affective-blue design (ABD)”) was not addressed. Facing the ever increasing demands on the development of BD, the aforementioned traditional KE method, especially its comprising data manipulating and model building schemes, needs to be further modified and expanded to solve currently encountered difficulties. Furthermore, to illustrate our proposed ABD methodology, here, we choose a computer-numerical-control (CNC) machine tool as the form design target since its aesthetic, sustainable, and economic appearance made of metal is becoming the main-stream crucial factor of purchase-or-not for customers. In the past, some scholars including me proposed several KE-based methodologies to study the form design of CNC machine tools [21, 27–29]. However, their investigations on the metal appearance of CNC machine tools were limited to customers’ aesthetic or affective needs and lacked of sustainable and economic considerations. Based on the above concerns, we propose a novel KE-based integral methodology for blue-affective product form design, which majorly contains a Kansei blue model (KBM), the KE scheme, and multiple data mining schemes. Meanwhile, we take a CNC lathe as the investigating target to illustrate the proposed methodology.


## 2. Methodology

First, we put forward a KBM to deal with the customers’ blue feelings about a target product of CNC lathe and its form design attributes. Second, the collected data of product image and product form are classified and analyzed based on the multiple data mining schemes which include FCM, the multidimensional scaling, and the factor analysis (FA). Third, the relationship between the semantic space and the product space is established by an integral machining learning scheme, including GST, the rough set theory (RST), and the support-vector regression (SVR).The manipulation procedure of our proposed methodology is shown in Figure1 and explained as follows: (i) Select the target product CNC lathe, (ii) divide the data space into a product space and a semantic space, (iii) collect data via questionnaire survey and find representatives using multiple data mining schemes, (iv) introduce blue images and blue design attributes from KBM, (v) obtain Kansei evaluation data via questionnaire survey, (vi) establish a mathematical model of mapping from form elements to product images and, (vii) verify the proposed prediction model.Figure 1
Methodology of affective-blue design for products.It is noted that, in this study, we choose a CNC lathe with metal cover as the target product to illustrate our proposed design methodology because that, from the viewpoints of customers, a good metal appearance of a CNC machine tool requires considering its usability, sustainability, and economy simultaneously. In the marketplace, there usually appears conflict among these factors. With regard to this problem, we may solve it via the proposed ABD methodology. A brief introduction for the major schemes of our proposed ABD methodology, including KBM, FCM, RST, GST, and SVR, are given as follows.


### 2.1. Kansei Blue Model

To implant blue concepts in conventional KE, a novel KBM is proposed. The KBM includes the exploration of products’ blue images and blue design elements, and the construction of an integral blue-image index.A total of 12 experts join the brainstorming experiment, who all have more than five-year experiences in CNC machine tool development. On the one hand, according to the translation result of 25 blue-design principles announced by Stelian et al. [30], which were derived from the 20 principles of BE published in public by Pauli [3], we analyze and extract these principles to obtain four clusters of blue attributes for images and design elements, namely, (i) blue configuration, (ii) blue function, (iii) blue interface, and (iv) blue composition. For each blue attribute, the possible blue images (affective words) as well as blue design elements are obtained via a brainstorming experiment. The results are shown in Table 1. On the other hand, we propose an integral blue image YB which can be used to describe both human’s virtual blue affection Yvb as well as concrete blue affection Ycb about a target product. The quantized rank of YB can be expressed in terms of B∗, called the integral blue image index (IBII) and defined as follows:(1)B∗=∑i=1nαifi+βm,where for ith virtual blue image Yvbi, αi is its predetermined weight 0≤αi≤1, fi is its semantic differential rank (7-scale, 1≤fi≤7, fi∈Z), and β is the predetermined weight of the cost for the product material 0<β<1, ∑=1nαi+β=1, and m is the rank level of material price in the marketplace for Ycb (7-scale, 1≤mi≤7, mi∈Z). To note that, since, in this study, we choose a CNC lathe as the target product, m is evaluated based on the price per kilogram of metal cover and expressed as the rank of cost level. And n is the number of virtual blue images. The virtual blue images are extracted from Table 1 by experts with regards to the product under consideration. Overall, the definition of IBII considers not only the economic aspect (price) but also the emotional aspect (blue feeling) about a product.Table 1
Blue images and design elements.
Blue clusterBlue imagesBlue design elementsBlue configuration(i) Easy assembling and disassembling (parts)(i) Assemble and disassemble function(ii) User-friendly manipulating (system or parts)(ii) Manipulation function(iii) Interchangeable or reconfigurable (system or parts)(iii) Interchangeable function(iv) Consolidating (space)(iv) StiffnessBlue function(i) Easy connecting and disconnecting (parts)(i) Connecting and disconnecting function(ii) Soft functioning (solar, gravity, etc.)(ii) Green energy utilization(iii) Flexible (system)(iii) Flexible function(iv) Automation(iv) Automation(v) Smart(v) Intelligence function(vi) Energy-saving(vi) Excellent physical property(vii) Resonance-free(vii) Advanced technology(viii) Feedback functioningBlue interface(i) Fault tolerating(i) Fault tolerance(ii) Homogeneous(ii) Identificability(iii) Unified(iii) Safety function(iv) Easy-to-recognize(iv) Antistupidity function(v) Protective (safety)(v) Consistency(vi) HomogeneityBlue composition(i) Green (material)(i) Green material(ii) Soft (components)(ii) Permeable material(iii) Permeable (components)(iii) Composite material(iv) Inexpensible (alternate)


### 2.2. Fuzzy C-Means Scheme

To classify the obtained quantified data via questionnaire survey, we adopt an FCM scheme [31] to better classify the collected product samples and determine the representative of each product group. In FCM, we firstly assign a membership to each data point corresponding to each cluster center. The summation of the membership for each data point equals to one. The memberships and cluster centers are updated according to the following formula:(2)μij=1∑k=1cdij/dik2/m−1,νj=∑i=1nμijmxi∑i=1nμijm,j=1,2,...,c,where n is the number of data points, m is the fuzziness index, m∈1,∞, and μij is the membership of ith data to jth cluster center. The main goal of FCM algorithm is to minimize the objective function:(3)JU,V=∑i=1n∑j=1cμijmxi−vj2,where xi−vj2 is the Euclidean distance between ith data and jth cluster center. The algorithm steps of FCM are as follows: (i) randomly choose a number of clusters, (ii) randomly assign a coefficient to each data point in clusters, (iii) repeat until the algorithm reaches convergence, (iv) compute the centroid for each cluster, and (v) compute the coefficient of each data point.


### 2.3. Integral Machine Learning Scheme

#### 2.3.1. Rough Set Theory

This study adopts RST, developed by Pawlak in 1982 [32], as a tool to determine the influences of design attributes (independent parameters) on people’s Kansei feelings (dependent parameters). The fundamental of RST is briefly introduced as follows:Assuming there is an information systemS=U,B, where U is the universe and B is a nonempty, finite set of attributes. B=CA∪DA, in which CA and DA are a finite set of condition and decision attributes, respectively. And, U means cases, and B represents design elements.Reducts are the minimal subsets of attributes that discern all equivalence classes of the relation forDA. The core is the common part of all reducts. A discernibility function is used to find the core of S=U,B. The discernibility matrix M=mij is defined as(4)mij=X∈CA:XNi≠XNj∧Y∈D,YNi≠YNj,where i, j = 1, 2, …, k, and k denotes the number of objects of U. To obtain elements mij, one should find the set of attributes which discern the objects Ni and Nj, and those do not belong to the same equivalence class of DA.The discernibility functionfA is a Boolean function, constructed as follows: (i) to each mij, a Boolean variable X is assigned; (ii) for each mij, the Boolean form of union operation is assigned; (iii) for different elements, the Boolean form of intersection operation is assigned. Accordingly, the discernibility function fA of all data can be constructed. Eventually, according to the absorption law [32], the final cores may be obtained. Through the decision rule of RST, the knowledge rule (influential core of design elements) of people’s Kansei about a product can be found.


#### 2.3.2. Grey System Theory

We adopt the GM (1,N) model of GST to obtain the weight coefficients of independent variables (design elements), which was proposed by Deng in 1989 [33]. The followings are the algorithm of GM (1, N).(i)
Building an initial sequence:(5)xi0k,i=1,2,3,⋯Nandk=1,2,3,…,n.(ii)
Accumulating the initial sequence:(6)x1=∑i=11x0i,∑i=12x0i,∑i=13x0i,⋯,∑i=1nx0i,where(7)xj1k=∑i=1kx0i,j=1,2,3,…,n.(iii)
Supposed that a first-order differential equation holds true for describing the relationship between independent and dependent variables:(8)dx10kdt+ax11k=b2x21k+b3x31k+⋯+bNxN1k.(iv)
Solving equation (8) by the difference approximation method to yield(9)x10k+az11k=∑j=2Nbjxj1k,where(10)z11k=0.5x11k+0:5x11k−1.Then, we rearrange equation (9) in the matrix form as(11)YN=Ba^,where(12)YNT=x102x103x104⋯x10n,a^T=ab2b3⋯bN,(13)B=−z112x212⋯xN12−z113x213⋯xN13⋮−z11nx21n⋯xN1n.(v)
Calculatinga^ by the method of least-square error as(14)a^=BTB−1BTYN.Hence, the weight values of the independent variables (design elements) can be obtained by taking norms ofb2∼bN. Through the knowledge about influential parameters of design elements, vast amounts of evaluation data can be effectively reduced for further modelling works.


#### 2.3.3. Support Vector Regression

Based on the consideration that SVR has a superior nonlinear mapping ability among machine learning schemes [34], we adopt this scheme to establish a precise mathematical relationship between design elements and Kansei images. The algorithm of SVR is introduced as follows:(i)
Give a known training set:(15)T=x1,y1,…,xm,ym∈X×Ym,wherexi∈X,X=Rn is the eigenvector and yi∈Y,Y=−1,1.(ii)
Choose a proper kernel functionKx,x′ and a proper parameter C, then solve the following optimal problem:(16)min12∑i=1j∑j=1myiyjωiωjKxi,xj−∑j=1mωj,s.t.∑i=1myiωi=0,0≤ω,≤C,i=1,…,m,and obtain an optimal solution ofΩ=ω1∗,ω2∗,…,ωm∗T.(iii)
Choose a properΩ, 0<Ω<C and calculate the threshold value:(17)θ=yj−∑i=1myiωi∗Kxi,xj.(iv)
Construct a decision function(18)fx=sgn∑i=1mωi∗yiKx,xi+θ.(v)
Train equation (18) with given data set and obtain the final regression parameters.


## 2.1. Kansei Blue Model

To implant blue concepts in conventional KE, a novel KBM is proposed. The KBM includes the exploration of products’ blue images and blue design elements, and the construction of an integral blue-image index.A total of 12 experts join the brainstorming experiment, who all have more than five-year experiences in CNC machine tool development. On the one hand, according to the translation result of 25 blue-design principles announced by Stelian et al. [30], which were derived from the 20 principles of BE published in public by Pauli [3], we analyze and extract these principles to obtain four clusters of blue attributes for images and design elements, namely, (i) blue configuration, (ii) blue function, (iii) blue interface, and (iv) blue composition. For each blue attribute, the possible blue images (affective words) as well as blue design elements are obtained via a brainstorming experiment. The results are shown in Table 1. On the other hand, we propose an integral blue image YB which can be used to describe both human’s virtual blue affection Yvb as well as concrete blue affection Ycb about a target product. The quantized rank of YB can be expressed in terms of B∗, called the integral blue image index (IBII) and defined as follows:(1)B∗=∑i=1nαifi+βm,where for ith virtual blue image Yvbi, αi is its predetermined weight 0≤αi≤1, fi is its semantic differential rank (7-scale, 1≤fi≤7, fi∈Z), and β is the predetermined weight of the cost for the product material 0<β<1, ∑=1nαi+β=1, and m is the rank level of material price in the marketplace for Ycb (7-scale, 1≤mi≤7, mi∈Z). To note that, since, in this study, we choose a CNC lathe as the target product, m is evaluated based on the price per kilogram of metal cover and expressed as the rank of cost level. And n is the number of virtual blue images. The virtual blue images are extracted from Table 1 by experts with regards to the product under consideration. Overall, the definition of IBII considers not only the economic aspect (price) but also the emotional aspect (blue feeling) about a product.Table 1
Blue images and design elements.
Blue clusterBlue imagesBlue design elementsBlue configuration(i) Easy assembling and disassembling (parts)(i) Assemble and disassemble function(ii) User-friendly manipulating (system or parts)(ii) Manipulation function(iii) Interchangeable or reconfigurable (system or parts)(iii) Interchangeable function(iv) Consolidating (space)(iv) StiffnessBlue function(i) Easy connecting and disconnecting (parts)(i) Connecting and disconnecting function(ii) Soft functioning (solar, gravity, etc.)(ii) Green energy utilization(iii) Flexible (system)(iii) Flexible function(iv) Automation(iv) Automation(v) Smart(v) Intelligence function(vi) Energy-saving(vi) Excellent physical property(vii) Resonance-free(vii) Advanced technology(viii) Feedback functioningBlue interface(i) Fault tolerating(i) Fault tolerance(ii) Homogeneous(ii) Identificability(iii) Unified(iii) Safety function(iv) Easy-to-recognize(iv) Antistupidity function(v) Protective (safety)(v) Consistency(vi) HomogeneityBlue composition(i) Green (material)(i) Green material(ii) Soft (components)(ii) Permeable material(iii) Permeable (components)(iii) Composite material(iv) Inexpensible (alternate)


## 2.2. Fuzzy C-Means Scheme

To classify the obtained quantified data via questionnaire survey, we adopt an FCM scheme [31] to better classify the collected product samples and determine the representative of each product group. In FCM, we firstly assign a membership to each data point corresponding to each cluster center. The summation of the membership for each data point equals to one. The memberships and cluster centers are updated according to the following formula:(2)μij=1∑k=1cdij/dik2/m−1,νj=∑i=1nμijmxi∑i=1nμijm,j=1,2,...,c,where n is the number of data points, m is the fuzziness index, m∈1,∞, and μij is the membership of ith data to jth cluster center. The main goal of FCM algorithm is to minimize the objective function:(3)JU,V=∑i=1n∑j=1cμijmxi−vj2,where xi−vj2 is the Euclidean distance between ith data and jth cluster center. The algorithm steps of FCM are as follows: (i) randomly choose a number of clusters, (ii) randomly assign a coefficient to each data point in clusters, (iii) repeat until the algorithm reaches convergence, (iv) compute the centroid for each cluster, and (v) compute the coefficient of each data point.


## 2.3. Integral Machine Learning Scheme

### 2.3.1. Rough Set Theory

This study adopts RST, developed by Pawlak in 1982 [32], as a tool to determine the influences of design attributes (independent parameters) on people’s Kansei feelings (dependent parameters). The fundamental of RST is briefly introduced as follows:Assuming there is an information systemS=U,B, where U is the universe and B is a nonempty, finite set of attributes. B=CA∪DA, in which CA and DA are a finite set of condition and decision attributes, respectively. And, U means cases, and B represents design elements.Reducts are the minimal subsets of attributes that discern all equivalence classes of the relation forDA. The core is the common part of all reducts. A discernibility function is used to find the core of S=U,B. The discernibility matrix M=mij is defined as(4)mij=X∈CA:XNi≠XNj∧Y∈D,YNi≠YNj,where i, j = 1, 2, …, k, and k denotes the number of objects of U. To obtain elements mij, one should find the set of attributes which discern the objects Ni and Nj, and those do not belong to the same equivalence class of DA.The discernibility functionfA is a Boolean function, constructed as follows: (i) to each mij, a Boolean variable X is assigned; (ii) for each mij, the Boolean form of union operation is assigned; (iii) for different elements, the Boolean form of intersection operation is assigned. Accordingly, the discernibility function fA of all data can be constructed. Eventually, according to the absorption law [32], the final cores may be obtained. Through the decision rule of RST, the knowledge rule (influential core of design elements) of people’s Kansei about a product can be found.


### 2.3.2. Grey System Theory

We adopt the GM (1,N) model of GST to obtain the weight coefficients of independent variables (design elements), which was proposed by Deng in 1989 [33]. The followings are the algorithm of GM (1, N).(i)
Building an initial sequence:(5)xi0k,i=1,2,3,⋯Nandk=1,2,3,…,n.(ii)
Accumulating the initial sequence:(6)x1=∑i=11x0i,∑i=12x0i,∑i=13x0i,⋯,∑i=1nx0i,where(7)xj1k=∑i=1kx0i,j=1,2,3,…,n.(iii)
Supposed that a first-order differential equation holds true for describing the relationship between independent and dependent variables:(8)dx10kdt+ax11k=b2x21k+b3x31k+⋯+bNxN1k.(iv)
Solving equation (8) by the difference approximation method to yield(9)x10k+az11k=∑j=2Nbjxj1k,where(10)z11k=0.5x11k+0:5x11k−1.Then, we rearrange equation (9) in the matrix form as(11)YN=Ba^,where(12)YNT=x102x103x104⋯x10n,a^T=ab2b3⋯bN,(13)B=−z112x212⋯xN12−z113x213⋯xN13⋮−z11nx21n⋯xN1n.(v)
Calculatinga^ by the method of least-square error as(14)a^=BTB−1BTYN.Hence, the weight values of the independent variables (design elements) can be obtained by taking norms ofb2∼bN. Through the knowledge about influential parameters of design elements, vast amounts of evaluation data can be effectively reduced for further modelling works.


### 2.3.3. Support Vector Regression

Based on the consideration that SVR has a superior nonlinear mapping ability among machine learning schemes [34], we adopt this scheme to establish a precise mathematical relationship between design elements and Kansei images. The algorithm of SVR is introduced as follows:(i)
Give a known training set:(15)T=x1,y1,…,xm,ym∈X×Ym,wherexi∈X,X=Rn is the eigenvector and yi∈Y,Y=−1,1.(ii)
Choose a proper kernel functionKx,x′ and a proper parameter C, then solve the following optimal problem:(16)min12∑i=1j∑j=1myiyjωiωjKxi,xj−∑j=1mωj,s.t.∑i=1myiωi=0,0≤ω,≤C,i=1,…,m,and obtain an optimal solution ofΩ=ω1∗,ω2∗,…,ωm∗T.(iii)
Choose a properΩ, 0<Ω<C and calculate the threshold value:(17)θ=yj−∑i=1myiωi∗Kxi,xj.(iv)
Construct a decision function(18)fx=sgn∑i=1mωi∗yiKx,xi+θ.(v)
Train equation (18) with given data set and obtain the final regression parameters.


## 2.3.1. Rough Set Theory

This study adopts RST, developed by Pawlak in 1982 [32], as a tool to determine the influences of design attributes (independent parameters) on people’s Kansei feelings (dependent parameters). The fundamental of RST is briefly introduced as follows:Assuming there is an information systemS=U,B, where U is the universe and B is a nonempty, finite set of attributes. B=CA∪DA, in which CA and DA are a finite set of condition and decision attributes, respectively. And, U means cases, and B represents design elements.Reducts are the minimal subsets of attributes that discern all equivalence classes of the relation forDA. The core is the common part of all reducts. A discernibility function is used to find the core of S=U,B. The discernibility matrix M=mij is defined as(4)mij=X∈CA:XNi≠XNj∧Y∈D,YNi≠YNj,where i, j = 1, 2, …, k, and k denotes the number of objects of U. To obtain elements mij, one should find the set of attributes which discern the objects Ni and Nj, and those do not belong to the same equivalence class of DA.The discernibility functionfA is a Boolean function, constructed as follows: (i) to each mij, a Boolean variable X is assigned; (ii) for each mij, the Boolean form of union operation is assigned; (iii) for different elements, the Boolean form of intersection operation is assigned. Accordingly, the discernibility function fA of all data can be constructed. Eventually, according to the absorption law [32], the final cores may be obtained. Through the decision rule of RST, the knowledge rule (influential core of design elements) of people’s Kansei about a product can be found.


## 2.3.2. Grey System Theory

We adopt the GM (1,N) model of GST to obtain the weight coefficients of independent variables (design elements), which was proposed by Deng in 1989 [33]. The followings are the algorithm of GM (1, N).(i)
Building an initial sequence:(5)xi0k,i=1,2,3,⋯Nandk=1,2,3,…,n.(ii)
Accumulating the initial sequence:(6)x1=∑i=11x0i,∑i=12x0i,∑i=13x0i,⋯,∑i=1nx0i,where(7)xj1k=∑i=1kx0i,j=1,2,3,…,n.(iii)
Supposed that a first-order differential equation holds true for describing the relationship between independent and dependent variables:(8)dx10kdt+ax11k=b2x21k+b3x31k+⋯+bNxN1k.(iv)
Solving equation (8) by the difference approximation method to yield(9)x10k+az11k=∑j=2Nbjxj1k,where(10)z11k=0.5x11k+0:5x11k−1.Then, we rearrange equation (9) in the matrix form as(11)YN=Ba^,where(12)YNT=x102x103x104⋯x10n,a^T=ab2b3⋯bN,(13)B=−z112x212⋯xN12−z113x213⋯xN13⋮−z11nx21n⋯xN1n.(v)
Calculatinga^ by the method of least-square error as(14)a^=BTB−1BTYN.Hence, the weight values of the independent variables (design elements) can be obtained by taking norms ofb2∼bN. Through the knowledge about influential parameters of design elements, vast amounts of evaluation data can be effectively reduced for further modelling works.


## 2.3.3. Support Vector Regression

Based on the consideration that SVR has a superior nonlinear mapping ability among machine learning schemes [34], we adopt this scheme to establish a precise mathematical relationship between design elements and Kansei images. The algorithm of SVR is introduced as follows:(i)
Give a known training set:(15)T=x1,y1,…,xm,ym∈X×Ym,wherexi∈X,X=Rn is the eigenvector and yi∈Y,Y=−1,1.(ii)
Choose a proper kernel functionKx,x′ and a proper parameter C, then solve the following optimal problem:(16)min12∑i=1j∑j=1myiyjωiωjKxi,xj−∑j=1mωj,s.t.∑i=1myiωi=0,0≤ω,≤C,i=1,…,m,and obtain an optimal solution ofΩ=ω1∗,ω2∗,…,ωm∗T.(iii)
Choose a properΩ, 0<Ω<C and calculate the threshold value:(17)θ=yj−∑i=1myiωi∗Kxi,xj.(iv)
Construct a decision function(18)fx=sgn∑i=1mωi∗yiKx,xi+θ.(v)
Train equation (18) with given data set and obtain the final regression parameters.


## 3. Case Study

A case study of blue-affective form design for a CNC lathe is conducted based on our proposed novel methodology as follows:


### 3.1. Experiment

We arrange 120 subjects in experimental studies. These subjects are divided into three groups. Group I has 40 members, including 20 males and 20 females. In Group I, each member has experience for more than 5 years in using CNC machine tools. Their works are to extract the sample representatives. Group II has 40 members, including 20 males and 20 females. In Group II, each member is a professional designer with experience for more than 5 years in designing CNC machine tools. Their works are to perform the morphological investigation and analysis. Group III has 30 members, including 15 males and 15 females. In Group III, each member has experience for more than 3 years in using CNC machine tools. Their works are to perform product evaluation.


### 3.2. Product Samples and Form Attributes Collection and Refinement

We firstly chose 120 CNC lathes of different models and makers in the marketplace all over the world, in which they entered the market during 2011–2021. Eventually, seventy different styles of CNC lathe samples, excluding those used for specific purposes or too exaggerated forms, are chosen to construct the product space. These samples are presented in pictures in the way of as similar as possible in contrasts, sizes, and easy to be comparable in experiments.Secondly, we ask the subjects of the Group I to classify these 70 extracted samples into 2∼10 groups based on their similarity degrees using the Kawakida Jirou method [35]. A similarity matrix is thus obtained and transformed into a dissimilarity matrix. Then, we apply the multidimensional scaling scheme to solve the dissimilarity matrix. Eventually, a classification result of 4 groups was obtained (stress: 0.05103 which meets an empirical suggested level of 0.05 [36]). Furthermore, we use the FCM clustering method to obtain the representative of each group. The obtained result of samples and their representative of the first sample group is shown in Figure 2 and Table 2.Figure 2
Configuration of samples and their representative of the first group.Table 2
Product samples of the first group and their representative.
SampleDistanceSampleDistanceNo. 10.711No. 90.598No. 20.715No. 100.810No. 30.801No. 110.815No. 40.635No. 120.728No. 50.721No. 130.592No. 60.614No. 140.719No. 7 (representative)0.891No. 150.499No. 80.662The form design attributes are chosen by the subjects of Group II, which are style, color, material, and technology. A morphological analysis is conducted by the subjects of Group II as well as to extract the form features from CNC lathe samples. The obtained 9 design elements (X1∼X9) are listed in Table 3.Table 3
Morphological analysis results of product samples.
Design attributeDesign elementTypesStyleX1: whole figureEdge-cut, round, compoundX2: front doorRectangle, polygon, flatX3: manipulation boxEmbedded, suspensory, supportedColorX4: color typeCold, medium, warmX5: numbers of colorOne, two, multipleMaterialX6: surface materialMetal, plastic, compoundX7: textureSmooth, rough, multipleTechnologyX8: lightNo, less LED, large LEDX9: totemNo, single, multipleBlue attributeX10: blue symbolNo, less green symbols, large green symbolsX11: blue materialNo, less biodegradable, largely biodegradable


### 3.3. Product Images and Representatives

Here, we adopt the affective (or Kansei) adjective word pairs to describe the customer’s psychological feelings and perceptions about the appearance of CNC lathes. Comparing to the conventional ways of using only single affective word at a time to describe the customers’ feelings about a product, our new idea of using a word pair has the advantage of illustrating humans’ feeling more inclusively and explanatorily. However, the adopted word pairs must follow the restriction of close-related but without conflict with each other. So far, this treatment is an innovative idea in which it is an extension of the KE scheme. With this manipulation, eventually, a total of 50 Kansei word pairs describing the customers’ integral feelings about the collected 70 product samples are extracted from magazines, experts, literature, articles, catalogs, web sites, and users by the subjects of Group II. After omitting those too irrational, similar, or exaggerate words, finally, we get 23 medium-level Kansei word pairs. Then, a questionnaire interview is performed by the subjects of Group II. A result of four high-level Kansei word pairs is obtained via FA (shown in Table4), which are upright and firm Y1, mellow and round Y2, special and fashionable Y3, and simple and noble (Y4).Table 4
Results of high-level Kansei word pairs (C. = Component, Con. = Contribution, Acc. = Accumulation, EV = Eigenvalue).
High-level Kansei wordsMiddle-level Kansei wordsC.1C.2C.3C.4EVCon. (%)Acc. Con. (%)Upright and firm (Y1)Old0.683.2733.7533.75Traditional0.27Conveninent−0.91Rigid0.756Easy0.81Mellow and round (Y2)Round0.942.8828.1761.92Mature−0.86Lovely0.77Plentiful0.54Special and fashionable (Y3)Complete new0.942.8828.1761.92Splendid0.78Heterogeneous0.65Special−0.55Simple and noble (Y4)Simple0.952.0014.1998.67Respectable0.92Generous0.83


### 3.4. KBM Implantation

Considering people’s blue feelings about the appearance of the selected CNC lathes, on the one hand, we now properly select the virtual Kansei blue images from Table1 as follows: interchangeable and reconfigurable (Yb1, selected from blue attribute I), easy connecting and easy-to-recognize (Yb2, selected from blue attribute II and III), and soft and flexible (Yb3, selected from blue attribute IV) based on suggestions by members of Group II. The concrete blue image (Ym) is chosen as the cost of material. Furthermore, the weight values of blue images of Yb1, Yb2, Yb3, and Ym are, respectively, determined as α1=0.11, α2=0.18, α3=0.30, and β=0.41. Based on the above weights, we may calculate the integral blue image index from equation (1). On the other hand, the blue design elements are obtained from Table 1 via questionnaire survey by members of Group II as follows: blue symbol (X10, merged from blue attribute I, II, and III) and green material (X11, selected from blue attribute IV), as shown in Table 3.Eventually, we may combine these virtual and concrete blue images and design elements with previously obtained ones to construct complete Kansei evaluation parameters which include 5 dependent image parameters ofY1∼Y4 and B∗, and 11 independent design parameters of X1∼X11. Subsequently, a Kansei evaluation survey can be performed with regards to these parameters.


### 3.5. Kansei Evaluation

For evaluating the relationship between the subjective feeling of customers about CNC lathes (parametersY1∼Y4 and B∗) and their design elements, we now perform an experiment of evaluation. A questionnaire survey with a 7-scale semantic differential scheme was done to 30 subjects of Group III for evaluating their affection about the 40 extracted CNC lathe samples. The obtained evaluation results of Y1∼Y4 and B∗ are listed in Table 5.Table 5
Kansei evaluation results of extracted samples.
SY1Y2Y3Y4B∗SY1Y2Y3Y4B∗S12.183.713.332.192.84S415.343.132.182.475.01S23.694.934.083.723.85S423.283.503.344.763.22S35.114.802.383.542.77S436.113.443.864.682.76S45.293.523.844.814.42S446.063.173.914.362.56S56.032.585.733.404.87S454.324.554.775.243.93S62.184.014.723.544.69S464.054.234.713.442.87S73.193.335.234.754.57S473.452.334.525.393.59S85.883.854.514.054.61S484.192.273.695.203.19S96.245.383.445.212.96S493.351.995.385.104.51S102.942.474.375.895.97S506.211.655.244.064.28S115.104.874.986.115.94S513.795.555.783.463.22S124.563.853.195.442.96S524.296.072.062.953.55S136.084.156.425.494.27S534.016.082.982.953.12S145.674.223.384.494.17S544.557.342.352.763.63S155.176.284.693.224.87S554.675.922.483.783.36S165.204.794.093.224.36S564.235.232.913.993.29S172.995.793.963.992.02S574.875.342.554.102.87S183.542.985.842.692.67S584.985.443.274.262.95S193.784.564.432.772.78S595.335.673.544.442.22S204.215.775.223.703.67S605.025.883.694.552.12S211.903.213.352.783.33S615.404.153.213.633.22S225.435.464.513.783.20S625.204.765.224.674.01S234.614.883.692.923.19S635.374.182.723.872.97S244.553.372.813.442.87S645.665.333.075.853.93S253.672.502.104.553.60S656.355.514.705.013.61S266.014.823.985.342.99S665.873.934.763.483.91S273.295.874.584.726.01S675.914.364.774.065.73S283.733.914.524.276.32S684.624.544.225.695.16S295.034.293.044.553.01S692.306.026.333.174.28S302.984.664.113.253.46S702.044.225.783.134.94S314.234.564.826.044.27S712.882.313.895.674.98S324.282.903.656.874.74S723.883.712.184.212.92S335.834.493.384.942.99S734.774.213.373.214.32S345.363.933.734.174.25S744.014.163.143.913.38S355.734.304.234.973.89S754.064.193.165.094.25S365.464.174.833.653.01S764.353.103.124.863.39S374.973.433.913.192.01S773.562.472.573.903.15S382.397.324.353.911.99S783.713.863.994.202.48S394.895.363.893.642.75S793.655.234.303.773.12S403.164.354.993.223.04S803.776.124.944.062.82To note that, during the next modelling work, we randomly chose 35 samples for training and 5 samples for verification among the 40 extracted samples.


### 3.6. Kansei Data Mining

Based on the Kansei evaluation results of 40 samples listed in Table5, we now use RST to trim the ignorable data. In equation (3), the X1∼X11 are set as the independent variables, and Y1∼Y4 and B∗ are set as the dependent variables. Through calculation via RST, we obtain the following five rules:Rule 1:(19)X1∧X3∧X8∧X9⟶Y1.Rule 2:(20)X1∧X2∧X3∧X8∧X9⟶Y2.Rule 3:(21)X1∧X2∧X3∧X6∧X7∧X8∧X9∧X10∧X11⟶Y3.Rule 4:(22)X1∧X2∧X3∧X6∧X7∧X8∧X9⟶Y4.Rule 5:(23)X1∧X2∧X3∧X8∧X9∧X10∧X11⟶B∗.Equation (19) indicates that the design elements of X1, X3, X8, and X9 have significant influences on customers’ Kansei of upright and firm Y1. And, equation (20) reveals that X1, X2, X3, X8, and X9 have vital influences on customers’ Kansei of mellow and round Y2. And, equation (21) shows that all design elements of X1∼X11, except X4 (color type) and X5 (number of color), have essential influences on special and fashionable Y3. And, equation (22) indicates that among X1∼X11, except X4 (color type), X5 (number of color), X10 (interchangeable element), and X11 (green element), every design element has important influence on simple and noble Y4. Finally, equation (23) demonstrates that a total of seven design elements: X1,X2,X3,X8,X9,X10, and X11 have significant influences on customer’s blue Kansei B∗.Furthermore, we are going to explore the rank order as well as the weight values of influential design elements. First, we only consider the design elements that have significant influences on their corresponding high-level Kansei images, as indicated in equations (19)–(23). Second, we apply the GM (1, N) scheme of GST to calculate the weight coefficient of influential design elements via equations (5)–(14). The obtained results are shown as follows:ForY1:(24)a⌢T=a,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12=0.31,−0.35,−0.28,−,−,−,−,0.22,0.17,−,−.ForY2(25)a⌢T=0.23,−0.43,0.25,0.41,−,−,−,−,0.14,0.11,−,−.ForY3:(26)a⌢T=0.38,−0.31,0.15,0.29,−,−,0.59,0.52,0.27,0.24,0.32,0.36.ForY4:(27)a⌢T=0.46,−0.46,0.41,0.44,−,−,0.16,0.20,0.37,0.33,−,−.ForB∗:(28)a⌢T=0.14,−0.49,0.29,0.21,−,−,−,−,0.34,0.26,0.63,0.58,where b2∼b12 means the weight coefficients of X1∼X11, respectively.In addition, to clearly understand the relative importance among design elements with respective to their Kansei images, the above results of equations (24)–(28) are further normalized and drawn in Figures 3(a)–3(e). From these figures, designers may easily know that, for a given product image, which design elements should be taken into consideration and we may correctly catch their relative importance.Figure 3
Influences of design elements on product images. (a) Influences of design elements onY1. (b) Influences of design elements on Y2. (c) Influences of design elements on Y3. (d) Influences of design elements on Y4. (e) Influences of design elements on B∗.
(a)(b)(c)(d)(e)


### 3.7. Modelling of Customer Affection

To precisely establish a mathematic model of the nonlinear relationship between each high-level Kansei image and its influential design elements, we adopt an SVR scheme, as shown in equations (15)–(18). Among these equations, we adopt the radial basis function (RBF) as the kernel function:(29)Kx,xi=exp−x−xi2γ2,and the mean-square error (MSE) together with the squared correlation coefficient to express the goodness of fit for regression results, which are, respectively, defined as(30)MSE=1n∑i=1nfx−yi2,(31)R2=n∑i=1nfxiyi−∑i=1nfxi∑i=1nyi2n∑i=1nf2xi−∑i=1nfxi2n∑i=1nyi2−∑i=1nyi2.Through calculations via equations (29)–(31) in which the five high-level Kansei images of Y1∼Y4 and B∗ are selected as dependent variables and their respectively influential design elements, obtained from RST inferences (equations (19)–(23)), as independent variables, we may obtain proper regression relationships between product images and design elements. Using the aforementioned 40 sample data, we train the SVR model with randomly chosen 35 data among them. Eventually, a satisfying trained result that the mean-square errors are smaller than 5×10−5 for all five product images is obtained as follows:(i)
ForY1, C = 0.262, γ2 = 7.234, MSE = 0.0000267, and R2 = 0.967(ii)
ForY2, C = 0.391, γ2 = 3.222, MSE = 0.0000533, and R2 = 0.985(iii)
ForY3, C = 0.112, γ2 = 6.655, MSE = 0.0000349, and R2 = 0.992(iv)
ForY4, C = 0.401, γ2 = 10.018, MSE = 0.0000381, and R2 = 0.977(v)
ForB∗, C = 0.454, γ2 = 7.234, MSE = 0.0001441, and R2 = 0.915


### 3.8. Verification

We use the remained five sample data to test the trained SVR model. The obtained test results are shown in Figure4. The absolute errors between the predicted and the measured high-level Kansei images of samples S1, S2, S3, S4, and S5 are, respectively, −0.12, −0.13, 0.15, −0.19, and 0.18 (corresponding relative errors: −2.5%, −4.1%, 2.9%, −3.5%, and 4.5%). Overall, the verification results are satisfying.Figure 4
Verification results of measured and predicted integral blue image.


## 3.1. Experiment

We arrange 120 subjects in experimental studies. These subjects are divided into three groups. Group I has 40 members, including 20 males and 20 females. In Group I, each member has experience for more than 5 years in using CNC machine tools. Their works are to extract the sample representatives. Group II has 40 members, including 20 males and 20 females. In Group II, each member is a professional designer with experience for more than 5 years in designing CNC machine tools. Their works are to perform the morphological investigation and analysis. Group III has 30 members, including 15 males and 15 females. In Group III, each member has experience for more than 3 years in using CNC machine tools. Their works are to perform product evaluation.


## 3.2. Product Samples and Form Attributes Collection and Refinement

We firstly chose 120 CNC lathes of different models and makers in the marketplace all over the world, in which they entered the market during 2011–2021. Eventually, seventy different styles of CNC lathe samples, excluding those used for specific purposes or too exaggerated forms, are chosen to construct the product space. These samples are presented in pictures in the way of as similar as possible in contrasts, sizes, and easy to be comparable in experiments.Secondly, we ask the subjects of the Group I to classify these 70 extracted samples into 2∼10 groups based on their similarity degrees using the Kawakida Jirou method [35]. A similarity matrix is thus obtained and transformed into a dissimilarity matrix. Then, we apply the multidimensional scaling scheme to solve the dissimilarity matrix. Eventually, a classification result of 4 groups was obtained (stress: 0.05103 which meets an empirical suggested level of 0.05 [36]). Furthermore, we use the FCM clustering method to obtain the representative of each group. The obtained result of samples and their representative of the first sample group is shown in Figure 2 and Table 2.Figure 2
Configuration of samples and their representative of the first group.Table 2
Product samples of the first group and their representative.
SampleDistanceSampleDistanceNo. 10.711No. 90.598No. 20.715No. 100.810No. 30.801No. 110.815No. 40.635No. 120.728No. 50.721No. 130.592No. 60.614No. 140.719No. 7 (representative)0.891No. 150.499No. 80.662The form design attributes are chosen by the subjects of Group II, which are style, color, material, and technology. A morphological analysis is conducted by the subjects of Group II as well as to extract the form features from CNC lathe samples. The obtained 9 design elements (X1∼X9) are listed in Table 3.Table 3
Morphological analysis results of product samples.
Design attributeDesign elementTypesStyleX1: whole figureEdge-cut, round, compoundX2: front doorRectangle, polygon, flatX3: manipulation boxEmbedded, suspensory, supportedColorX4: color typeCold, medium, warmX5: numbers of colorOne, two, multipleMaterialX6: surface materialMetal, plastic, compoundX7: textureSmooth, rough, multipleTechnologyX8: lightNo, less LED, large LEDX9: totemNo, single, multipleBlue attributeX10: blue symbolNo, less green symbols, large green symbolsX11: blue materialNo, less biodegradable, largely biodegradable


## 3.3. Product Images and Representatives

Here, we adopt the affective (or Kansei) adjective word pairs to describe the customer’s psychological feelings and perceptions about the appearance of CNC lathes. Comparing to the conventional ways of using only single affective word at a time to describe the customers’ feelings about a product, our new idea of using a word pair has the advantage of illustrating humans’ feeling more inclusively and explanatorily. However, the adopted word pairs must follow the restriction of close-related but without conflict with each other. So far, this treatment is an innovative idea in which it is an extension of the KE scheme. With this manipulation, eventually, a total of 50 Kansei word pairs describing the customers’ integral feelings about the collected 70 product samples are extracted from magazines, experts, literature, articles, catalogs, web sites, and users by the subjects of Group II. After omitting those too irrational, similar, or exaggerate words, finally, we get 23 medium-level Kansei word pairs. Then, a questionnaire interview is performed by the subjects of Group II. A result of four high-level Kansei word pairs is obtained via FA (shown in Table4), which are upright and firm Y1, mellow and round Y2, special and fashionable Y3, and simple and noble (Y4).Table 4
Results of high-level Kansei word pairs (C. = Component, Con. = Contribution, Acc. = Accumulation, EV = Eigenvalue).
High-level Kansei wordsMiddle-level Kansei wordsC.1C.2C.3C.4EVCon. (%)Acc. Con. (%)Upright and firm (Y1)Old0.683.2733.7533.75Traditional0.27Conveninent−0.91Rigid0.756Easy0.81Mellow and round (Y2)Round0.942.8828.1761.92Mature−0.86Lovely0.77Plentiful0.54Special and fashionable (Y3)Complete new0.942.8828.1761.92Splendid0.78Heterogeneous0.65Special−0.55Simple and noble (Y4)Simple0.952.0014.1998.67Respectable0.92Generous0.83


## 3.4. KBM Implantation

Considering people’s blue feelings about the appearance of the selected CNC lathes, on the one hand, we now properly select the virtual Kansei blue images from Table1 as follows: interchangeable and reconfigurable (Yb1, selected from blue attribute I), easy connecting and easy-to-recognize (Yb2, selected from blue attribute II and III), and soft and flexible (Yb3, selected from blue attribute IV) based on suggestions by members of Group II. The concrete blue image (Ym) is chosen as the cost of material. Furthermore, the weight values of blue images of Yb1, Yb2, Yb3, and Ym are, respectively, determined as α1=0.11, α2=0.18, α3=0.30, and β=0.41. Based on the above weights, we may calculate the integral blue image index from equation (1). On the other hand, the blue design elements are obtained from Table 1 via questionnaire survey by members of Group II as follows: blue symbol (X10, merged from blue attribute I, II, and III) and green material (X11, selected from blue attribute IV), as shown in Table 3.Eventually, we may combine these virtual and concrete blue images and design elements with previously obtained ones to construct complete Kansei evaluation parameters which include 5 dependent image parameters ofY1∼Y4 and B∗, and 11 independent design parameters of X1∼X11. Subsequently, a Kansei evaluation survey can be performed with regards to these parameters.


## 3.5. Kansei Evaluation

For evaluating the relationship between the subjective feeling of customers about CNC lathes (parametersY1∼Y4 and B∗) and their design elements, we now perform an experiment of evaluation. A questionnaire survey with a 7-scale semantic differential scheme was done to 30 subjects of Group III for evaluating their affection about the 40 extracted CNC lathe samples. The obtained evaluation results of Y1∼Y4 and B∗ are listed in Table 5.Table 5
Kansei evaluation results of extracted samples.
SY1Y2Y3Y4B∗SY1Y2Y3Y4B∗S12.183.713.332.192.84S415.343.132.182.475.01S23.694.934.083.723.85S423.283.503.344.763.22S35.114.802.383.542.77S436.113.443.864.682.76S45.293.523.844.814.42S446.063.173.914.362.56S56.032.585.733.404.87S454.324.554.775.243.93S62.184.014.723.544.69S464.054.234.713.442.87S73.193.335.234.754.57S473.452.334.525.393.59S85.883.854.514.054.61S484.192.273.695.203.19S96.245.383.445.212.96S493.351.995.385.104.51S102.942.474.375.895.97S506.211.655.244.064.28S115.104.874.986.115.94S513.795.555.783.463.22S124.563.853.195.442.96S524.296.072.062.953.55S136.084.156.425.494.27S534.016.082.982.953.12S145.674.223.384.494.17S544.557.342.352.763.63S155.176.284.693.224.87S554.675.922.483.783.36S165.204.794.093.224.36S564.235.232.913.993.29S172.995.793.963.992.02S574.875.342.554.102.87S183.542.985.842.692.67S584.985.443.274.262.95S193.784.564.432.772.78S595.335.673.544.442.22S204.215.775.223.703.67S605.025.883.694.552.12S211.903.213.352.783.33S615.404.153.213.633.22S225.435.464.513.783.20S625.204.765.224.674.01S234.614.883.692.923.19S635.374.182.723.872.97S244.553.372.813.442.87S645.665.333.075.853.93S253.672.502.104.553.60S656.355.514.705.013.61S266.014.823.985.342.99S665.873.934.763.483.91S273.295.874.584.726.01S675.914.364.774.065.73S283.733.914.524.276.32S684.624.544.225.695.16S295.034.293.044.553.01S692.306.026.333.174.28S302.984.664.113.253.46S702.044.225.783.134.94S314.234.564.826.044.27S712.882.313.895.674.98S324.282.903.656.874.74S723.883.712.184.212.92S335.834.493.384.942.99S734.774.213.373.214.32S345.363.933.734.174.25S744.014.163.143.913.38S355.734.304.234.973.89S754.064.193.165.094.25S365.464.174.833.653.01S764.353.103.124.863.39S374.973.433.913.192.01S773.562.472.573.903.15S382.397.324.353.911.99S783.713.863.994.202.48S394.895.363.893.642.75S793.655.234.303.773.12S403.164.354.993.223.04S803.776.124.944.062.82To note that, during the next modelling work, we randomly chose 35 samples for training and 5 samples for verification among the 40 extracted samples.


## 3.6. Kansei Data Mining

Based on the Kansei evaluation results of 40 samples listed in Table5, we now use RST to trim the ignorable data. In equation (3), the X1∼X11 are set as the independent variables, and Y1∼Y4 and B∗ are set as the dependent variables. Through calculation via RST, we obtain the following five rules:Rule 1:(19)X1∧X3∧X8∧X9⟶Y1.Rule 2:(20)X1∧X2∧X3∧X8∧X9⟶Y2.Rule 3:(21)X1∧X2∧X3∧X6∧X7∧X8∧X9∧X10∧X11⟶Y3.Rule 4:(22)X1∧X2∧X3∧X6∧X7∧X8∧X9⟶Y4.Rule 5:(23)X1∧X2∧X3∧X8∧X9∧X10∧X11⟶B∗.Equation (19) indicates that the design elements of X1, X3, X8, and X9 have significant influences on customers’ Kansei of upright and firm Y1. And, equation (20) reveals that X1, X2, X3, X8, and X9 have vital influences on customers’ Kansei of mellow and round Y2. And, equation (21) shows that all design elements of X1∼X11, except X4 (color type) and X5 (number of color), have essential influences on special and fashionable Y3. And, equation (22) indicates that among X1∼X11, except X4 (color type), X5 (number of color), X10 (interchangeable element), and X11 (green element), every design element has important influence on simple and noble Y4. Finally, equation (23) demonstrates that a total of seven design elements: X1,X2,X3,X8,X9,X10, and X11 have significant influences on customer’s blue Kansei B∗.Furthermore, we are going to explore the rank order as well as the weight values of influential design elements. First, we only consider the design elements that have significant influences on their corresponding high-level Kansei images, as indicated in equations (19)–(23). Second, we apply the GM (1, N) scheme of GST to calculate the weight coefficient of influential design elements via equations (5)–(14). The obtained results are shown as follows:ForY1:(24)a⌢T=a,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12=0.31,−0.35,−0.28,−,−,−,−,0.22,0.17,−,−.ForY2(25)a⌢T=0.23,−0.43,0.25,0.41,−,−,−,−,0.14,0.11,−,−.ForY3:(26)a⌢T=0.38,−0.31,0.15,0.29,−,−,0.59,0.52,0.27,0.24,0.32,0.36.ForY4:(27)a⌢T=0.46,−0.46,0.41,0.44,−,−,0.16,0.20,0.37,0.33,−,−.ForB∗:(28)a⌢T=0.14,−0.49,0.29,0.21,−,−,−,−,0.34,0.26,0.63,0.58,where b2∼b12 means the weight coefficients of X1∼X11, respectively.In addition, to clearly understand the relative importance among design elements with respective to their Kansei images, the above results of equations (24)–(28) are further normalized and drawn in Figures 3(a)–3(e). From these figures, designers may easily know that, for a given product image, which design elements should be taken into consideration and we may correctly catch their relative importance.Figure 3
Influences of design elements on product images. (a) Influences of design elements onY1. (b) Influences of design elements on Y2. (c) Influences of design elements on Y3. (d) Influences of design elements on Y4. (e) Influences of design elements on B∗.
(a)(b)(c)(d)(e)


## 3.7. Modelling of Customer Affection

To precisely establish a mathematic model of the nonlinear relationship between each high-level Kansei image and its influential design elements, we adopt an SVR scheme, as shown in equations (15)–(18). Among these equations, we adopt the radial basis function (RBF) as the kernel function:(29)Kx,xi=exp−x−xi2γ2,and the mean-square error (MSE) together with the squared correlation coefficient to express the goodness of fit for regression results, which are, respectively, defined as(30)MSE=1n∑i=1nfx−yi2,(31)R2=n∑i=1nfxiyi−∑i=1nfxi∑i=1nyi2n∑i=1nf2xi−∑i=1nfxi2n∑i=1nyi2−∑i=1nyi2.Through calculations via equations (29)–(31) in which the five high-level Kansei images of Y1∼Y4 and B∗ are selected as dependent variables and their respectively influential design elements, obtained from RST inferences (equations (19)–(23)), as independent variables, we may obtain proper regression relationships between product images and design elements. Using the aforementioned 40 sample data, we train the SVR model with randomly chosen 35 data among them. Eventually, a satisfying trained result that the mean-square errors are smaller than 5×10−5 for all five product images is obtained as follows:(i)
ForY1, C = 0.262, γ2 = 7.234, MSE = 0.0000267, and R2 = 0.967(ii)
ForY2, C = 0.391, γ2 = 3.222, MSE = 0.0000533, and R2 = 0.985(iii)
ForY3, C = 0.112, γ2 = 6.655, MSE = 0.0000349, and R2 = 0.992(iv)
ForY4, C = 0.401, γ2 = 10.018, MSE = 0.0000381, and R2 = 0.977(v)
ForB∗, C = 0.454, γ2 = 7.234, MSE = 0.0001441, and R2 = 0.915


## 3.8. Verification

We use the remained five sample data to test the trained SVR model. The obtained test results are shown in Figure4. The absolute errors between the predicted and the measured high-level Kansei images of samples S1, S2, S3, S4, and S5 are, respectively, −0.12, −0.13, 0.15, −0.19, and 0.18 (corresponding relative errors: −2.5%, −4.1%, 2.9%, −3.5%, and 4.5%). Overall, the verification results are satisfying.Figure 4
Verification results of measured and predicted integral blue image.


## 4. Conclusion

This study proposes a novel methodology for blue-affective form design of products. The term “blue-affective product design” means we simultaneously consider people’s requirements of affection, sustainability, and economy for designing products. The highlight of our proposed methodology includes three aspects. First, we address a new Kansei blue model for determining blue images and blue design elements, which can be successfully merged with the traditional KE as an expansion to the field of blue design problems. Second, we adopt the advanced integral data mining schemes, including RST and GST to find the kernel influential design elements for each product image. Third, we use an excellent machine learning scheme of SVR for establishing a precise prediction model of product images. Verification results show that the proposed methodology has good prediction ability for blue image with only a maximum of 4.5% among all test cases. Through this study, we may clearly understand the influences of design elements on blue as well as other images, meanwhile, expand the application range of KE to the area of blue product design. By applying the proposed novel blue-affective methodology, designers may correctly evaluate and catch the form design trend of designing blue and affective products.In engineering applications, nowadays, for buying a high-price CNC machine tool, the factors of affection, sustainability, and economy play a decisive role in the marketplace. This paper provides an effective mathematical methodology based on KE for designers to correctly catch the influences of these important factors for well designing or evaluating the form of CNC machine tools.



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*Source: 5019588-2022-04-27.xml*