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Original Article

Understanding customer requirements through quantitative analysis of an improved fuzzy Kano’s model

Proc IMechE Part B: J Engineering Manufacture 2017, Vol. 231(4) 699–712 Ó IMechE 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954405415598894 journals.sagepub.com/home/pib

Lina He, Xinguo Ming, Miao Li, Maokuan Zheng and Zhitao Xu

Abstract Customer requirement analysis has become a primary concern for companies who compete in the global market. Kano’s model, as a customer-driven tool, has been widely used for customer requirement analysis in product improvement. Although a number of authors have improved the traditional Kano’s model, there has been a limitation of dealing with the fuzzy and uncertainty of human thought under multi-granularity linguistic environment. Furthermore, the traditional Kano’s model faces problems regarding quantitative data computation and customer requirements importance assessment. In this article, an improved fuzzy Kano’s model is proposed to analyze customer requirements under uncertain environment. A 2-tuple linguistic fuzzy Kano’s questionnaire is developed to model the uncertainty and diversity of customers’ assessments using 2-tuple linguistic variables under multi-granularity linguistic environment. Then, a comprehensive and systematic methodology is presented to prioritize customer requirements through quantitative analysis of improved fuzzy Kano’s model. This method integrates subjective judgments assigned by decision maker, objective weights based on maximizing deviation method and customer satisfaction contribution to determine the priority ratings of customer requirements. A case study of combine harvester development is presented to evaluate the proposed model.

Keywords Kano’s model, customer requirements, 2-tuple fuzzy-linguistic model, quantitative analysis

Date received: 4 December 2014; accepted: 13 July 2015

Introduction As competition for new markets and customers increased, customer requirements (CRs) have been widely recognized as one of the primary factors determining the success for product design and development.1,2 Manufacturing enterprises make an effort to understand and fulfill CRs to increase customer satisfaction (CS) by improving their products or services.3–5 Various methods and tools have been developed accordingly to help companies obtain a better understanding of CRs. Among them, the Kano’s model has been widely practiced in industries as an effective tool for understanding CRs and their impact on CS.6,7

Problems In general, Kano’s model is employed to elicit customers’ preferences toward products and services through questionnaire and extract CS. The Kano’s questionnaire and Kano evaluation table are used to categorize CRs into different Kano categories. The traditional

Kano’s questionnaire (TKQ) method uses binary data to model the customers’ preferences. However, customer judgments tend to be imprecise and ambiguous due to their inadequate information and experiences,8 so binary data are insufficient to capture preference,9 and linguistic information is needed to model and manage uncertainty. Moreover, because of the different background and discrimination ability, the customers involved in Kano’s questionnaire may prefer to express their linguistic preferences using different linguistic term

Shanghai Research Center for Industrial Informatics, Shanghai Key Lab of Advanced Manufacturing Environment, Institute of Computer Integrated Manufacturing, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai City, P.R. China Corresponding author: Xinguo Ming, Shanghai Research Center for Industrial Informatics, Shanghai Key Lab of Advanced Manufacturing Environment, Institute of Computer Integrated Manufacturing, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai 200240, P.R. China. Email: [email protected]

700 sets. Therefore, an effective approach to deal with the uncertain information expressed with multi-granularity linguistic terms in Kano’s model is highly needed. The Kano’s model is inherently customer driven, that is, it focuses exclusively on addressing the concerns of customers.10 However, the traditional Kano diagram only provides a rough sketch of the CS in relation to the product performance level and the qualitative descriptions of various Kano categories. In such a sense, limited quantitative analysis of the CRs is discussed in the traditional Kano’s model (TKM). The ultimate goal of CRs analysis is to provide decision support to product design. Although the Kano categories may enhance designers’ understanding of CRs, they fall short as accurate quantitative estimation. In practice, without accurate quantitative estimation, such a design support seldom holds true. Hence, the TKM faces problems regarding quantitative data computation and is deemed to be inadequate to facilitate decisions in product design. Considering the inherent deficiencies of TKM, fuzzy set theory has been used in Kano’s model to deal with the imprecision and uncertainty in CRs.9,11 Meanwhile, some quantitative analysis approaches have been incorporated into Kano’s model to prioritize CRs. The quantitative analysis approaches can be classified into two types: one approach utilizes the Kano evaluation results to adjust the raw weights of CRs,12–17 the other derives the importance weights of CRs from the Kano evaluation results.18,19 These studies make it possible to handle uncertain information or make quantitative analysis in TKM. However, they ignore the imprecision and uncertainty under multi-granularity linguistic environment and has limited quantitative analysis of the CRs. To our knowledge, there has been little work reported in the literature in which both the comprehensive quantitative analysis and the fuzzy questionnaire under multi-granularity linguistic environment in Kano’s model are addressed simultaneously.

Objectives and organization of this article To overcome the discussed problems, this study proposes an improved fuzzy Kano’s model (IFKM) for CRs analysis. In the IFKM, a 2-tuple linguistic fuzzy Kano’s questionnaire (TL-FKQ) is developed to use 2tuple linguistic representation model to deal with uncertainty and vagueness of human judgment under multigranularity linguistic environment. Furthermore, subjective judgments, objective information and impacts on CS derived from IFKM have been integrated to obtain quantitative and comprehensive CRs analysis. This article is structured as follows. The ‘‘Literature review’’ section briefly introduces the theoretical background of the Kano’s model, and the 2-tuple fuzzylinguistic model. ‘‘The proposed approach for CRs analysis’’ section describes the proposed approach in detail. The ‘‘Case study’’ section illustrates a case study of combine harvester to evaluate the proposed

Proc IMechE Part B: J Engineering Manufacture 231(4) Table 1. Kano evaluation table. Functional

Like Must-be Neutral Live with Dislike

Dysfunctional Like

Must-be

Neutral

Live with

Dislike

Q R R R R

A I I I R

A I I I R

A I I I R

O M M M Q

Source: Berger et al.21 A: attractive; O: one-dimensional; M: must-be; I: indifferent; R: reverse; Q: questionable.

Figure 1. Kano’s model.

approach. The discussion and conclusion are presented in the ‘‘Discussion’’ and ‘‘Conclusion’’ sections, respectively.

Literature review Kano’s model Kano et al.20 developed a two-dimensional model to explain the different relationship between CS and the performance of a product or a service. As shown in Table 1, the Kano’s model employs functional (the feature is present) and dysfunctional (the feature is not present) questionnaires and 5 3 5 evaluation table to determine different attributes.20 According to evaluation table, the product attribute can be classified into one of the Kano categories, including attractive, onedimensional, must-be, indifferent, reverse and questionable. Referring to Figure 1, Kano categories are briefly explained as follows:19,21,22

Attractive (A). The functional presence of these attributes will result in high level of CS, while their absence will not affect CS. One-dimensional (O). The functional presence of these attributes will generate CS, while their absence will result in non-satisfaction.

He et al.

Must-be (M). Customers take the presence of these attributes for granted. Insufficiency of these attributes will result in extreme non-satisfaction, but the sufficiency will not increase satisfaction level. Indifferent (I). The attributes in this category, whether present or not, will not affect satisfaction. Reverse (R). The presence of these attributes will generate non-satisfaction, and vice versa. Questionable (Q). This outcome indicates that either the responses do not make any logical sense, or the question is sent incorrectly.

The Kano categories of product attributes are evaluated according to response frequencies.23,24 The highest frequency represents the dominant customer view.25 The traditional Kano survey forces people to choose one answer from the survey, but it ignores the fuzzy and uncertainty factors that are related to human thinking when devising questionnaire.9 The fuzzy set theory provides a robust way to manage the uncertainty and vagueness of human judgment.26 Fuzzy set theory has been introduced into Kano’s model as an approach to effectively dealing with the inherent imprecision, vagueness of the human mentality and the languages.9,11,27 Lee and Huang9 developed FKQ for respondents to express their multifeeling in questionnaire items using membership and any numeric with their own wills. In addition, the fuzzy Kano’s model (FKM) is used for Kano evaluation to assist designers to get more and complete consumer’s real voice.9,11 However, FKQ consists of open-ended questions that require more time and effort from the respondents, and the FKM is a qualitative method.11 Based on FKM presented by Lee and Huang,9 Wu and Wang11 proposed a continuous fuzzy Kano’s model (C-FKM) by introducing a modified fuzzy Kano’s questionnaire (MFKQ) and a continuous approach for fuzzy Kano evaluation. The MFKQ uses membership and numerical data to represent customer’s preference and consists of closed-ended questions that are easy and quick to answer. The continuous approach for fuzzy Kano evaluation makes it possible to prioritize CRs with quantitative analysis based on an evaluation index. However, the use of numerical data in FKQ and MFKQ to represent uncertain information is not always adequate. It is more suitable for respondents to provide their preferences by means of linguistic variables instead of numerical ones regarding the uncertain knowledge they have about the problem.28 Moreover, because of different knowledge, background and discrimination ability, respondents may express their linguistic preferences in multi-granularity linguistic information. Furthermore, the quantitative analysis of CRs in C-FKM is basically determined by customers’ subjective evaluations and predefined influence values, which ignores the objective information, and may cause a subjective bias.

701

Quantitative evaluation of Kano’s model Kano’s model has been adopted by many researchers as a useful tool to quantify customer perceptions and achieve better design. Berger introduced two quantitative CS coefficients in Kano’s model, named as satisfaction index (SI) and dissatisfaction index (DI) to reflect the average impact of a CR on CS or dissatisfaction. Then, the CS coefficients have been modified and utilized as adjustment factor for re-prioritizing CRs to achieve maximum CS.12–14 Another weight adjustment method is to use Kano parameters that are assigned according to Kano categories.15–17 For instance, Chen and Chuang15 introduced an adjustment coefficient (K) and the raw weights were adjusted by multiplying with K. The value of K varies according to Kano category, and values of ‘‘4,’’ ‘‘2,’’ ‘‘1’’ and ‘‘0’’ were assigned to the attractive, one-dimensional, must-be and indifference categories, respectively. In addition, Chaudha et al.29 proposed to use the combination of CS coefficients and the respective K of Kano category as an adjust factor to re-prioritize CRs. These aforementioned approaches make it possible to quantify the information provided by the Kano’s model and integrate Kano’s model to decision support for enhancing CS. However, they ignore the imprecision and uncertainty in CRs. Moreover, the use of arbitrary K values leads to the subjectivity and arbitrariness. In fact, K values may vary in different circumstances. For instance, the priority list of Kano categories for growing-period products could be M . O . A . I, while for mature-period products, the priority list could be A . O . M . I. There is a need to develop an approach to determine suitable K values. Other approaches extend Kano’s model from qualitative descriptions to quantitative analysis to derive the importance weights of product attributes.18,19 Wang and Hsueh19 proposed to use Kano’s model to obtain the relative weight of CRs through normalizing the satisfaction range defined by SI and DI. However, this method ignores the imprecision and uncertainty in CRs. Moreover, they overlook the objective information that could be critical for the priorities of CRs. Wang18 introduced information entropy into FKM to derive the objective important weights of product attributes, and the approach is named as entropy-based fuzzy Kano’s model (E-FKM). In their study, information entropy is applied to measure the variation of discrete probability distribution among various Kano categories. However, as described in section ‘‘Kano’s model,’’ it is not adequate to use numerical data in FKQ to represent uncertain information. Moreover, they overlook the subjective assessments and multigranularity linguistic information.

The 2-tuple fuzzy-linguistic approach As a fuzzy-linguistic approach, the 2-tuple linguistic representation model is a continuous model for linguistic evaluation information representation, combining

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Proc IMechE Part B: J Engineering Manufacture 231(4)

numerical and linguistic data without information loss during the integration procedure.28,30 The 2-tuple fuzzy-linguistic representation model represents the linguistic information by a 2-tuple (si , a), where si represents the linguistic label of the predefined linguistic term set S = fs0 , . . . , sg g, and a indicates the distance to the central value of the ith linguistic term. This linguistic representation model defines a set of functions to facilitate linguistic computational processes: Definition 1. Let si 2 S be a linguistic term set. Then, the function u used to obtain the equivalent 2-tuple representation is defined as30 u : S ! S 3 ½0:5, 0:5Þ uðsi Þ = ðsi , 0Þ,

ð1Þ

si 2 S

Definition 2. Let S = fs0 , . . . , sg g be a linguistic term set, and b 2 ½0, g be a value representing the result of a symbolic aggregation operation. Then, the generalized translation function D used to translate b into a 2-tuple linguistic variable can be defined as30 D : ½0, g ! S 3 ½0:5, 0:5Þ si , i = Round(b) D(b) = ðsi , aÞ = a = b i, a 2 ½0:5, 0:5Þ

ð2Þ

Definition 3. Let S = fs0 , . . . , sg g be a linguistic term set and (si , a) be a 2-tuple. The reverse function D1 used to convert a 2-tuple linguistic variable into an equivalent numerical value b(b 2 ½0, g) can be defined as30 ð3Þ

D1 ðsi , aÞ = i + a = b

Definition 4. Let x = f(s1 , a1 ), . . . , (sn , an )g be a set of 2tuples, their arithmetic mean x is defined as30 ! ! n n 1X 1X 1 D ð s i , ai Þ = D b x = D ð4Þ n i=1 n i=1 i Definition 5. Let x = fðs1 , a1 Þ, . . . , ðsn , an Þg be a set of 2-tuples and w = (w1 , . . . , wn )T be the weight Pn set of 2tuples, with wi 2 ½0, 1, i = 1, 2, . . . , n, i = 1 wi = 1. The 2-tuple linguistic weighted average xe is defined as30 ! ! n n X X 1 e D ðsi , ai Þ wi = D bi wi x = D ð5Þ i=1

i=1

TFba : Sa ! Sb TFba

! a a D1 sai , aai ðb 1Þ s i , ai = D = sbj , abj a1 ð6Þ

The proposed approach for CRs analysis The objective of this research is to develop IFKM to better prioritize CRs. IFKM follows the theoretical foundation of TKM and FKM.9 A TL-FKQ is developed in IFKM to deal with the uncertainty and diversity of customers’ assessments under multi-granularity linguistic environment. Then, a quantitative approach is proposed to analyze the data gathered through IFKM. Finally, the quantitative analysis results are integrated to determine the priority ratings of CRs.

Improved FKM

where Round( ) is the usual rounding operation, si has the closest index label to b and a is the value of the symbolic translation.

D1 : S 3 ½0:5, 0:5Þ ! ½0, g

Definition 6. Let Sa = fsa0 , . . . , saa1 g and Sb = fsb0 , . . . , sbb1 g be two linguistic term sets. The linguistic transformation function TF is defined as31

In most actual situations, many respondents are involved in the Kano’s questionnaire. Because of the different background and discrimination ability, they may prefer to express their linguistic preferences using different linguistic term sets. Therefore, this study proposes a TL-FKQ based on 2-tuple linguistic representation model under multi-granularity linguistic environment. Unlike the original FKQ and MFKQ, a respondent can freely express self-feelings using a 2tuple (si , ai ) with different linguistic term sets on each question in TL-FKQ. Suppose that in a product design, V respondents denoted by Ck (k = 1, 2, . . . , V) and N CRs denoted by CRi (i = 1, 2, . . . , N) are considered in TL-FKQ. STk = fsT0 k , . . . , sT(Tkk 1) g is a linguistic term set used by respondent Ck , and S5 = fDL, LW, NT, MB, LKg is the basic linguistic term set (BLTS), where s50 = DL = dislike, s51 = LW = live with, s52 = NT = neutral, s53 = MB = must be, s54 = LK = like. Notice that the linguistic terms of BLTS are the five standard answers in the TKQ. Let (sTu k , aTu k )F, i and (sTv k , aTv k )D, i be the 2-tuples provided by Ck to express his or her feeling on CRi ’s functional and dysfunctional questions, respectively. Based on above assumptions or notations, the procedure of IFKM can be described as follows. Step 1. The multi-granular linguistic information (sTu k , aTu k )F, i and (sTv k , aTv k )D, i provided by Ck are unified into the BLTS using a transformation function TF (equation (6)) as follows

He et al.

TF5Tk

703

sTu k , aTu k F, i

0 = D@

D1

sTu k , aTu k

F, i

4

Tk 1

1 A

k = s5p , a5p

ð7Þ

F, i

TF5Tk

sTv k , aTv k

D, i

0 = D@

D1

sTv k , aTv k

D, i

Tk 1

k = s5q , a5q

4

where (x, y) cell belongs to the hth Kano category in the evaluation sheet (Table 1), and h = 1, 2, . . . , H represents the Kano categories (A, O, M, I, R, Q). For convenience, attribute level for CRi evaluated by Ck can be described as a vector PDki = (PDki1 , . . . , PDkiH )

1 A ð8Þ

D, i

where (s5p , a5p )kF, i and (s5p , a5p )kD, i represent Ck ’s feelings on CRi ’s functional and dysfunctional questions with BLTS. Step 2. Calculate the membership degrees of Ck ’s preference to the standard answers of Kano’s questionnaire. The membership degree ms5x ((s5p , a5p )kF, i )) of Ck ’s preference on CRi to the xth standard answer to the functional question can be obtained as follows 8 5 > > 1 ap x = p > > < 5 k a5p 50, x = p + 1 a ms5x s5p , a5p = p 5 > F, i > a5p \ 0, x = p 1 a > > : p 0 otherwise ð9Þ where ms5x ( ) is the membership function for linguistic label, s5x 2 S5 . The membership degree ms5y ((s5q , a5q )kD, i ) of Ck ’s preference on CRi to the yth standard answer of the dysfunctional question can be obtained as 8 5 > 1 aq y = q > > < 5 k > a5q 50, y = q + 1 a ms5y s5q , a5q = q > D, i > a5q \ 0, y = q 1 a5 > > : q 0 otherwise ð10Þ Step 3. Calculate the possibility degrees among Kano categories of Ck ’s preference on CRi . Let and Funki = fms5x ((s5p , a5p )kF, i ), x = 0, 1, . . . , 4g Dyski = fms5y ((s5q , a5q )kD, i ), of

ms5x ((s5p , a5p )kF, i )

y = 0, 1, . . . , 4g be the sets

and ms5y ((s5q , a5q )kD, i ). Using matrix

algebra, a 5 3 5 fuzzy relation matrix MDki is obtained via (Funki )T 3 (Dyski ). The membership degree (MDkixy ) of Ck ’s preference to (x, y) cell is determined by the following formula k k MDkixy = ms5x s5p , a5p 3 ms5y s5q , a5q ð11Þ F, i

D, i

The possibility degree PDkih to the hth Kano category for CRi evaluated by Ck can be obtained as follows X PDkih = MDkixy ð12Þ

Step 4. Calculate the probability distribution among Kano categories of CRi . Once the possibility degree of CRi is gathered from all respondents, its mean value PDih is aggregated as V P

PDih =

k=1

PDkih

V

ð13Þ

For convenience, the percentages among various Kano categories of CRi can be described as an vector, PDi = (PDi1 , PDi2 , . . . , PDiH ), the Kano category estimations of CRs can be denoted as a matrix PD = (PDij )N 3 H

ð14Þ

Quantitative analysis of IFKM The importance weight of CR is a critical step for customer-oriented product development to achieve higher CS, and systematic quantitative analysis of Kano’s model should be committed to properly acquire the final importance weights of CRs in order to keep related product improvement successful. Different CRs may not be of the same importance to a particular respondent, and a certain CR may not be of the same importance to different respondents.11 Thus, it is necessary to analyze the subjective importance weights to prioritize CRs. However, the subjective importance weights of CRs are solely determined according to the preference or judgments of decision makers and may cause a subjective bias. The objective importance weights should be utilized in CRs analysis to balance the influence of subjective factors. In addition, CRs in different kinds of the Kano’s categories affect CS in a different way. Thus, the important weights for achieving the desired CS of CRs are different and are effected by the Kano’s categories for CRs. To achieve the total CS in an economic way, the importance rating for achieving the desired CS of a CR, defined as Kano importance weights, should be taken into account. To make accurate and deep understanding of CRs, this section conducts comprehensive quantitative analysis of IFKM, including subjective importance weights

704


analysis, objective importance weights analysis and Kano importance weights analysis. Then, the quantitative results are integrated to determine the final importance weights of CRs. Determining the subjective importance weights of CRs. This article adopts a self-stated importance questionnaire in parallel with the TL-FKQ to determine the subjective importance weights of CRs. Respondents are asked to estimate the raw importance of each CR on a particular linguistic term set S = (s0 , s1 , . . . , sT1 ). The linguistic terms provided by respondents are transformed into 2tuples with the following equation sub ð15Þ uðst Þ = ðst , 0Þ = wsub t , atw The relative frequency fit of linguistic term st on CRi is obtained using fit =

nit T1 P

ð16Þ

nit

t=0

where nit is the number of responses presented as st on CRi . The 2-tuple weighted average of subjective importance weights on CRi can be calculated as sub sub sub w , aw i = xew wsub t , atw i , fit ! T1 X ð17Þ sub sub 1 D wt , atw i fit =D t=0

The normalized subjective importance weight of CRi can be obtained as D1 wsub , asub w sub i nwi = N ð18Þ P 1 sub sub D w , aw i i=1

For convenience, the vector of the normalized subjective importance weights of CRs can be described as sub sub ð19Þ NWsub = nwsub 1 , nw2 , . . . , nwN

difference is bigger among all percentage values of all Kano categories under CRi , it means that CRi plays an important role on the evaluation, and a higher importance weight should be assigned to CRi . The maximizing deviation method proposed by Wang34 is used to determine the attribute weights. The deviation method is selected here to compute the difference of percentage values of Kano categories. For CRi , let Dij (Wob ) be the deviation value of the jth Kano category to all the other Kano categories. It can be defined as H X PDij PDik wob , Dij Wob = i k=1

i = 1, 2, . . . , N,

j = 1, 2, . . . , H

where wob represents the objective importance weight i of CRi . For convenience, the objective importance weights of CRs can be expressed as Wob = ob ob (wob 1 , . . . , wi , . . . , wN ). ob Let Di (W ) be the deviation value of all Kano categories to all the other Kano categories for CRi . It can be defined as H H X H X X PDij PDik wob , Di Wob = Dij Wob = i j=1

i = 1, 2, . . . , N,

j=1 k=1

j = 1, 2, . . . , H

ð21Þ

Based on above analysis, the reasonable weight vector Wob has to be chosen to maximize the total deviation of all Kano categories for all the CRs. Suppose the weight vector Wob satisfies the unitization constraint N X

wob i

2

ð22Þ

=1

i=1

Therefore, the maximizing deviation model is constructed as follows N X MaxD Wob = Di Wob i=1 N X H X H X PDij PDik wob = i

Determining the objective importance weights of CRs. The objective weights are determined by solving the mathematical models based on objective methods, including entropy method, standard deviation method, maximizing deviation method and so on.32,33 Entropy method is applied to attributes’ discrete percentages among Kano categories for deriving the objective importance weights of product attributes by Wang.18 It assumes that when an attribute possesses small variation (i.e. balanced distribution) among Kano categories, it has lower importance weight, and vice versa. For the Kano categories evaluation results represented in equation (14), if the difference is smaller among all percentage values of all Kano categories under CRi , it means that CRi has less impact on the evaluation, and a lower importance weight should be assigned to CRi . On the contrary, if the

ð20Þ

i=1 j=1 k=1

s:t:

8 > < > :

N P i=1

wob i 50,

wob i

2

ð23Þ

=1

i = 1, 2, . . . , N

Equation (23) is a non-linear programming model. According to the proof provided by Li et al.,35 the optimal solution wob i can be obtained with the following equation H P H P

wob i

jPDij PDik j

j=1 k=1

= vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !ffi2 , u N H P H uP P t jPDij PDik j i=1

i = 1, 2, . . . , N

j=1 k=1

ð24Þ

He et al.

705

Table 2. Membership function of linguistic scale. Linguistic term set T7

Fuzzy number

Linguistic term set T5

Fuzzy number

t70 = VL7 : very less important t71 = FL7 : fairly less important t72 = L7 : less important t73 = E7 : equally important t74 = MI7 : more important t75 = FM7 : fairly more important t76 = VM7 : very more important

(0, 0, 1) (0, 1, 3) (1, 3, 5) (3, 5, 7) (5, 7, 9) (7, 9, 10) (9, 10, 10)

t50 = VL5 : very less important t51 = L5 : less important t52 = E5 : equally important t53 = MI5 : more important t54 = VM5 : very more important

(0, 0, 2.5) (0, 2.5, 5) (2.5, 5, 7.5) (5, 7.5, 10) (7.5, 10, 10)

Then, wob i can be normalized as nwob i =

wob i N P i=1

,

ð25Þ

i = 1, 2, . . . , N

wob i

For convenience, the vector of the normalized objective importance weights of CRs can be described as ob ob NWob = nwob 1 , nw2 , . . . , nwN

ð26Þ

Determining the Kano importance weights of CRs. A Kano’s questionnaire helps categorize CRs related to consumer satisfaction into different types of qualities and indicates how much attention should be paid to each CR to achieve the desired CS.15 In this section, Kano importance weight based on the Kano classification is used to re-prioritize the CRs for enhancing CS. Let KC = fKC1 , . . . , KCH g be the set of Kano categories (A, O, M, I, R, Q), KW = fKW1 , . . . , KWH g be the weight vector for KC. As described in section ‘‘Quantitative evaluation of Kano’s model,’’ the importance weights of Kano categories may vary in different circumstances. In this article, KW values are achieved using the fuzzy pairwise comparison method. Assume that U decision makers DMk (k = 1, 2, . . . , U) to evaluate the importance weights of Kano categories. DMk assesses the relative importance of any two elements (KCi , KCj ) (i, j = 1, 2, . . . , H) with a linguistic variable parameterized by triangular fuzzy number a~kij = (akijl , akijm , akiju ), where akijl , akijm , and akiju are described by the measures between 0 and 10, corresponding to lower bound, the modal value and the upper bound, respectively. The relative importance fuzzy membership functions of linguistic term set T7 given in Table 2 are used in the proposed model. Assume the DMk give his or hers judgments on the KC with a triangular fuzzy comparison matrix which can be represented by 2 6 6 A~k = 6 4

(1, 1, 1) (ak21l , ak21m , ak21u ) .. .

(ak12l , ak12m , ak12u ) (1, 1, 1) .. .

(akH1l , akH1m , akr1u ) (akH2l , akH2m , akH2u )

where (akjil , akjim , akjiu ) = (1=akijl , 1=akijm , 1=akiju ) for i 6¼ j, and (akjil , akjim , akjiu ) = (1, 1, 1) for i = j. Then the normalized triangular fuzzy weight g= vector of KC, which is expressed as KW g g g ( KW 1 , KW 2 , . . . , KW H ) = ((KW1l , KW1m , KW1u ), (KW2l , KW2m , KW2u ), . . . , (KWHl , KWHm , KWHu )), can be obtained based on the collection of triangular fuzzy comparison matrixes. To determine the fuzzy weight vector, the fuzzy logarithmic least squares method (FLLSM) developed by Wang et al.36 can be employed to solve the triangular fuzzy comparison matrixes. The optimization model of the FLLSM can be described as follows Minf =

H H U X X X i = 1 j = 1, j6¼i k = 1

2 lnKWil lnKWju ln akijl 2 + lnKWim lnKWjm ln akijm 2 + lnKWiu lnKWjl ln akiju Þ 8 H P > > > KWil + KWju 51 > > > j = 1, j6¼i > > > > H > P > > KWjl 41 > KWiu + > > j = 1, j6¼i < s:t: H P > > KWim = 1 > > > i=1 > > > H > P > > > (KWiu + KWil ) = 2 > > > i=1 > : 0 \ KWil 4KWim 4KWiu

The detailed formulation process and meanings of the objective and associated constraints for the optimization model of FLLSM are not discussed here and can be referred in reference of Wang et al.36 Equation (28) is a constrained non-linear optimization model,

3 . . . (ak1Hl , ak1Hm , ak1Hu ) . . . (ak2Hl , ak2Hm , ak2Hm ) 7 7 7 .. .. 5 . . ...

ð28Þ

(1, 1, 1)

ð27Þ

706


whose constraints are all linear and can be solved without difficulty by Microsoft Excel Solver or professional optimization software packages such as LINGO or MATLAB.36 The optimum solution to the above model directly forms normalized fuzzy triangular g i = (KWil , KWim , KWiu ). The normalized weight KW fuzzy triangular weight can be defuzzificated by equation (29) to obtain the crisp important weight KWi =

KWil + 2KWim + KWiu 4

ð29Þ

wi =

Kano nwsub 3 nwob i i 3 nwi , N P sub ob Kano nwi 3 nwi 3 nwi

i = 1, 2, . . . , N

i=1

ð33Þ ob Kano Of course, a weighted sum of nwsub i , nwi and nwi can also produce a reasonable wi , if preferred. For convenience, the final importance weights of CRs can be denoted as a vector

W = ðw1 , w2 , . . . , wN Þ

ð34Þ

(wKano ) i

Then, Kano importance weights of CRi can be determined by a mathematical aggregation of the importance weights of Kano categories weighted by the corresponding membership degrees wKano = PDi 3 KWT = i

H X

PDij 3 KWj ,

ð30Þ

j=1

i = 1, 2, . . . , N

The normalized Kano importance weight (nwKano ) of i CRi can be obtained as nwKano = i

wKano i N P wKano i

ð31Þ

i=1

For convenience, the normalized Kano importance ratings of CRs can be described as a vector NWKano = (nwKano , nwKano , . . . , nwKano ) 1 2 N

Case study To demonstrate the applicability performance of the proposed methodology, a case study of CRs analysis in combine harvester development is described in this section. W company is a manufacturer that designs combine harvester. According to the attributes which W company currently provides, this case study focuses on nine major CRs which are identified to represent the biggest concerns of the customers. They are ‘‘good operating flexibility’’ (CR1 ), ‘‘high threshing efficiency’’ (CR2 ), ‘‘beautiful appearance’’ (CR3 ), ‘‘high security’’ (CR4 ), ‘‘accurate vehicle guidance system’’ (CR5 ), ‘‘little energy consumption’’(CR6 ), ‘‘good driving comfort’’ (CR7 ), ‘‘easy maintenance’’ (CR8 ) and ‘‘low price’’ (CR9 ). The steps of the case to be taken are described in the following.

ð32Þ

Step 1: Kano survey Determining the final importance weights of CRs The subjective importance weight represents the respondents’ preference or judgments, the objective importance weight can effectively balance the influence of subjective factors, while Kano importance weight represents the impact on desired CS. CR with larger subjective importance weight, larger objective importance weight and larger Kano importance weight should receive higher attention. Therefore, CRi ’s final importance weight is determined jointly by its subjective importance weight, objective importance weigh and Kano importance weight as

TL-FKQs were designed and distributed to various customers and engineers. In this research, 160 effective samples were collected. Each respondent was required to use 2-tuples to answer the functional and dysfunctional questions with respect to each CR in the TLFKQ. In addition to BLTS S5 , linguistic term sets S3 and S7 (Table 3) were used for the functional and dysfunctional questions. Figure 2 shows part of the TLFKQ. Take respondent 1 (C1 ) as an example, the answer with respect to CR2 ’s functional question (‘‘If the combine harvester has high threshing efficiency, how do you feel?’’) was (s74 , 0.2), the answer with respect to CR2 ’s dysfunctional question (‘‘If the combine

Table 3. Linguistic labels for TL-FKQ. Linguistic term set S7

Linguistic term set S5

Linguistic term set S3

s70 = DL7 : dislike s71 = MDL7 : medium dislike s72 = LW: live with s73 = N: neutral s74 = MB: must-be s75 = MLK: medium like s76 = LK: like

s50 = DL: dislike s51 = LW: live with s52 = N: neutral s53 = MB: must-be s54 = LK: like

s30 = DL3 : dislike s31 = N3 : neutral s32 = LK3 : like

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Figure 2. A part of the TL-FKQ used in the survey on combine harvester.

Table 4. Experimental results through IFKM.

CR1 CR2 CR3 CR4 CR5 CR6 CR7 CR8 CR9

A (%)

O (%)

M (%)

I (%)

R (%)

Q (%)

18 22 10 7 49 20 59 23 8

13 18 56 13 12 36 12 51 70

62 50 29 76 23 25 13 16 18

7 10 5 3 13 13 15 10 4

0 0 0 1 3 6 1 0 0

0 0 0 0 0 0 0 0 0

A: attractive; O: one-dimensional; M: must-be; I: indifferent; R: reverse; Q: questionable.

harvester does not have high threshing efficiency, how do you feel?’’) was (s71 ,20.1). Equations (7–10) are then used to obtain and analyze Kano categories for CR2 evaluated by C1 . Fun12 = ð0, 0, 0:8, 0:2, 0Þ Dys12 = ð0:4, 0:6, 0, 0, 0Þ

Using (Fun12 )T 3 (Dys12 ), a 5 3 5 fuzzy relation matrix MD12 is obtained for the Kano two-dimensional attribute classification 2

0 0 0 6 0 0 0 6 MD12 = 6 0:32(M) 0:48(I) 0 6 4 0:08(M) 0:12(I) 0 0 0 0

0 0 0 0 0

3 0 07 7 07 7 05 0

The two-dimensional attribute classification with respect to CR2 evaluated by C1 is obtained based on Kano evaluation table (Table 1)

PD12

0 , = A 0 , = A

0 0:32 + 0:08 0:48 + 0:12 0 0 , , , , O M I R Q 0 0:4 0:6 0 0 , , , , O M I R Q

Once all respondents have completed their surveys on CRs, the results are aggregated and displayed in Table 4. For instance, CR2 is concluded as 22% ‘‘attractive,’’ 26% ‘‘one-dimensional,’’ 32% ‘‘must-be’’ and 20% ‘‘indifferent,’’ and similar explanations could be applied to the other CRs.

Step 2: Determining the subjective importance weights of CRs In parallel with TL-FKQ, customers were asked to assess the raw importance of each CR with linguistic term set T5 (Table 2), as shown in Figure 2. Table 5 shows the relative frequencies of these linguistic terms for nine CRs. According to equation (17), a 2-tuple weighted average is calculated to infer the subjective

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Table 5. Data on subjective importance weights of CRs. CRs

Relative frequencies VL

CR1 CR2 CR3 CR4 CR5 CR6 CR7 CR8 CR9

5

0 0 0.03 0 0.01 0.02 0.01 0.01 0.01

L

5

0 0.01 0.15 0.01 0 0.11 0.09 0.11 0.08

5

5

5

E

MI

VM

0.05 0.05 0.41 0.09 0.14 0.39 0.42 0.12 0.24

0.09 0.14 0.27 0.31 0.51 0.37 0.32 0.31 0.47

0.86 0.80 0.14 0.59 0.34 0.11 0.16 0.45 0.20

Average subjective important weights (2-tuple)

Normalized subjective importance weights

(VM5 , 0:19) (VM5 , 0:27) (E5 , 0:34) (MI5 , 0:48) (MI5 , 0:13) (E5 , 0:44) (MI5 , 0:47) (MI5 , 0:08) (MI5 , 0:23)

0.140 0.137 0.086 0.127 0.115 0.089 0.093 0.113 0.101

CR: customer requirement; VL: very less important; FL: fairly less important; L: less important; E: equally important; MI: more important.

importance of each CR. Using equation (18), the vector of the normalized subjective importance weights for nine CRs is obtained as NWsub = sub sub sub sub sub sub sub sub nw1 , nwsub 2 , nw3 , nw4 , nw5 , nw6 , nw7 , nw8 , nw9 = ð0:14, 0:137, 0:086, 0:127, 0:115, 0:089, 0:093, 0:113, 0:101Þ

Step 3: Determining the objective importance weight of CRs 2

ð1, 1, 1Þ 6 1 1 1 6 , , 6 7 5 3 6 6 1 1 1 6 , , A~1 = 6 6 9 7 5 6 1 1 1 6 6 10 , 9 , 7 6 4 1 1 1 , , 10 10 9

ð3, 5, 7Þ

ð5, 7, 9Þ

ð7, 9, 10Þ

ð1, 1, 1Þ 1 1 1 , , 9 7 5 1 1 1 , , 10 9 7 1 1 1 , , 10 10 9

ð5, 7, 9Þ

ð7, 9, 10Þ

ð1, 1, 1Þ 1 1 1 , , 9 7 5 1 1 1 , , 10 10 9

(5, 7, 9)

Subsequently, based on the percentages among discrete Kano categories in Table 4, the objective importance weights of CRs are derived using maximizing deviation method (MDA). Using equations (23) and (24), the vector of the normalized objective importance weights of these nine CRs is obtained as ob ob ob ob ob ob ob ob NWob = nwob 1 , nw2 , nw3 , nw4 , nw5 , nw6 , nw7 , nw8 , nw9 = (0:119, 0:104, 0:120, 0:1350:098, 0:078, 0:109, 0:106, 0:131)

Step 4: Determining Kano importance weights of CRs

categories. The ‘‘Questionable’’ category is not considered in determining the importance weight of the CRs since it can be revised by changing the Kano’s questionnaire. The product development strategy is the main factor considered in this evaluation. There are eight DMs (product designers and development experts) that were invited to evaluate the relative importance of five Kano categories (A, O, M, I, R) with linguistic term set T7 (as shown in Table 2). The fuzzy pairwise comparison matrix A~1 provided by DM1 is obtained as

ð1, 1, 1Þ 1 1 1 , , 9 7 5

ð9, 10, 10Þ

3

7 ð9, 10, 10Þ 7 7 7 7 ð9, 10, 10Þ 7 7: 7 7 ð5, 7, 9Þ 7 7 7 5 ð1, 1, 1Þ

Once eight DMs have completed their linguistic evaluations on KCs, the five fuzzy weights are achieved using equation (28). According to equation (29), these fuzzy weights are converted into crisp measures, and importance weights of KCs are obtained as KW = ðKW1 , KW2 , KW3 , KW4 , KW5 Þ = (0:48, 0:30, 0:19, 0:03, 0)

Then, according to the percentages among discrete Kano categories (Table 4) and the importance weights of KCs, the vector of the normalized Kano importance weights of CRs can be obtained using equations (31) and (32) as

In this step, the fuzzy pairwise comparison approach is used to achieve the important weights of the Kano NWKano = nwKano , nwKano , nwKano , nwKano , nwKano , nwKano , nwKano , nwKano , nwKano 1 2 3 4 5 6 7 8 9 = ð0:098, 0:103, 0:109, 0:087, 0:128, 0:102, 0:140, 0:119, 0:114Þ

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Figure 3. Results of the quantitative analysis.

Step 5: Determining the final importance ratings of CRs The final importance rating of each CR is decided by its subjective importance weight, objective importance weight and Kano importance weight. Using equation (33), the vector of the final importance weights of CRs is determined as W = ðw1 , w2 , w3 , w4 , w5 , w6 , w7 , w8 , w9 Þ = (0:134, 0:120, 0:092, 0:122, 0:118, 0:058, 0:115, 0:117, 0:123)

As show in Figure 3, CR with larger subjective importance weight, larger objective importance weight and larger Kano importance weight gets larger final importance weights and should receive higher attention. Specially, the top four priorities present an order of CR1 . CR9 . CR4 . CR5 and this indicates that W company should pay higher attention to get ‘‘good operating flexibility,’’ ‘‘low price,’’ ‘‘high security’’ and ‘‘accurate vehicle guidance system.’’

Discussion To validate the effectiveness of the IFKM method, three typical Kano’s model of the published researches are selected to conduct a comparative study. They are TKM,21 E-FKM18 and C-FKM.11 Details of the three published models are not discussed here and can be referred in the literature.11,18,21 In section ‘‘Literature review,’’ TKM is mentioned as a qualitative method without fuzzy information; C-FKM and E-FKM are mentioned to incorporate fuzzy set theory and

quantitative evaluation into Kano’s model simultaneously for CR analysis. To signify the difference of TKM, E-FKM, C-FKM and IFKM, further comparisons of these four approaches on Kano questionnaires and analysis results are provided. First, the comparison of TKQ used in TKM, FKQ used in E-FKM, MFKQ proposed in C-FKM and TLFKQ developed in this study is conducted. In TKQ, respondents are forced to choose one answer from the survey. In FKQ, respondents express their feelings about each question by assigning a percentage to each answer. In MFKQ, the five standard answers (dislike, live with, neutral, expect and enjoy) in Kano’s questionnaire are presented on ‘‘1 to 5’’ scale, and respondents express their feelings by choosing a numerical value ranged in [1, 5]. The answers of five respondents to the issue of ‘‘If the combine harvester has or does not have high threshing efficiency, how do you feel?’’ are listed in Table 6. In comparison of Table 6, it is found that the binary logic questionnaire of TKQ only considers crisp descriptions and cannot handle uncertainty of human thinking. FKQ and MFKQ use numerical data to represent the uncertainty and ambiguity in Kano’s questionnaire. However, the use of numerical-based modeling to represent uncertain information is not always adequate, and it is more suitable for respondents to provide their preferences by means of linguistic variables under multi-granularity linguistic environment.20 As a fuzzy-linguistic approach, the 2tuple representation model used in TL-FKQ assists respondents to express their feelings using different linguistic term sets, which can improve the accuracy and understanding of the results.

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Table 6. Answers for TFQ, FKQ, MFKQ and TL-FKQ. If the combine harvester has or does not have high threshing efficiency, how do you feel?

TKQ

LK Respondent 1 Respondent 2 Respondent 3 Respondent 4 Respondent 5

Functional Dysfunctional Functional Dysfunctional Functional Dysfunctional Functional Dysfunctional Functional Dysfunctional

FKQ

MB

N

O

LW

O

O

O

O

O

O O

DL

O O

LK (%)

MB (%)

N (%)

20

50

30

30

70

45

55

80

20

50

50 40

LW (%)

DL (%)

50

50

80

20

40

60

30

70

30

30

MFKQ

TL-FKQ

4.3 1.7 5.0 1.0 3.7 1.5 4.0 2.0 4.6 2.6

(s74 , 0.2) (s71 , 20.1) (s32 , 20.3) (s31 , 20.4) (s75 , 20.2) (s70 , 0.2) (s54 ,20.4) (s51 , 20.3) (s32 , 0) (s31 , 20.1)

TKQ: traditional Kano’s questionnaire; FKQ: fuzzy Kano’s questionnaire; MFKQ: modified fuzzy Kano’s questionnaire; TL-FKQ: 2-tuple linguistic fuzzy Kano’s questionnaire; LK: like; MB: must-be; N: neutral; LW: live with; DL: dislike.

Then, comparison of CR analysis based on the corresponding Kano’s models is conducted and the results are shown in Table 7. In TKM, CRs are classified into different Kano categories according to the Kano evaluation table in Table 1. Designers rank CRs based on the Kano categories in the following order: must-be . one-dimensional . attractive . indifferent.21 However, such approaches cannot distinguish CRs within the same category. Hence, the qualitative analysis of TKM is deemed to be inadequate to facilitate decisions in product design. Compared with the TKM, EFKM, C-FKM and IFKM can help designers prioritize CRs based on the quantitative analysis. As can be seen from Table 7, the three models lead to different Kano evaluation results and ranking orders. One reason for this is because they tackle uncertain information of Kano’s questionnaire in different manners, which has been discussed above. Another reason lies in the different quantitative analysis methods adopted by these models. E-FKM derives the objective important weights of CRs using information entropy, which cannot consider the subjective judgment and the impact of each CR on desired CS. C-FKM prioritizes CRs using an evaluation index, which is determined by the subjective importance weights and the influence values considering the contribution of CS based on Kano evaluation results. However, this approach ignores to compensate the subjective factors with objective information. While IFKM determines the priority ratings of CRs by integration of the subjective judgment with self-stated importance questionnaire, the objective importance weights are acquired using MDA and the importance ratings of achieving the desired CS obtained with fuzzy pairwise comparison and FLLSM. Thus, the IFKM allows quantitative analysis of CRs in a thorough and comprehensive manner and prioritizes CRs more accurately than TKM, E-FKM and C-FKM.

Overall, the IFKM can improve the Kano’s model by developing a TL-FKQ to deal with the uncertainty under multi-granularity linguistic environment and presenting a systematic and comprehensive approach to make quantitative analysis of CRs to rate the final importance of CRs.

Conclusion Determining the final importance weights of CRs is a fundamental problem in product development. In this article, a systematic and operational approach is proposed to get a better understanding of CRs through quantitative analysis of IFKM. The IFKM develops a TL-FKQ to deal with the imprecision and uncertainty in CRs effectively based on 2-tuple linguistic representation model under multi-granularity linguistic environment. With TL-FKQ, linguistic assessment information is managed as a continuous range, without information loss during the integration procedure. Meanwhile, the IFKM-based quantitative analysis method is proposed to determine the final importance weights of CRs. The proposed methodology is a comprehensive weighting mechanism with the integration of subjective judgments, objective information and the importance weights of achieving desired CS of CRs. It provides a way for Kano’s model to be integrated with other mathematical models or tools for exploiting data gathered through IFKM in a systematic and comprehensive way. To fully illustrate the proposed approach, a case study of combine harvester development is provided. With the proposed method, decision makers can understand CRs in a more accurate way and make more subtle decisions. Finally, the future research potentials of the proposed approach are pointed out: in addition to the Kano survey results, more factors that affect the priorities of CRs may be considered; more accurate methods

Cat.: category; Ent.: entropy; Pri.: priorities; OIW: objective importance weight; EI: evaluation index; SIW: subjective importance weight; KIW: Kano importance weight; FIW: final importance weight; CRs: customer requirement; TKM: traditional Kano’s model; C-FKM: continuous fuzzy Kano’s model; IFKM: improved fuzzy Kano’s model; A: attractive; O: one-dimensional; M: must-be; I: indifferent; R: reverse; Q: questionable.

0.134 0.120 0.092 0.122 0.118 0.058 0.115 0.117 0.123 0.098 0.103 0.110 0.087 0.127 0.102 0.138 0.120 0.115 0.119 0.104 0.120 0.135 0.098 0.078 0.109 0.106 0.131 2 4 9 3 5 8 7 6 1 CR1 CR2 CR3 CR4 CR5 CR6 CR7 CR8 CR9

33 12 27 52 54 21 61 52 33

41 81 49 70 13 52 29 59 67

75 59 61 21 77 63 34 31 24

11 6 23 17 16 24 36 17 36

0 2 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0

M O M O M M A O O

10 12 10 18 8 18 52 40 20

30 64 52 54 28 28 23 36 23

58 21 38 25 64 50 20 12 49

2 3 0 3 0 4 5 10 8

0 0 0 0 0 0 0 2 0

0 0 0 0 0 0 0 0 0

0.711 0.790 0.854 0.789 0.768 0.921 0.910 0.806 0.874

0.183 0.133 0.093 0.134 0.147 0.050 0.057 0.123 0.080

1 4 6 3 2 9 8 5 7

0.154 0.119 0.050 0.124 0.110 0.075 0.099 0.104 0.165

0.14 0.137 0.086 0.127 0.115 0.089 0.093 0.113 0.101

FIW KIW OIW SIW Pri. A O

M

I

R

Q

Cat. A

O

M

I

R

Q

Ent.

OIW

Pri.

EI

IFKM C-FKM E-FKM TKM CRs

Table 7. CRs analysis results of TFM, E-FKM, C-FKM and IFKM.

1 4 8 3 5 9 7 6 2

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