# A Novel Approach Based on Kano Model, Interval 2-Tuple Linguistic Representation Model, and Prospect Theory for Apperceiving Key Customer Requirements

Authors: Aijun Liu; Qiuyun Zhu; Haiyang Liu; Hui Lu; Sang-Bing Tsai
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

The precisely perception of key customer requirements (CRs) is critically important for customer collaborative product innovation (CCPI) design. A novel approach is proposed based on the Kano model, interval 2-tuple linguistic representation model, and prospect theory. First of all, a Kano model is constructed to preliminarily screen the relatively important product function attributes. For the uncertain and vague information of CRs, an interval 2-tuple linguistic representation model is proposed to determine the weight of CRs. Then, the comprehensive prospects value is utilized for sorting the innovative programs based on the prospect theory. Finally, a numerical example is given to verify the scientific and validity of the proposed method.


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## Body

## 1. Introduction

With the increasingly fierce market competition, as well as more and more personalized and diversified CRs, it is very critical for the modern manufacturing enterprises to grasp customers’ key requirements in a relatively short time because of the complexity of decision-making problems and the fuzziness of decision-making environments (Liu and Wang [1]). What is more, integrating the CRs into the product design is very important for successful product development in CCPI, which can effectively enhance the communication between enterprises and customers and then improve the performance of enterprises. For example, Franke and Von Hippel [2] proposed a study to satisfy heterogeneous customer requirements via innovation toolkits, and the case of Apache security software proved that collaborative innovation can bring rich profits to the company. Besides, Lilien et al. [3] compared and analyzed the CCPI process of 3M in the United States and illustrated the clear benefits of customer innovation with actual sales data. Nowadays, this method has been widely used in product design (Song et al. [4]; Dahl et al. [5]). It is well known that the key CRs is the core of CCPI; however, due to the expression of key CRs it is too subjective and vagueness to be accurately obtained. Based on this, we integrate Kano model, the interval 2-tuple linguistic representation model, and prospect theory to determine the key customer requirements.Over the past decade, the way of identifying key customer requirements including qualitative and quantitative methods was developed. About qualitative method, Chen et al. [6] proposed an ontology learning CRs representation system, the system which preprocessed customer statements by language processing tools. Wang and Tseng [7]; Wang and Tseng [8] put forward the concept of customer demand bias and employed probability analysis methods to analyze CRs. Liu et al. [9] proposed a system management approach for demand management in industrial design. Violante et al. [10] developed a user-centric approach that can meet the specific requirements of the company and help organizations effectively identify selection tools. Sheng et al. [11] took the product service system as the research object, constructed the quality house, and determined the attribute weight of the product and service. Carulli et al. [12] proposed a method for capturing CRs based on virtual reality technology, which was commonly used in the early stages of product design to deduce CRs and reduce overall cost. In order to solve the problem of inaccurate customer demand, Kwong and Bai [13] introduced the fuzzy number on the basis of traditional AHP and proposed the fuzzy AHP to determine the importance of customer demand. In the process of product collaborate design, Halimahtun [14] used a system framework approach to conceptualize the current and future customer demand for automotive electronics. The qualitative method is simple and easy to operate, but its subjectivity is too strong to reflect the essential differences between items; the results obtained are more abstract. The application effect of qualitative method is unconvincing.As for quantitative method, Li et al. [15] combined minimum deviation method, the Balanced Scorecard, the analytic hierarchy process (AHP), the proportional method, and so on and proposed a system operation method that can make better use of product competition and preference information. Due to the ambiguity and uncertainty of the customers’ requirements, Wang and Tseng [16] established a probability-based Bayesian classifier by using existing customer selection data, the classifier classified CRs based on the flexibility of customer demand. Finally, the case proved that this method had obvious advantages in customer demand classification. Aguwa et al. [17] developed a new approach to measure customer satisfaction by considering quantitative factors such as quantitative data, design parameters, drawing output, and decision-making templates for means of measurement. This method can reduce errors and shorten the engineering development time. Liu et al. [18] used language intuitionistic fuzzy number to describe the decision maker’s language information. Then comparative analysis method is used to prove the validity of the proposed method. Nahm et al. [19] proposed two methods of customer preference and customer satisfaction assessment; the former provided a way to capture incomplete and uncertain information about the customer and the latter built a customer satisfaction model based on competitive benchmarking; finally, the effectiveness of the proposed method was proved by a door design example. Wu et al. [20] integrated the gray relational theory into the Quality Function Deployment (QFD), this method, taking the uncertainty and advancement of CRs into account, was utilized to analyze dynamic CRs. Liu et al. [21] presented an approach to address the dependent attribute problem leading to a function form with design attributes as independent variables and proved the potential to optimize the design specification. Takai and Ishii [22] analyzed and compared two methods for identifying representative needs affinity diagram (AD) and subjective clustering (SC); the CRs analysis of the next generation particle accelerator was used to demonstrate the scientific nature of the proposed method. The establishment of the key customer requirements is crucial to CCPI, and the weight of key customer requirements is the core of innovation program selection. The fuzzy language information in fuzzy decision is often expressed by fuzzy number (Liu et al. [23]; Liu and Chen [24]), language scale, and interval 2-tuple linguistic representation model. All research results suggest that constructing interval 2-tuple linguistic representation model is an effective method to donate the information of decision-makers. Based on 2-tuples and intervals, Dong et al. [25] proposed a linguistic computational model, summarized the numerical scale approach, and conducted comparative analysis to justify the effectiveness of the interval version of the 2-tuple fuzzy linguistic representation model. Herrera and Martinez [26]; Herrera and Martinez [27] pointed out that the binary semantic representation model was widely used to solve the multiattribute decision-making problem based on language evaluation information; it had high expression accuracy. Li et al. [28] and Li et al. [29] proposed the personalized individual semantics in 2-tuple linguistic model. Dong et al. [30] propose a connection between the linguistic hierarchy model and the numerical scale model. They also prove the equivalence of the linguistic computational models by equating the model. Chen et al. [31] analyzed three types of fusion approaches to manage the fusion process in group decision-making with heterogeneous preference structures and reviewed the different transformation functions among utility values, preference orderings, numerical preference relations, and multigranular linguistic preference relation. Dong et al. [32] considered four formats of information, i.e., real numbers, intervals, linguistic variables, and triangular fuzzy numbers and proposed framework to solve complex and dynamic multiple attribute group decision-making problems. As can be seen from the above literature, interval 2-tuple linguistic can handle the information of decision-makers well in a fuzzy environment. Based on this, we use the interval 2-tuple linguistic representation model to collect and express the information of decision-makers and then determine the key customer requirements in CCPI. In the process of CCPI design, due to the constraints of resources and costs, the degree of implementation of key customer requirements can not always reach the maximum. Therefore, it is necessary to choose a better innovative scheme. The selection of innovative scheme is a process of MCMD. Liu [33] combined the power average operator with Heronian mean operator and extended them to process interval-valued intuitionistic fuzzy information and presented fuzzy multiple attribute group decision-making. Liu and Li [34] extended the power Bonferroni mean operator (PBM) to process interval-valued intuitionistic fuzzy numbers (IVIFNs) and applied them to solve the MAGDM problems. Lahdelma and Salminen [35] proposed a new decision-making method based on the combination of the prospect theory and the Stochastic Multicriteria Acceptability Analysis (SMAA) for stochastic multiattribute decision-making with incomplete preference information. Based on the interaction operational laws of intuitionistic fuzzy sets (IFSs) Liu et al. [36] extended the PBM operator and the PGBM operator, and then they proposed a novel MAGDM method. Grabisch et al. [37]; Grabisch et al. [38] presented both a constructive view and a descriptive view on alternatives evaluation in the process of multicriteria decision analysis. The descriptive approach was concerned with characterizations of models of preference, whereas the constructive approach aimed at building preferences by questioning the decision maker. The result of quantitative methods is more intuitive, concise, accurate, and effective than qualitative method. However, its operation often has some difficulties; especially some related factors are difficult to quantify, affecting the accuracy of quantification.Based on this, we combine qualitative and quantitative methods to determine the key requirements of customers. This paper integrates the Kano model, the interval 2-tuple linguistic representation model, and the prospect theory; Kano model as a qualitative method is proposed to identify the initial requirements of customers. It is simple and easy to operate. Because of the difference of customers’ knowledge structure, experience, and other objective or subjective factors, some CRs expression may be uncertain linguistic preference. The interval 2-tuple linguistic representation model and the prospect theory are proposed to deal with the uncertainty. The interval 2-tuple linguistic representation model could be more accurate in terms of vague linguistic preference and less information loss in fuzzy information processing. Therefore, it is appropriate to select the 2-tuple linguistic representation model to illustrate fuzzy linguistic preference in the process of determining CRs’ weight. Because CRs are diversity, enterprises can not meet completely; based on this, we used prospect theory to evaluate the products’ comprehensive prospects value in order to achieve the maximum level of customer satisfaction.The remainder of this paper is organized in the following manner: Section2 is CRs analysis based on the Kano model. Section 3 is the innovative product program selection based on the prospect theory. In Section 4, an empirical example is provided to demonstrate the applicability of the proposed method. Comparative analysis is given in Section 5. Finally, some conclusions and future research directions are summarized in Section 6.The article frame work we proposed is shown in Figure1.Figure 1
The method we proposed.


## 2. Analysis of CRs Based on Kano Model

The customer can not specify the desired product attributes accurately in a real buying scenario. It is unscientific to determine the true requirements of customers simply by a simple questionnaire. Therefore, systematic methodological tools to clarify the real requirements of customer are necessary. Kano model as a valid method is proposed to identify the key CRs.


### 2.1. Identification of the Initial CRs of a Product

The Kano model, as a relative accuracy expression of CRs, is used to realize CRs and their effect on customer satisfaction (CS). It can classify different CRs and find attractive requirements of products. Promoting enterprises produce more popular products which can stand out from similar products.According to the size of the CRs impact on CS, Kano model divides CRs into five types requirements, which are must-be requirements, one-dimensional requirements, attractive requirements, indifference requirements, and reverse requirements, as shown in Figure2.Figure 2
Kano model of customer satisfaction.The horizontal axis is the satisfaction degree of one specific CR and the vertical axis means the satisfaction degree of CS.Must-Be Requirements (M). Customers will accept if this attribute is provided; otherwise they will feel extremely dissatisfied.One-Dimensional Requirements (O). CS is a linear function of the satisfaction degree of a certainly CR. High satisfaction degree leads to high satisfaction and low satisfaction degree leads to low satisfactionAttractive Requirements (A). Customers will be very satisfied if the requirement is met; if the requirement is not met they will accept the product with satisfaction also.Indifference Requirements (I). Regardless of the fact that requirement is satisfied or not, CS will not be impacted.Reverse Requirements (R). Customers do not want the attribute in the product, and absence of this attribute increases the degree of CS.


### 2.2. Determine the Type of CRs Based on Kano Model

Establishing the Kano model of CRs is vital for a product design, and the common tools for determining the initial CRs are Kano questionnaire, Kano assessment table, and Kano survey results table. The main steps are as follows.Step 1.
Design the Kano questionnaire. The Kano model provides a format for obtaining customer answers on each potential product attribute. The Kano questionnaire is shown in Table1.Table 1
Kano questionnaire table.
Requirement Problem Dislike Could understand Neutral Of course Like R i Products meet the requirement (select one)  √ Products do not meet the requirement (select one)   √From Table1, we can know that customers have to select one of the states out ofDislike,Could understand,Neutral,Of course, andLike from the product meet the requirement side, if the requirement is met in the product. Customers also have to select one of the states from the products do not meet the requirement side.Step 2.
The Kano questionnaire was issued. All possible combinations of customer answers and the corresponding type of product attribute are summarized in Table2.Table 2
Kano evaluation table.
Dysfunctional question: “If [the product] did not satisfied [feature x],how do you feel?” Like Of course Neutral Could understand Dislike Functional question: If [the product] satisfied [feature x], how would you feel? Like Q A A A O Of course R I I I M Neutral R I I I M Could understand R I I I M Dislike R R R R QAs seen from Table2, besides the five types of requirement have involved, there is one more type of requirement called Q, where Q represents a questionable answer and the answer is invalid. It occurs when customers select like or dislike from both functional and dysfunctional sides.Step 3.
By combining the two answers in the Kano evaluation table (Table2), the product criterion can be identified as attractive, must-be, one-dimensional, indifference, or reversal; the results are shown in Table 3.Table 3
Classification table of requirements.
Requirements A O M I R Total number of questionnaires Kano category R 1 20 25 15 22 18 100 O R 2 15 25 15 15 30 100 R ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯In order to maximize CS, we should consider the following points (Sharif Ullah and Tamaki [39]):(i)
Keep must-be attributes(ii)
As far as possible to meet the one-dimensional attributes and charm attributes(iii)
Avoid indifferent attributes as many as possible(iv)
Avoid reverse attributesStep 4.
Calculate satisfaction coefficient and dissatisfaction coefficient.The quantitative analysis of Kano’s model begins with calculating CS and DS (Ji et al. (2014)). Due to the diversification of CRs, CS and DS values only indicate the average contribution of one CR to CS, which can be represented by the number of customers who are satisfied or dissatisfied with a certain CR. From Table3, we can sum up the number of attractive attributes NA, one-dimensional attributes NO, must-be attributes NM, and indifferent attributes NI, and then we can get the value of CSi and CDSi by formulations (1) and (2):1CSi=NA+NONA+NO+NM+NI2CDSi=-NM+NONA+NO+NM+NIStep 5.
According to Table4, CSi−CDSi relationship functions could be obtained (Ji et al. [40]).Table 4
C S i−CDSi relationship functions.
Kano category A B f y i s i = A f y i + B A C S i - D S i e - 1 - C S i - e D S i e - 1 e y i s i = C S i - D S i e - 1 e y i - C S i - e D S i e - 1 O C S i - D S i D S i y i s i = C S i - D S i y i + D S i M e ( C S i - D S i ) e - 1 e C S i - D S i e - 1 - e y i s i = - e C S i - D S i e - 1 e y i + e C S i - D S i e - 1Step 6.
A rank for CRs is made according to the value ofsi.The flow chart based on Kano model is shown in Figure3.Figure 3
The flow chart based on Kano model.


### 2.3. Weight Determination of CRs

In product design, it is very difficult for product design decision-makers due to the vagueness and uncertainty of the CRs. In order to solve this difficult, Lin et al. [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic.It is used for representing the linguistic assessment information by means of a 2-tuplesi,αi, where si is a linguistic label from predefined linguistic term set S and αi is the value of symbolic translation (Dong et al. [42]; Wei [43]; Zhang [44]; Zhang [45]; Gangurde and Akarte [46]; Liu and Chen [47]; Qin and Liu [48]; Wang et al. [49]). See Figure 4.Figure 4
Common linguistic hierarchies.Definition 1.
LetS=s0,s1,…,sg be a linguistic term set, and α represents the deviation between the linguistic information and the closest linguistic phrase in the initial linguistic evaluation set S, the real number. β∈0,g is the aggregation operation result of these elements of S, then the 2-tuple linguistic information is obtained by the following function f:3f:0,g⟶S×-0.5,0.54fβ=si,α,si,i=roundβα=β-i,α∈-0.5,0.5whereround is a rounding operation and i∈0,g.Correspondingly, the real numberβ can be obtained by the 2-tuple linguistic information according to the following function f-1.5f-1:S×-0.5,0.5⟶0,g6f-1si,α=i+α=β7si∈S⟹si,0∈S-where formula(7) represents the conversion between a linguistic term and a 2-tuple linguistic consists in adding a value 0 as symbolic translation.Definition 2.
LetX=s1,α1,s2,α2,…,sn,αn be a set of 2-tuples, let w=w1,w2,…,wnT be the weight vector, where wi∈0,1,i=1,2,…,n,∑i=1nwi=1, and the 2-tuple weighted average (TWA) operator is defined as8TWAX=f1n∑j=1nwj▵-1rj,αj=1n∑j=1nwjβjAs information aggregation plays a very significant role in the process of making decision, aggregation operators with 2-tuple linguistic information have attracted many scholars’ attention. If the 2-tuples are from different linguistic term sets, they cannot be aggregated directly and should be conducted tedious transformation before aggregation operation, to avoid complicated computation, we proposed some aggregation operators with interval-valued 2-tuple linguistic information. Besides, we discuss their desired definition.Definition 3.
Let the linguistic evaluation set beS=s0,s1,…,sg,si,α1,sj,α2 which is called the interval 2-tuple linguistic, where si and sj belong to the evaluation set S and i≤j,α1<α2. The interval number β1,β2β1,β2∈0,1,β1≤β2 can be obtained by the following function f:9fβ1,β2=si,α1,sj,α2,sii=roundβ1∗gsjj=roundβ2∗gα1=β1-ig,α1∈-0.5g,0.5gα2=β2-jg,α2∈-0.5g,0.5gOn the contrary, the interval 2-tuple linguisticsi,α1,sj,α2 can be converted into interval numbers by function f-1:10f-1si,α1,sj,α2=ig+α1,jg+α2=β1,β2Particularly, ifsi=sj and αi=αj, then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable.Definition 4.
LetX={s1,α1,s1′,α1′,s2,α2,s2′,α2′, …,sn,αn,sn′,αn′} be a set of 2-tuples, let w=w1,w2,…,wnT be the weight vector, where wi∈0,1,i=1,2,…,n,  ∑i=1nwi=1, and the interval 2-tuple weighted average (ITWA) operator is defined as11ITWAs1,α1,s1′,α1′,s2,α2,s2′,α2′,…,sn,αn,sn′,αn′=f∑i=1nwif-1si,αi,∑i=1nwif-1si′,αi′This approach is introduced to deal with information assessed in different linguistic scales by using the extension principle and the interval 2-tuple linguistic representation model. It is a computing model as shown in Figure5Figure 5
The flow chart based on the interval 2-tuple linguistic information.In summary, the process of determining the weight of CRs is as follows.Step 1.
Set the linguistic evaluation setS=s0,s1,…,sg.Step 2.
Evaluate requirementi and requirement j according to evaluator Rk, and get the measure value uijk,vijk, where k=1,2,…,l,  uijk,vijk∈S,i,j=1,2,…,n.Step 3.
Obtain the linguistic complementary judgment matrixRk=uijk,vijkn×n according to the measure value, and the weight vector of the evaluator is wk=(w1,w2,…,wl),where ∑k=1lwk=1.Step 4.
Convert the linguistic complementary judgment matrixRk to the interval 2-tuple linguistic judgment matrix Rk′:12Rk′=uijk,0,vijk,0n×nStep 5.
The interval 2-tuple linguisticuijk,0,vijk,0 is transformed into the corresponding interval number cijk,dijk by the inverse function f-1.Step 6.
Aggregate the number of intervalscijk,dijk and get the interval 2-tuple linguistic comprehensive evaluation matrix R~:13R~=cij,dijn×n=∑wkcijk,∑wkdijkn×nStep 7.
R = s i j , s i j ′ m × n is the evaluation matrix, where i=1,2,…,m;j=1,2,…n, then the comprehensive weight interval of the evaluation object i is14θi=γi,γi′=∑i=1nsijn,∑i=1nsij′nStep 8.
If the evaluation objecti is not inferior to the evaluation object k and θi≥θki,k=1,2,…,m, then get pik by pairwise comparison according to the comprehensive evaluation value from Step7, and the formula is as follows:15pik=pθi≥θk=max⁡1-max⁡γk′-γiγi′-γi+γk′-γk,0,0
Then obtain the following probability matrixP:16P=Pikm×n=P11P12⋯P1mP21P22⋯P2m⋮⋮⋮⋮Pm1Pm2⋯PmmAmong them, the rank vector of possible degree matrix is obtained:17φi=∑k=1mPik+m/2-1mm-1Step 9.
We obtain the ranking vectorφi of the probability matrix P. According to the size of φi obtain the weights of different CRs.The flow chart based on the interval 2-tuple linguistic information is shown in Figure5.


## 2.1. Identification of the Initial CRs of a Product

The Kano model, as a relative accuracy expression of CRs, is used to realize CRs and their effect on customer satisfaction (CS). It can classify different CRs and find attractive requirements of products. Promoting enterprises produce more popular products which can stand out from similar products.According to the size of the CRs impact on CS, Kano model divides CRs into five types requirements, which are must-be requirements, one-dimensional requirements, attractive requirements, indifference requirements, and reverse requirements, as shown in Figure2.Figure 2
Kano model of customer satisfaction.The horizontal axis is the satisfaction degree of one specific CR and the vertical axis means the satisfaction degree of CS.Must-Be Requirements (M). Customers will accept if this attribute is provided; otherwise they will feel extremely dissatisfied.One-Dimensional Requirements (O). CS is a linear function of the satisfaction degree of a certainly CR. High satisfaction degree leads to high satisfaction and low satisfaction degree leads to low satisfactionAttractive Requirements (A). Customers will be very satisfied if the requirement is met; if the requirement is not met they will accept the product with satisfaction also.Indifference Requirements (I). Regardless of the fact that requirement is satisfied or not, CS will not be impacted.Reverse Requirements (R). Customers do not want the attribute in the product, and absence of this attribute increases the degree of CS.


## 2.2. Determine the Type of CRs Based on Kano Model

Establishing the Kano model of CRs is vital for a product design, and the common tools for determining the initial CRs are Kano questionnaire, Kano assessment table, and Kano survey results table. The main steps are as follows.Step 1.
Design the Kano questionnaire. The Kano model provides a format for obtaining customer answers on each potential product attribute. The Kano questionnaire is shown in Table1.Table 1
Kano questionnaire table.
Requirement Problem Dislike Could understand Neutral Of course Like R i Products meet the requirement (select one)  √ Products do not meet the requirement (select one)   √From Table1, we can know that customers have to select one of the states out ofDislike,Could understand,Neutral,Of course, andLike from the product meet the requirement side, if the requirement is met in the product. Customers also have to select one of the states from the products do not meet the requirement side.Step 2.
The Kano questionnaire was issued. All possible combinations of customer answers and the corresponding type of product attribute are summarized in Table2.Table 2
Kano evaluation table.
Dysfunctional question: “If [the product] did not satisfied [feature x],how do you feel?” Like Of course Neutral Could understand Dislike Functional question: If [the product] satisfied [feature x], how would you feel? Like Q A A A O Of course R I I I M Neutral R I I I M Could understand R I I I M Dislike R R R R QAs seen from Table2, besides the five types of requirement have involved, there is one more type of requirement called Q, where Q represents a questionable answer and the answer is invalid. It occurs when customers select like or dislike from both functional and dysfunctional sides.Step 3.
By combining the two answers in the Kano evaluation table (Table2), the product criterion can be identified as attractive, must-be, one-dimensional, indifference, or reversal; the results are shown in Table 3.Table 3
Classification table of requirements.
Requirements A O M I R Total number of questionnaires Kano category R 1 20 25 15 22 18 100 O R 2 15 25 15 15 30 100 R ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯In order to maximize CS, we should consider the following points (Sharif Ullah and Tamaki [39]):(i)
Keep must-be attributes(ii)
As far as possible to meet the one-dimensional attributes and charm attributes(iii)
Avoid indifferent attributes as many as possible(iv)
Avoid reverse attributesStep 4.
Calculate satisfaction coefficient and dissatisfaction coefficient.The quantitative analysis of Kano’s model begins with calculating CS and DS (Ji et al. (2014)). Due to the diversification of CRs, CS and DS values only indicate the average contribution of one CR to CS, which can be represented by the number of customers who are satisfied or dissatisfied with a certain CR. From Table3, we can sum up the number of attractive attributes NA, one-dimensional attributes NO, must-be attributes NM, and indifferent attributes NI, and then we can get the value of CSi and CDSi by formulations (1) and (2):1CSi=NA+NONA+NO+NM+NI2CDSi=-NM+NONA+NO+NM+NIStep 5.
According to Table4, CSi−CDSi relationship functions could be obtained (Ji et al. [40]).Table 4
C S i−CDSi relationship functions.
Kano category A B f y i s i = A f y i + B A C S i - D S i e - 1 - C S i - e D S i e - 1 e y i s i = C S i - D S i e - 1 e y i - C S i - e D S i e - 1 O C S i - D S i D S i y i s i = C S i - D S i y i + D S i M e ( C S i - D S i ) e - 1 e C S i - D S i e - 1 - e y i s i = - e C S i - D S i e - 1 e y i + e C S i - D S i e - 1Step 6.
A rank for CRs is made according to the value ofsi.The flow chart based on Kano model is shown in Figure3.Figure 3
The flow chart based on Kano model.


## 2.3. Weight Determination of CRs

In product design, it is very difficult for product design decision-makers due to the vagueness and uncertainty of the CRs. In order to solve this difficult, Lin et al. [41] proposed the concept of interval 2-tuple linguistic and investigated the possibility of interval 2-tuples linguistic.It is used for representing the linguistic assessment information by means of a 2-tuplesi,αi, where si is a linguistic label from predefined linguistic term set S and αi is the value of symbolic translation (Dong et al. [42]; Wei [43]; Zhang [44]; Zhang [45]; Gangurde and Akarte [46]; Liu and Chen [47]; Qin and Liu [48]; Wang et al. [49]). See Figure 4.Figure 4
Common linguistic hierarchies.Definition 1.
LetS=s0,s1,…,sg be a linguistic term set, and α represents the deviation between the linguistic information and the closest linguistic phrase in the initial linguistic evaluation set S, the real number. β∈0,g is the aggregation operation result of these elements of S, then the 2-tuple linguistic information is obtained by the following function f:3f:0,g⟶S×-0.5,0.54fβ=si,α,si,i=roundβα=β-i,α∈-0.5,0.5whereround is a rounding operation and i∈0,g.Correspondingly, the real numberβ can be obtained by the 2-tuple linguistic information according to the following function f-1.5f-1:S×-0.5,0.5⟶0,g6f-1si,α=i+α=β7si∈S⟹si,0∈S-where formula(7) represents the conversion between a linguistic term and a 2-tuple linguistic consists in adding a value 0 as symbolic translation.Definition 2.
LetX=s1,α1,s2,α2,…,sn,αn be a set of 2-tuples, let w=w1,w2,…,wnT be the weight vector, where wi∈0,1,i=1,2,…,n,∑i=1nwi=1, and the 2-tuple weighted average (TWA) operator is defined as8TWAX=f1n∑j=1nwj▵-1rj,αj=1n∑j=1nwjβjAs information aggregation plays a very significant role in the process of making decision, aggregation operators with 2-tuple linguistic information have attracted many scholars’ attention. If the 2-tuples are from different linguistic term sets, they cannot be aggregated directly and should be conducted tedious transformation before aggregation operation, to avoid complicated computation, we proposed some aggregation operators with interval-valued 2-tuple linguistic information. Besides, we discuss their desired definition.Definition 3.
Let the linguistic evaluation set beS=s0,s1,…,sg,si,α1,sj,α2 which is called the interval 2-tuple linguistic, where si and sj belong to the evaluation set S and i≤j,α1<α2. The interval number β1,β2β1,β2∈0,1,β1≤β2 can be obtained by the following function f:9fβ1,β2=si,α1,sj,α2,sii=roundβ1∗gsjj=roundβ2∗gα1=β1-ig,α1∈-0.5g,0.5gα2=β2-jg,α2∈-0.5g,0.5gOn the contrary, the interval 2-tuple linguisticsi,α1,sj,α2 can be converted into interval numbers by function f-1:10f-1si,α1,sj,α2=ig+α1,jg+α2=β1,β2Particularly, ifsi=sj and αi=αj, then the interval 2-tuple linguistic variable becomes a 2-tuple linguistic variable.Definition 4.
LetX={s1,α1,s1′,α1′,s2,α2,s2′,α2′, …,sn,αn,sn′,αn′} be a set of 2-tuples, let w=w1,w2,…,wnT be the weight vector, where wi∈0,1,i=1,2,…,n,  ∑i=1nwi=1, and the interval 2-tuple weighted average (ITWA) operator is defined as11ITWAs1,α1,s1′,α1′,s2,α2,s2′,α2′,…,sn,αn,sn′,αn′=f∑i=1nwif-1si,αi,∑i=1nwif-1si′,αi′This approach is introduced to deal with information assessed in different linguistic scales by using the extension principle and the interval 2-tuple linguistic representation model. It is a computing model as shown in Figure5Figure 5
The flow chart based on the interval 2-tuple linguistic information.In summary, the process of determining the weight of CRs is as follows.Step 1.
Set the linguistic evaluation setS=s0,s1,…,sg.Step 2.
Evaluate requirementi and requirement j according to evaluator Rk, and get the measure value uijk,vijk, where k=1,2,…,l,  uijk,vijk∈S,i,j=1,2,…,n.Step 3.
Obtain the linguistic complementary judgment matrixRk=uijk,vijkn×n according to the measure value, and the weight vector of the evaluator is wk=(w1,w2,…,wl),where ∑k=1lwk=1.Step 4.
Convert the linguistic complementary judgment matrixRk to the interval 2-tuple linguistic judgment matrix Rk′:12Rk′=uijk,0,vijk,0n×nStep 5.
The interval 2-tuple linguisticuijk,0,vijk,0 is transformed into the corresponding interval number cijk,dijk by the inverse function f-1.Step 6.
Aggregate the number of intervalscijk,dijk and get the interval 2-tuple linguistic comprehensive evaluation matrix R~:13R~=cij,dijn×n=∑wkcijk,∑wkdijkn×nStep 7.
R = s i j , s i j ′ m × n is the evaluation matrix, where i=1,2,…,m;j=1,2,…n, then the comprehensive weight interval of the evaluation object i is14θi=γi,γi′=∑i=1nsijn,∑i=1nsij′nStep 8.
If the evaluation objecti is not inferior to the evaluation object k and θi≥θki,k=1,2,…,m, then get pik by pairwise comparison according to the comprehensive evaluation value from Step7, and the formula is as follows:15pik=pθi≥θk=max⁡1-max⁡γk′-γiγi′-γi+γk′-γk,0,0
Then obtain the following probability matrixP:16P=Pikm×n=P11P12⋯P1mP21P22⋯P2m⋮⋮⋮⋮Pm1Pm2⋯PmmAmong them, the rank vector of possible degree matrix is obtained:17φi=∑k=1mPik+m/2-1mm-1Step 9.
We obtain the ranking vectorφi of the probability matrix P. According to the size of φi obtain the weights of different CRs.The flow chart based on the interval 2-tuple linguistic information is shown in Figure5.


## 3. Selection of Innovative Schemes Based on Prospect Theory

Due to restrictions on resources such as technology, cost, and equipment, the innovation efficiency is not obvious in CCPI design process. Therefore, the prospects theory is proposed in the case of customer demand which has been identified, which considers the company’s technology, cost, advanced equipment, and the conflict between the demand and the impact of psychological factors of the customers. According to the customer satisfaction and the expected value of each attribute of the product, we can calculate the comprehensive prospect value and determine the optimal product scheme by using the prospect theory.


### 3.1. Gains and Loss Value of Product Attributes

Firstly, we regard aspiration-levels as reference points. Then, gains and losses of alternatives are obtained by the corresponding formulas. Since attribute values are represented in the three types: crisp number, interval number, and intuitive trapezoidal fuzzy number, there are three possible types for comparing an attribute value with an aspiration level (see Figure6),Figure 6
The types of attribute value.In Figure6, type one represents the situation that attribute value is crisp numbers; type two represents the situation that attribute values are interval numbers; type three represents the situation that attribute values are intuitive trapezoidal fuzzy number.Assuming that aspiration level is clear number, the attribute value has three types: clear number, interval number, and intuitive trapezoidal fuzzy number. For the three types of attribute values, the specific description is as follows: wherexil is representing the value of attribute l of supplier i (see Tables 5 and 6).Table 5
Possible cases of position relationships between attribute value and aspiration level.
Type Cases Position relationships between attribution value and aspiration level Type one Case one (a) xil≥el Case one (b) xil<el  Type two Case two (a) xil1>el Case two (b) xil1≤el≤xil2 Case two (c) xil2<el  Type three Case three (a) el<ail Case three (b) ail≤el≤dil Case three (c) dil<elTable 6
Variable symbol description.
Variable Meaning S = S 1 , S 2 , … , S i , … , S m A set ofm alternative products I = I 1 , I 2 , … , I i , … , I l The set of product attributes E = e 1 , e 2 , … , e n Expectation vector of requirements I C Attribute sets whose attribute values are distinct numbers I Q Attribute sets whose attribute values are interval numbers I F Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers N = 1,2 , … , n Product attribute sets M = 1,2 , … , m Scheme numbers( 1 ) If Il∈IC, let xil=xil′, where xil′ is clear number, and i∈M,l∈NK.( 2 ) If Il∈IQ, let xil=x-il, where x-il is an interval number x-il=xil1,xil2. Assuming that the attribute values are randomly obtained in the interval xil1,xil2 and are uniformly distributed, the probability density function is filx: 18filx=1xil2-xil1,xil1≤x≤xil20,other,i∈M,l∈N( 3 ) If Ij∈IF, let xil=x~il, where x~il is intuitive trapezoidal fuzzy number x~il=ail,bil,cil,dil;ϕx,ail1,bil,cil,dil1;τx, and 0≤ϕx≤1, 0≤τx≤1, ϕx+τx≤1, ail,bil,cil,dil,ail1,dil1∈R, and the membership function ϕilx is as shown:19ϕilx=x-ailbil-ail,ail≤x≤bilϕil,bil≤x≤cildil-xdil-cil,cil≤x≤dil0,othersi∈M,l∈NIfail,bil,cil,dil=ail1,bil,cil,dil1, the intuitionistic trapezoidal fuzzy number x~il=ail,bil,cil,dil;ϕx,τil.


### 3.2. Calculating the Gains and Losses Value

Let the expect valuee=e1,e2,…,el of customers as the reference point in this paper. Then, calculate the gains and loss of each attribute value relative to the reference point. When the attribute value is a clear number, we obtain the gains and losses value of product attribute according to the calculation formula shown in Table 7.Table 7
Calculation formula when the attribute value is a clear number.
Attribute type The relationship between attribute value and the reference point Calculation of gain (Gil) and loss value (Lil) I l ∈ I K x i l ′ < e l G i l = 0 ,  i ∈ M ,  l ∈ N   ( 20 ) L i l = x i l ′ - e i l  i ∈ M ,   l ∈ N   ( 21 ) x i l ′ ≥ e l G i l = x i l ′ - e i l  i ∈ M ,   l ∈ N   ( 22 ) L i l = 0  i ∈ M ,   l ∈ N   ( 23 )When the attribute value is the number of intervals, according to the attribute value and the position of the reference point, the formula of each attribute value of the innovation scheme is shown in Table8.Table 8
The calculation formula when the attribute value is the interval number.
Attribute type The relationship between attribute value and the reference point Calculation of gain (Gil) and loss value (Lil) x i l 2 < e l Gil=0,i∈M,l∈N (24) L i l = ∫ x i l 1 x i l 2 x - e l f i l x d x  i ∈ M ,   l ∈ N (25) I l ∈ I I x i l 1 ≤ e l ≤ x i l 2 G i l = ∫ e l x i l 2 x - e l f i l x d x   i ∈ M ,   l ∈ N (26) L i l = ∫ x i l 1 e l x - e l f i l x d x   i ∈ M ,   l ∈ N (27) x i l 1 > e l G i l = ∫ x i l 1 x i l 2 x - e l f i l x d x  i ∈ M ,   l ∈ N (28) L i l = ∫ x i l 1 x i l 2 ( e l - x ) f i l ( x ) d x  i ∈ M ,   l ∈ N (29)When the attribute value is intuitionistic trapezoidal fuzzy number, according to the relative position of the attribute value and the reference point, the formula of each attribute value of the innovation scheme is shown in Table9.Table 9
Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers.
Attribute type The relationship between attribute value and the reference point Calculation of gain (Gil) and loss value (Lil) e l ≤ a i l Gil=∫aildijx-elϕilxdxi∈M,l∈N (30) Lil=0i∈M,l∈N (31) I l ∈ I F a i l ≤ e l ≤ d i l Gil=∫eldilx-elϕilxdxi∈M,l∈N (32) Lil=∫ailelx-elϕilxdxi∈M,l∈N (33) e l ≥ d i l Gil=0i∈M,l∈N (34) Lil=∫aildilx-elϕilxdxi∈M,l∈N (35)


### 3.3. Calculating the Prospect Values and Ranking

For the gain matrixGt=Gilm∗n and the loss matrix Lt=Lilm∗n of each scheme, calculate the prospective value of the candidate product. Based on prospect theory, the value of gain matrix Gil is36vil+=Gila,i∈M,l∈NThe valueVil- of loss is37vil-=-λ-Lilb,i∈M,l∈Nwherea and b represent the degree of concavity and convexity of the loss region and gain region of the value function,0<a<1,0<b<1, and λ indicates the loss degree of the decision maker λ>1. Among them, a and b greater, decision-makers incline to risk more, and λ greater, the ability of decision-makers to avoid losses is greater.Due to the difference in the dimension of the product attribute value is so large that we use the range transformation method to reduce the dimension; the new gain and loss values of each innovation scheme are obtained by formulas(38)-(39).38Vil+=vil+-min⁡vil+max⁡vil+-min⁡vil+39Vil-=vil--min⁡vil-max⁡vil--min⁡vil-40Vil=Vil+-Vil-,i∈M,l∈NAccording to formula(40), the prospect decision matrix can be obtained.The flow chart based on prospect theory is shown in Figure7.Figure 7
The flow chart based on prospect theory.


## 3.1. Gains and Loss Value of Product Attributes

Firstly, we regard aspiration-levels as reference points. Then, gains and losses of alternatives are obtained by the corresponding formulas. Since attribute values are represented in the three types: crisp number, interval number, and intuitive trapezoidal fuzzy number, there are three possible types for comparing an attribute value with an aspiration level (see Figure6),Figure 6
The types of attribute value.In Figure6, type one represents the situation that attribute value is crisp numbers; type two represents the situation that attribute values are interval numbers; type three represents the situation that attribute values are intuitive trapezoidal fuzzy number.Assuming that aspiration level is clear number, the attribute value has three types: clear number, interval number, and intuitive trapezoidal fuzzy number. For the three types of attribute values, the specific description is as follows: wherexil is representing the value of attribute l of supplier i (see Tables 5 and 6).Table 5
Possible cases of position relationships between attribute value and aspiration level.
Type Cases Position relationships between attribution value and aspiration level Type one Case one (a) xil≥el Case one (b) xil<el  Type two Case two (a) xil1>el Case two (b) xil1≤el≤xil2 Case two (c) xil2<el  Type three Case three (a) el<ail Case three (b) ail≤el≤dil Case three (c) dil<elTable 6
Variable symbol description.
Variable Meaning S = S 1 , S 2 , … , S i , … , S m A set ofm alternative products I = I 1 , I 2 , … , I i , … , I l The set of product attributes E = e 1 , e 2 , … , e n Expectation vector of requirements I C Attribute sets whose attribute values are distinct numbers I Q Attribute sets whose attribute values are interval numbers I F Attribute sets whose attribute values are intuitionistic trapezoidal fuzzy numbers N = 1,2 , … , n Product attribute sets M = 1,2 , … , m Scheme numbers( 1 ) If Il∈IC, let xil=xil′, where xil′ is clear number, and i∈M,l∈NK.( 2 ) If Il∈IQ, let xil=x-il, where x-il is an interval number x-il=xil1,xil2. Assuming that the attribute values are randomly obtained in the interval xil1,xil2 and are uniformly distributed, the probability density function is filx: 18filx=1xil2-xil1,xil1≤x≤xil20,other,i∈M,l∈N( 3 ) If Ij∈IF, let xil=x~il, where x~il is intuitive trapezoidal fuzzy number x~il=ail,bil,cil,dil;ϕx,ail1,bil,cil,dil1;τx, and 0≤ϕx≤1, 0≤τx≤1, ϕx+τx≤1, ail,bil,cil,dil,ail1,dil1∈R, and the membership function ϕilx is as shown:19ϕilx=x-ailbil-ail,ail≤x≤bilϕil,bil≤x≤cildil-xdil-cil,cil≤x≤dil0,othersi∈M,l∈NIfail,bil,cil,dil=ail1,bil,cil,dil1, the intuitionistic trapezoidal fuzzy number x~il=ail,bil,cil,dil;ϕx,τil.


## 3.2. Calculating the Gains and Losses Value

Let the expect valuee=e1,e2,…,el of customers as the reference point in this paper. Then, calculate the gains and loss of each attribute value relative to the reference point. When the attribute value is a clear number, we obtain the gains and losses value of product attribute according to the calculation formula shown in Table 7.Table 7
Calculation formula when the attribute value is a clear number.
Attribute type The relationship between attribute value and the reference point Calculation of gain (Gil) and loss value (Lil) I l ∈ I K x i l ′ < e l G i l = 0 ,  i ∈ M ,  l ∈ N   ( 20 ) L i l = x i l ′ - e i l  i ∈ M ,   l ∈ N   ( 21 ) x i l ′ ≥ e l G i l = x i l ′ - e i l  i ∈ M ,   l ∈ N   ( 22 ) L i l = 0  i ∈ M ,   l ∈ N   ( 23 )When the attribute value is the number of intervals, according to the attribute value and the position of the reference point, the formula of each attribute value of the innovation scheme is shown in Table8.Table 8
The calculation formula when the attribute value is the interval number.
Attribute type The relationship between attribute value and the reference point Calculation of gain (Gil) and loss value (Lil) x i l 2 < e l Gil=0,i∈M,l∈N (24) L i l = ∫ x i l 1 x i l 2 x - e l f i l x d x  i ∈ M ,   l ∈ N (25) I l ∈ I I x i l 1 ≤ e l ≤ x i l 2 G i l = ∫ e l x i l 2 x - e l f i l x d x   i ∈ M ,   l ∈ N (26) L i l = ∫ x i l 1 e l x - e l f i l x d x   i ∈ M ,   l ∈ N (27) x i l 1 > e l G i l = ∫ x i l 1 x i l 2 x - e l f i l x d x  i ∈ M ,   l ∈ N (28) L i l = ∫ x i l 1 x i l 2 ( e l - x ) f i l ( x ) d x  i ∈ M ,   l ∈ N (29)When the attribute value is intuitionistic trapezoidal fuzzy number, according to the relative position of the attribute value and the reference point, the formula of each attribute value of the innovation scheme is shown in Table9.Table 9
Calculation formula for attribute values as intuitionistic trapezoidal fuzzy numbers.
Attribute type The relationship between attribute value and the reference point Calculation of gain (Gil) and loss value (Lil) e l ≤ a i l Gil=∫aildijx-elϕilxdxi∈M,l∈N (30) Lil=0i∈M,l∈N (31) I l ∈ I F a i l ≤ e l ≤ d i l Gil=∫eldilx-elϕilxdxi∈M,l∈N (32) Lil=∫ailelx-elϕilxdxi∈M,l∈N (33) e l ≥ d i l Gil=0i∈M,l∈N (34) Lil=∫aildilx-elϕilxdxi∈M,l∈N (35)


## 3.3. Calculating the Prospect Values and Ranking

For the gain matrixGt=Gilm∗n and the loss matrix Lt=Lilm∗n of each scheme, calculate the prospective value of the candidate product. Based on prospect theory, the value of gain matrix Gil is36vil+=Gila,i∈M,l∈NThe valueVil- of loss is37vil-=-λ-Lilb,i∈M,l∈Nwherea and b represent the degree of concavity and convexity of the loss region and gain region of the value function,0<a<1,0<b<1, and λ indicates the loss degree of the decision maker λ>1. Among them, a and b greater, decision-makers incline to risk more, and λ greater, the ability of decision-makers to avoid losses is greater.Due to the difference in the dimension of the product attribute value is so large that we use the range transformation method to reduce the dimension; the new gain and loss values of each innovation scheme are obtained by formulas(38)-(39).38Vil+=vil+-min⁡vil+max⁡vil+-min⁡vil+39Vil-=vil--min⁡vil-max⁡vil--min⁡vil-40Vil=Vil+-Vil-,i∈M,l∈NAccording to formula(40), the prospect decision matrix can be obtained.The flow chart based on prospect theory is shown in Figure7.Figure 7
The flow chart based on prospect theory.


## 4. Case Study

In order to enhance market competitiveness, an Electronic Manufacturing Enterprise in Xi’an has designed five innovation schemes for mobile phones. Moreover, this enterprise uses the proposed method to determine the optimal scheme. According to the mobile phone function, it has identified 35 types of CRs (AppendixA.1), and a market survey of whether or not to provide the demand item based on the Kano model is conducted to screen out ten relatively important requirements towards customer satisfaction (Appendix A.3). Five experts Rkk=1,2,3,4,5 are invited to participate in the evaluation of the importance of CRs that affected customer satisfaction. As such, experts R1 and R2 use nine elements of the linguistic evaluation set S=s0,s1,s2,s3,s4,s5,s6,s7,s8, experts R3 and R4 employ even elements of the linguistic evaluation set X=x0,x1,x2,x3,x4,x5,x6, and last, experts R5 adopt five elements of the linguistic evaluation set Y=y0,y1,y2,y3,y4. Experts’ opinions are shown in Appendix B.1. The weight vector corresponding to the experts’ opinions is w=(0.25,0.25,0.2,0.2,0.1), and finally five key attributes are determined as being the most important product attributes in the five innovative evaluation schemes (see Table 10). These key attributes are the following: operating system (I1), CPU core count (I2), antitheft tracking (I3), fingerprint sensor (I4), and battery capacity (I5). Based on the prospect theory, the customer’s expectation value of a product attribute is taken as the reference point, and the proposed method is used to determine the optimal scheme. The calculation steps are discussed in the following.Table 10
The experts’ evaluation results based on prospect theory.
attribute Innovation schemes Customer expectative values S1 S2 S3 S4 S5 I1 −4 0 0 0 - 4 8 I2 ( 1560,1750 ) ( 1500,1800 ) ( 1500,1800 ) ( 1500.1680 ) ( 1500,1800 ) 1680 I3 ( [ 5,6 , 8,9 ] ;  0.7,0.3 ) ( [ 6,7 , 8,9 ] ; 0.5,0.4 ) ( [ 6,7 , 8,9 ] ; 0.8,0.2 ) ( [ 4,6 , 7,9 ] ; 0.8,0.1 ) ( [ 5,7 , 8,9 ] ; 0.6,0.3 ) 8 I4 ( [ 5,7 , 8,9 ] ;  0.7,0.2 ) ( [ 4,5 , 6,8 ] ; 0.6,0.4 ) ( [ 6,7 , 8,9 ] ; 0.5,0.4 ) ( [ 5,7 , 8,9 ] ; 0.6,0.3 ) ( [ 5,6 , 8,9 ] ; 0.6,0.4 ) 7 I5 ( [ 6,7 , 8,9 ] ;  0.8,0.2 ) ( [ 5,6 , 8,9 ] ; 0.7,0.3 ) ( [ 5,7 , 8,9 ] ; 0.8,0.2 ) ( [ 5,6 , 7,9 ] ; 0.7,0.3 ) ( [ 5,6 , 8,9 ] ; 0.7,0.3 ) 6Step 1.
Obtain the five experts’ linguistic evaluation values with respect to the five attributes of the above-mentioned five innovation schemes (AppendixB.1).Step 2.
Determine the gain and loss values of each innovation scheme based on formula(19)–(36), and the results are shown in Tables 11 and 12.Table 11
The gain value of the innovation schemes.
Attribute The gain value of the innovation schemes Customer expectative values S1 S2 S3 S4 S5 I1 0 0 0 0 0 8 I2 245/19 24 24 0 24 1680 I3 21/10 1/6 13/30 1/12 1/6 8 I4 61/60 1/12 11/12 29/30 29/30 7 I5 27/10 77/30 167/60 51/20 77/30 6Table 12
The loss value of the innovation schemes.
Attribute The loss value of the innovation schemes Customer expectative values S1 S2 S3 S4 S5 I1 −4 0 0 0 −4 8 I2 −720/19 −54 −54 −90 −54 1680 I3 −9/2 −11/12 −4/3 −257/60 −59/30 8 I4 −2/3 −149/60 −1/6 −2/3 −2/3 7 I5 0 −1/6 −1/12 0 −1/6 6Step 3.
Determine the new gain and loss values of each innovation scheme when the influence of the dimension is eliminated according to the formula ((37) and (38)); the results are shown in Tables 13 and 14.Table 13
The new gain value of the innovation schemes after eliminated influence of dimension.
Attribute The new gain value of the innovation schemes Customer expectative values S1 S2 S3 S4 S5 I1 0.000 0.000 0.000 0.112 0.000 8 I2 0.579 1.000 1.000 0.000 1.000 1680 I3 0.117 0.013 0.029 0.007 0.013 8 I4 0.062 0.007 0.057 0.059 0.059 7 I5 0.146 0.140 0.150 0.139 0.140 6Table 14
The new loss value of the innovation schemes after eliminated influence of dimension.
Attribute The new loss value of the innovation schemes Customer expectative values S1 S2 S3 S4 S5 I1 0.935 1.000 1.000 1.000 0.935 8 I2 0.533 0.362 0.362 0.000 0.362 1680 I3 0.928 0.982 0.975 0.931 0.965 8 I4 0.987 0.958 0.996 0.987 0.987 7 I5 1.000 0.996 0.998 1.000 0.996 6Step 4.
Obtain the prospect value of each attribute value as shown in Table15.Table 15
The prospect values of the innovation schemes.
Attribute The prospect value of the innovation schemes Customer expectative values S1 S2 S3 S4 S5 I1 - 0.935 - 1.000 - 1.000 - 0.888 - 0.935 8 I2 0.046 0.638 0.638 0.000 0.638 1680 I3 - 0.811 - 0.970 - 0.946 - 0.925 - 0.953 8 I4 - 0.925 - 0.951 - 0.940 - 0.927 - 0.927 7 I5 - 0.854 - 0.856 - 0.848 - 0.861 - 0.856 6Step 5.
Calculate the weights of the CRs and rank.It can be observed from the weight of the indicatorsφ=0.114,0.112,0.110,0.105,0.104 (Appendix B.5) that the standardization of the weight of the indicators was ω=0.2092,0.2055,0.2018,0.1927,0.1908.According to the formula(40), the comprehensive prospect of each scheme is u=-0.6910,-0.6203,-0.6118,-0.7153,-0.5989, so the merits of the innovative program are S5≻S3≻S2≻S1≻S4.The proposed hybrid method provides a systemic analytical model for apperceiving the key customer requirements and obtaining the optimal innovation schemes. According to the Kano model, ten relatively important requirements towards customer satisfaction are screened out (AppendixA.3); combined with experts’ opinion, five indicators, i.e., operating system (I1), CPU core count (I2), antitheft tracking (I3), fingerprint sensor (I4), and battery capacity (I5), are determined as the most important indicators. And then with the help of interval 2-tuple linguistic, we easily obtain the weights of these indicators. Finally, based on the prospect theory, the comprehensive prospect value of each scheme is calculated; it is suggested that the optimal innovative scheme is S5.


## 5. Comparative Analysis

In order to verify the validity of the developed method, the Technique for Order of Preference by Similarity to an Ideal Solution (TOPSIS) (Gangurde et al. 2013) and the Vlse Kriterjumska Optimizacija I Kompromisno Resenje (VIKOR) (Qin et al. 2015) were compared with the methods proposed in this paper (see Tables16–18).Table 16
The result of TOPSIS method.
TOPSIS Scheme The ideal solution The negative solution Similarity degree S 1 0.126 0.125 0.499 S 2 0.051 0.003 0.05 S 3 0.04 0.013 0.248 S 4 0.131 0.139 0.514 S 5 0.017 0.041 0.707Table 17
The result of VIKOR method.
VIKOR Scheme U i R i Q i S 1 0.367 0.191 0.18 S 2 0.726 0.209 1 S 3 0.491 0.209 0.672 S 4 0.561 0.206 0.706 S 5 0.411 0.18 0.062Table 18
The results of the three methods.
Method Evaluation results Prospect theory S 5 ≻ S 3 ≻ S 2 ≻ S 1 ≻ S 4 TOPSIS S 5 ≻ S 4 ≻ S 1 ≻ S 3 ≻ S 2 VIKOR S 5 ≈ S 1 ≈ S 3 ≈ S 4 ≈ S 2From Table16, it is obvious that Q5≻Q1≻Q3≻Q4≻Q2, but for the fact that 0.18-0.062<1/5-1 and by the formula 0.18-0.062<1/m-1, we can know thatS1,S2,S3,S4, andS5 are all close to the ideal scheme.From Table18, we can see that the sorted results are quite different, the result of the proposed MCDM model based on prospect theory is S5≻S3≻S2≻S1≻S4, the TOPSIS method obtains result as S5≻S4≻S1≻S3≻S2, and the VIKOR method proves that there is no obvious difference between these innovative schemes. However, the optimal solution is always scheme S5. From our results, we can see that the VIKOR method has a low degree of discrimination, and because the TOPSIS method relies solely on the data itself and is prone to reverse the phenomenon, so it is appropriate to evaluate the innovation schemes with the prospect theory. The prospect theory takes full account of decision-makers’ psychological factors and behavioral science. It weighs both gains and losses, making the evaluation more comprehensive and objective. The decision result is closer to the actual situation and can better guide the production activities of enterprises.


## 6. Conclusion

Customer requirement is the initial information source and basis for product collaborative design and is key to the success of CCPI. Based on the fuzzy characteristics, as well as the dynamicity, diversity and individuation of CRs, a Kano model was constructed to identify and filter the initial requirements of customers in this paper; secondly, the weights of CRs were determined by the proposed interval 2-tuple linguistic representation model; finally, a comprehensive evaluation for the innovation schemes was given based on the prospect theory. In this process, some practical results have been obtained.( 1 ) The Kano model focuses on the analysis of factors that affect customer satisfaction. Through this model, we are able to capture the product attributes which can greatly improve customer satisfaction.( 2 ) Interval 2-tuple linguistic representation model is more accurate when expressing the vague language of customers and experts. In addition, it is a great advantage to accurately convert the decision-makers’ linguistic information due to little information loss.( 3 ) This paper introduces the prospect theory into the process of CCPI, from the perspective of product design options, and considers the subjective attitude of decision-makers fully. The scheme chosen based on the prospect theory is more scientific and makes the actual process of decision-making more efficient.



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