Construction of house of quality for new product planning: A 2-tuple fuzzy linguistic approach

Computers in Industry 73 (2015) 117–127

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Construction of house of quality for new product planning: A 2-tuple fuzzy linguistic approach Wen-Chang Ko [1_TD$IF]* [1_TD$IF]Department of Information Management, Kun Shan University, No. 195, Kunda Rd., Yongkang Dist., Tainan City 710, Taiwan, ROC

A R T I C L E I N F O

A B S T R A C T

Article history: Received 23 January 2015 Received in revised form 6 July 2015 Accepted 14 July 2015 Available online 5 September 2015

A house of quality (HOQ) diagram is used to analyze the critical factors involved in the quality function deployment (QFD) processes for the new product planning (NPP). The principal tasks of the QFD acting process comprise describing and scoring customer requirements (CRs); determining design requirements (DRs), the relationship between CRs and DRs, the correlations among CRs, and the correlations among DRs. Finally, the DRs can be scored by these assessments in NPP. This study proposes various methods of scoring the requirements of current and potential customers to reflect the knowledge and preference differences among different customers regarding CRs. The CR scores provided by different customers can be assessed by using linguistic, numerical, and interval values, or can be assessed using linguistic label sets with different granularity. A 2-tuple fuzzy linguistic computational approach is adopted to aggregate the CR importance scores obtained from customers by using various methods. In addition, to accurately rate the DRs, a modified relationship between CRs and DRs is proposed. The proposed HOQ construction model is practical because it prevents the loss of information during the QFD process for NPP. An example is used to demonstrate the applicability of the proposed model. ß 2015 Elsevier B.V. All rights reserved.

Keywords: House of quality (HOQ) 2-Tuple fuzzy linguistic modeling New product planning (NPP) Quality function deployment (QFD) Group decision-making (GDM)

1. Introduction Quality function deployment (QFD) is a customer-oriented analytical tool that is widely used in new product development (NPD) and product improvement. QFD provides a systematic approach for translating customer requirements (CRs) into design requirements (DRs) to meet customers’ expectations by bridging the perception gap between customers and a QFD team, distinguishing the company from its competitors in dynamic and global markets. Since QFD was introduced in the mid-1960s, researchers and companies in several industries and professional fields have successfully used QFD to improve the quality of new product planning (NPP), design, and development, as well as the communication relating to groups, teamwork, and customer satisfaction [1–6]. In the NPP process, a house of quality (HOQ) diagram (Fig. 1) is used to describe the value of the factors involved in QFD processes, including customer requirements (CRs), design requirements (DRs), relationships between CRs and DRs, and correlations among the DRs [7,8]. Fig. 1 shows the structure of a HOQ. A QFD team consists of experts and designers who identify

* [4_TD$IF]Tel.: +886 939 487 012; fax: +886 6 205 0587. E-mail address: [email protected] http://dx.doi.org/10.1016/j.compind.2015.07.008 0166-3615/ß 2015 Elsevier B.V. All rights reserved.

and manage a set of requirements expressed by various customers score CRs according to their value in the NPP based on various customer assessments, and develop numerous DRs that affect the CRs. Furthermore, a QFD team evaluates the relationships between CRs and DRs and the correlations among the DRs, as well as scores the DRs. Scoring the CRs is a critical task, especially when the process is implemented with numerous customers during the early stage of the QFD processes. The scores of the CRs are determined using various approaches. Carnevalli and Miguel [4] indicated that, in most of the literature, the CRs are scored by using brainstorming and effect–cause–effect diagrams in focus groups sessions, the Kano model, and fuzzy logic. For example, researchers have employed the Kano model [9,10], fuzzy numbers [11,12], and fuzzy logic inference [13] to classify, determine, and derive the scores of the CRs. Because some researchers have viewed scoring the CRs as a form of multi-criteria decision making, they employed the analytic hierarchy process (AHP) [14], the fuzzy AHP [15], and the fuzzy analytic network process (FANP) [16,17] to score the CRs during QFD processes. However, these studies ignored the practical scenario of group decision-making (GDM) in evaluating the CRs. The numerous studies have adopted the GDM approach to score the CRs in QFD processes. Kwong et al. [11] used linguistic terms employing fuzzy numbers to classify customer needs. Karsak [18]

[(Fig._1)TD$IG]

W.-C. Ko / Computers in Industry 73 (2015) 117–127

118

Correlations among DRs

Importance score of CRs

Customer Requirements CRs

Design Requirements DRs

Rij Relationships between CRs and DRs

Importance rating of DRs Fig. 1. The house of quality (HOQ).

and Chen and Ko [19,20] employed Kaufmann and Gupta’s idea [21] and adopted the fuzzy Delphi method gathering the opinions of current and potential customers to score the CRs based on Bojadziev and Bojadziev’s [22] consensus measure. Ho et al. [23] proposed an integrated group decision-making system to score the CRs. However, these studies only adopted a unique format to represent the assessments of the CRs. In practice, the unique representation format might not satisfy the GDM process. Chen et al. [24] proposed using a systematic procedure to score the CRs by using a GDM approach and developed a modified fuzzy clustering approach to identify a consensus among the various perspectives of different experts in a fuzzy environment. Ertay et al. [25] employed a fuzzy weighted average as a fuzzy group decision-making approach to combine multiple preference score to determine the weights of the CRs. Bu¨yu¨ko¨zkan and Feyziog˘lu [26] and Bu¨yu¨ko¨zkan et al. [27] proposed a uniform group decision-making approach to aggregate the various evaluation methods that different decision makers used to score the CRs by applying fuzzy sets to collaborative circumstances. However, only current customers were considered in these studies, and the potential customers’ opinions in the CR evaluation process were ignored. Unlike the existing approaches, multiple forms of information (i.e., non-homogeneous information) are considered in this study to score the requirements of current and potential customers and reflect the knowledge and preference differences among them in the CR evaluation process. The scoring of the requirements of different customers can be represented as either linguistic, numerical, or interval values or can be assessed using linguistic label sets that have different granularities. This study adopts a 2-tuple fuzzy linguistic computational approach [28], which is an extension of the symbolic model [29], to aggregate the scores of the CRs from different customers by using various methods because it performs adequately in a non-homogeneous information management context [30–32]. Current and potential customers were considered experts and the Delphi method was employed by using the non-homogeneous information to score the CRs. Conversely, the evaluation of other information in HOQ, such as the relationships between CRs and DRs, and the corrections of the DRs is determined by the QFD team members, who work in the same firm. QFD members usually apply a scale system by using the same language and rules for the evaluation activities, such as 13-9, or 1-5-9, which represent linguistic expressions such as ‘‘weak,’’ ‘‘moderate,’’ and ‘‘strong’’ [7,8], or represent fuzzy sets [19,20,33–37], because these assessments are usually fuzzy during

the NPP process. Some researchers have also adopted the GDM perspective to determine the relationships between CRs and DRs, and the modifications of DRs in the HOQ diagram. Although the GDM scenario and the multiple types of presentation of the various members of the QFD teams were considered in Bu¨yu¨ko¨zkan and Feyziog˘lu [26] and Bu¨yu¨ko¨zkan et al.’s studies [27], the correlations among DRs were ignored in these studies. In general, a QFD team, especially emphasized cross-functional work for NPP, adopts unique rules with same language in the evaluation processes to communicate efficiently during QFD activities. To replicate this practical feature, the 2-tuple fuzzy linguistic representation model was adopted as a unique representation method in this study. QFD teams can adopt to represent their assessments for HOQ construction. Unlike the conventional HOQ model, the correlations among the CRs are considered in the proposed HOQ construction model. In the conventional HOQ, the relationships Rij represents the degree to DRj, affects CRi. Considering that assessments of the correlations among the CRs to CRi and the correlations among the DRs to DRj might affect the initial assessment of Rij, a modified relationship is proposed by combining the initial assessment of relationships Rij, the correlations among the CRs to CRi, and the correlations among the DRs to DRj to reflect the influence from the correlations among the CRs and the correlations among the DRs to obtain the more reasonable assessments of relationships in HOQ model. Based on the CR scores and the modified relationships between CRs and DRs, the scores of the DRs can be determined by using the 2tuple fuzzy linguistic computational approaches. The remainder of this paper is organized as follows. Section 2 introduces the various methods of assessing the CRs, the 2-tuple fuzzy linguistic representation model, and the aggregation model of the non-homogeneous information from which the 2-tuple fuzzy linguistic computational approaches are adopted to score the CRs. In the aggregation model, the 2-tuple fuzzy Delphi method is proposed to assess the consensus regarding each CR. Section 3 presents the use of the 2-tuple fuzzy linguistic representation model in QFD construction procedures. The modified relationships between CRs and DRs are also described. Section 4 provides an example of a semiconductor packing case to demonstrate the applicability of the proposed QFD construction model. A fuzzy HOQ construction model is discussed and compared with the proposed model. Finally, Section 5 presents this study’s conclusion. 2. Assessment forms and aggregation model for CRs evaluation In this study, the scores of the CRs were determined by using various assessment forms from current and potential customers to reflect the differences in their knowledge, expression, and preferences. The importance scores of the CRs from different customers could be represented using linguistic, numerical, and interval values [32,38,39] because of their common use, or can be assessed in the linguistic label sets with different granularity [32,40], which were necessary to evaluate different degrees of uncertainty regarding the CRs. To aggregate the various assessments of the CRs, an aggregation model was proposed to homogenize the uniform format by converting the assessments from various representation forms into a defined linguistic domain, namely a basic linguistic term set (BLTS) [40]. The consideration of how to select the BLTS is also included in [40]. The BLTS is illustrated in Fig. 2. In Fig. 2, the linguistic terms in the BLTS could be defined as a fuzzy number in accordance with the fuzzy set theory. In order to aggregate the various assessments of the CRs, the various assessments from different customers could be transformed from fuzzy sets in a BLTS into a 2-tuple fuzzy linguistic representation model. Besides, to obtain consensual outcomes from the CRs evaluation, the Delphi method was applied in this aggregation model. The various representation formats of the assessment, 2-tuple fuzzy linguistic representation model,

[(Fig._2)TD$IG]

W.-C. Ko / Computers in Industry 73 (2015) 117–127

s0 s1 s2 s3 s4 s5 s6

s7

s8 s9 s10 s11 s12 s13 s14

1

119

term and e is a numerical value indicating the symbolic translation.   Let S ¼ s0 ; s1 ; . . . ; s j ; . . . ; sg be a linguistic term set, and let t be a value representing the outcome of an aggregating information of the linguistic symbols, t 2 [0,g] and t 2 = {0,. . .,g}. A 2-tuple fuzzy linguistic assessment could be expressed as the equivalent information to t by using the following function:

V : ½0; g ! S  ½0:5;  0:5Þ   j ¼ roundðt Þ Vðt Þ ¼ s j ; e ; with s j ; e ¼ t  j; e 2 ½0:5; 0:5Þ 0 0

0.5

1.0

Fig. 2. The linguistic terms of the BLTS.

aggregation model, and proposed 2-tuple fuzzy Delphi method are introduced below. 2.1. The representation formats of the assessment 2.1.1. Linguistic representation form Applying the linguistic evaluation system, namely, a linguistic label set including several ordered linguistic terms, is determined in advance. Different customers might use different linguistic terms (or granularity) in their linguistic label set. For example, the linguistic label set Sm ¼ fs0 ¼ VL; s1 ¼ L; s2 ¼ SM; s3 ¼ MM; s4 ¼ M; s5 ¼ SH; s6 ¼ MH; s7 ¼ H; s8 ¼ VHg is defined to evaluate each of the CR scores for the mth customer’s evaluation, where the linguistic term set {VL, L, SM, MM, M, SH, MH, H, VH} is denoted in linguistic terms as {very low, low, slightly moderate, moderately moderate, moderate, slightly high, moderately high, high, very high}; however, the linguistic label set Sn ¼ fs0 ¼ VL ; s1 ¼ L ; s2 ¼ SM ; s3 ¼ M  ; s4 ¼ SH ; s5 ¼ H ; s6 ¼ VH g is used for the nth customer, while the linguistic term set {*VL, *L, *SM, *M, *SH, *H, *VH} is denoted as {very low, low, slightly moderate, moderate, slightly high, high, high, very high}. The mth customer provides the assessments using the linguistic terms for m either the absolute linguistic preference of CRi, lm or the i 2S m relative linguistic preference lij 2 S , reflecting the relative preference degree of CRi to CRj. In this study, the linguistic terms are characterized using membership functions in the interval [0,1] to reflect the uncertainty in assessing a problem. 2.1.2. Numerical representation form A numerical value x can be viewed as a utility function in [0,1]. The mth customer assesses in the numerical utility values to denote either the absolute preference degree of CRi, xm i , or the relative preference degree by which CRi is preferred to CRj, where the relative preference can be expressed as xm ij. 2.1.3. Interval-valued representation form The interval-valued assessment is commonly used for practical ends because it can easily reflect the uncertainty in the evaluation problem. The mth customer’s assessments consisted of interval values assessed in [d, u], d  u, and d; u 2 [0,1] to represent either the absolute degree of preference of CRi, ½d; um i or the relative degree to which CRi is preferred to CRj, ½d; um ij. 2.2. The 2-tuple fuzzy linguistic representation model The 2-tuple fuzzy linguistic representation model extends the ordinal linguistic approach based on the concept of symbolic translation to implement the processes of easily computing with words without losing information [28,30]. A pair of values (s, e) is used to represent a linguistic assessment, where s is a linguistic

(1)

where round () is the rounding operation, sj has the closest index label to t, and e is the numerical value of the symbolic translation. The inverse function originating from a 2-tuple fuzzy linguistic representation is expressed as

V1 : S ½0:5; 0:5Þ ! ½0; g; V1 s j ; e ¼ j þ e ¼ t :

(2)

In addition, a 2-tuple negation operator is expressed as      1  : Neg s j ; e ¼ V g  V s j; e

(3)

Compared with the ordinal or symbolic linguistic approach, the 2-tuple fuzzy linguistic representation model allows for the computation of linguistic assessment by using the function V and V1 without the loss of information [28,30]. 2.3. Aggregation model To aggregate the assessments of the formats with linguistic (with multi-granularity in the linguistic label sets), numerical, and interval-valued formats, Herrera et al. [32] proposed an aggregation approach to unify non-homogeneous information into a BLTS. Each assessment could be expressed using a fuzzy set in [0,1] on the BLTS. The relevant transformation processes are described in the following section. 2.3.1. Transform a linguisticassessment intoa fuzzy set in   a BLTS Let S ¼ w0 ; w1 ; . . . ; wg and SBLTS ¼ s0 ; s1 ; . . . ; s p be the linguistic term sets of the linguistic evaluation system of customers and the defined BLTS, such that, g  p. The linguistic assessment can be expressed as a fuzzy set in a BLTS by using the following transform function:

CS : S ! nF ðSBLTSÞ; o C S ðwi Þ sk ; eik ; k 2 f0; . . . ; pg i k

e ¼ max l

n

o min mwi ðlÞ; msk ðlÞ ;

8 wi 2 S; sk 2 SBLTS ;

(4)

ðÞ

where F(SBLTS) is the fuzzy set defined in the BLTS, ek 2 [0,1]; mwi ðÞ and msk ðÞ are the membership functions of the fuzzy sets associated with the linguistic terms wi and sk, respectively. 2.3.2. Transform a numerical assessment into a fuzzy set in a BLTS A numerical value E 2 [0,1] could be expressed as a fuzzy set in a BLTS by using the following transform function:

C E : ½0; 1! F ðSBLTS Þ;   C E ðEÞ ¼ ðs0 ;8 e0 Þ; . . . ; s p ; e p ; > 0; > > > > > > < E  ai ei ¼ msi ðEÞ ¼ bi  ai > > 1 > > > ci  E > > : ci  bi

  if E 2 = Support msi ðxÞ ; if ai  E  bi ;

(5)

if E ¼ bi ; if bi  E  ci ;

where the linguistic labels si 2 SBLST are represented by a triangular fuzzy number (ai, bi, ci); a, b, and c represent the lowest, the most

120

W.-C. Ko / Computers in Industry 73 (2015) 117–127

likely, and the highest levels of the triangular fuzzy number, respectively. 2.3.3. Transform an interval-valued assessment into a fuzzy set in a BLTS Let # = {IV: d  IV  u; IV 2 [0,1]} (if d = u, then IV = E), assuming that # prompted a representation in the membership function of fuzzy sets as follows: 8 <0 m# ð I Þ ¼ 1 : 0

if IV < d; if d  IV  u ; if IV > u ;

v

m m

Subsequently, an interval-valued assessment can be expressed as a fuzzy set in a BLTS using the following transform function:

C # : IV ! F ðSBLTS Þ; C # ðIVÞ ¼ fðsk ; eknÞ=k 2 f0; . . . ; pggo 8 IV 2 ½0; 1; sk 2 SBLTS ; ek ¼ max min m# ðIVÞ; msk ðIVÞ ;

(6)

I

where m#() and msk ðÞ are the membership function of the fuzzy sets associated with the interval-valued IV and sk, respectively. Herrera and Martinez [30] proposed a function used to transform a fuzzy set into a numerical value in the interval of the granularity of SBLTS, [0,p]. The transform function is expressed as follows: T : F ðSBLTS Þ ! ½0; p;

Pk¼ p

kek

T ðF ðSBLTS ÞÞ ¼ T ððsk ; ek Þ; k 2 f0; . . . ; pgÞ ¼ Pk¼0 k¼ p k¼0

ek

¼ t:

(7)

A fuzzy set can be determined according to the outcomes of Eqs. (4)–(6). By applying Eq. (1) to the outcome t of Eq. (7), an assessment of each CR is then determined and represented by means of the 2-tuple fuzzy linguistic representation model. 2.4. The 2-tuple fuzzy Delphi method In Herrera et al.’s idea [32], computing the membership degree of linguistic, numerical, and interval-valued assessments in fuzzy numbers associated with the linguistic terms of a BLTS, each assessment with various representation forms can be transformed into linguistic terms in a BLTS by using the 2-tuple fuzzy linguistic representation model. Suppose the CR evaluation is determined by using the Delphi method. Unlike the conventional Delphi method, in this study, the different experts allowed to adopt the different assessment forms to express their opinions in the Delphi processes. To facilitate the scoring processes to determine the consensus assessment to each CR, the ideas of Herrera et al. [32] and Herrera and Martinez [30] were applied into the Delphi method in this study. The 2-tuple fuzzy Delphi method is proposed to determine the consensus assessment to each CR in a GDM environment to reflect the differences in their knowledge, expression, and preferences. The 2-tuple fuzzy Delphi method consists of three steps for determining the consensual scores of the CRs. The relevant processes are described as follows. Step 1. The current and potential customers, acting in an expert role, score each CR. The score assigned by different experts could be presented in linguistic (with different granularity), numerical, and interval-valued formats as follows:

ki;m

8 m < li 2 Sm ; ¼ nm 2 ½0; 1 : i m ½d; ui 2 ½½0; 1; ½0; 1

where ki,m denotes the score of CRi according to the mth expert; l, n, and [d, u] represent the linguistic, numerical, and interval-valued assessment formats, respectively. By applying Eqs. (4)–(6), the linguistic, numerical, and interval-valued assessment of CRi can be transformed into a fuzzy set in a BLTS. Subsequently, by applying Eqs. (7) and (1), each expert’s assessment of CRi can be expressed using ti and the fuzzy linguistic 2-tuple representation model, respectively. Step 2. By computing the average of all ki,m, the formulation is expressed as follows: PM n t P m i;m ; i ¼ 1; 2; . . . ; I; k¯i ¼ m¼1 (9)

m ¼ 1; 2; . . . ; M;

i ¼ 1; 2; . . . ; I; (8)

where nm denotes the weight of the mth expert. For each expert’s assessment, the difference between ki,m and k¯ i is calculated and returned to each expert for the next reevaluation run. For obtaining the adequate revised assessment from each expert, the returned information should well explain the original assessment ki,m with ti,m, and the difference between k¯i and ki,m with ti,m, respectively, to each expert. Step 3. Each expert refers to the differences in Step 2 and provides the revised assessment of CRi as follows: 8 m < li 2 Sm  ki;m ¼  nm ; m ¼ 1; 2; . . . ; M; i 2 ½0; 1 : i  m ½ d; ui 2 ½½0; 1; ½0; 1 ¼ 1; 2; . . . ; I:

(10)

The  ki;m can also be transformed in to  t i by using Eq. (7) based on Eqs. (4)–(6) for the revised linguistic, numerical, and intervalvalued assessments of CRi. The average of all  ki;m ,  k¯ i , can also be determined by using Eq. (9). The difference between k¯i and  k¯ i can be measured as d ¼  k¯i  k¯ i :

(11)

This process could be repeated until two adjacent averages become reasonably close. The consensus criterion is assumed to be a small distance, such as d < 0.1. Once  t i , i = 1,. . .,I are determined using the 2-tuple fuzzy Delphi method, the consensus score of each CR can be calculated as follows: 

ki ¼ PI

ti

i¼1



ti

;

i ¼ 1; 2; . . . ; I:

(12)

3. The 2-tuple fuzzy linguistic HOQ construction model To determine the DRs that adequately satisfy the identified CRs, first, several candidate DRs are collected approximately based on the QFD team’s knowledge and experience. Second, according to the product development strategy and marketing position, the QFD team screens the critical DRs from the candidate DRs. Unlike the existing literature, in which the selection of critical DRs was ignored in the HOQ processes, three decision attributes, including the incremental unit cost, potential risk, and technical difficulty were considered in this study to screen the critical DRs in the HOQ construction model. Third, once the critical DRs are identified, the QFD team can then construct the HOQ based on the identified CRs and DRs; furthermore, evaluate the relevant relationships between CRs and DRs, and the correlations among the CRs and the DRs [17,41]. In the evaluation processes, as previously mentioned, the QFD team usually employed unique measuring methods or rules to communicate efficiently during the NPP process. To use the same measuring system and representation approach with the final assessments of CRs, the BLTS was adopted as a

W.-C. Ko / Computers in Industry 73 (2015) 117–127

measuring system and the 2-tuple fuzzy linguistic representation model was adopted as a unique representation method for selecting the critical DRs from the candidate DRs for each corresponding CR and evaluating the relationships between CRs and DRs, as well as assessing the correlations among the CRs and the DRs in the follow-up HOQ processes. In addition to determine DR scores, the effects of the correlations among the CRs and the DRs on the relationships between CRs and DRs were considered, and the modified relationships between CRs and DRs were determined by using the 2-tuple fuzzy linguistic approaches in the HOQ construction model. The relevant processes of the 2-tuple fuzzy linguistic HOQ construction model are described in the following section.

121

{(p  (V1(UCi,c(sj, e)), (p  (V1(Ric(sk, ek)), (p  (V1(TDi,c(sj, e))}, it can be determined as follows: 1

V0 ðdu Þ g u ¼ P3 : 0 1 ðdu Þ u¼1 V

(16)

Once the availability of each candidate DR is obtained, the critical DRs, CDRi,c, c = 1,. . .,C to CRi can be determined according to the prior screen condition Dðs0 ; e0 Þ. For example, the critical   DRs is identified with CRi when Ai;c s j ; e  Dðs0 ; e0 ÞCR , i c = 1,. . .,C. Eq. (14) is also applied to determine the assessments of the modified relationships between CRs and DRs by using the 2tuple fuzzy linguistic approach. The details are described in Section 3.2.

3.1. Selecting critical DRs 3.2. Calculating the modified relationship between CRs and DRs Based on the premise of customer satisfaction, selecting critical DRs from the candidate DRs is an important process underlying CR identification in HOQ construction processes. Several candidate DRs that affect the CRs are collected by the QFD team in advance. The critical DRs selected from the candidates by using relevant decision methods. Three decision attributes were considered, namely, the incremental unit cost, potential risk, and technical difficulty, in selecting critical DRs from the candidate DRs to satisfy the each corresponding CR. In general, lower levels of the incremental unit cost, risk, and technical difficulty resulted in a higher availability for the selection of critical DR. It is assuming that the candidate DRs, CDRi,c, c = 1,. . .,C, are collected to fit the CRi, the QFD team adopts the same BLTS as the measuring system and the 2-tuple fuzzy linguistic representation model as the representation form to evaluate each candidate DR. Let UCi,c(sj,e), Rii,c(sj,e), and TDi,c(sj,e), j = 1,. . .,p, be the assessments of the incremental unit cost, risk, and technical difficulty of the cth candidate DR to CRi, respectively. Considering that different decision attributes have a different weight g i;cðÞ to CRi for selecting critical DR, an ordered weighted geometric averaging (OWGA) operator [42,43] is then applied to aggregate the assessments of the adequate DR selection in this study. The OWGA operator is an extension of Yager’s ordered weighted averaging (OWA) operator [44]. An OWGA operator of dimension u (>1) is a mapping f : Ru ! R that is associated with a P weighting vector g ¼ ½g 1 ; g 2 ; . . . ; g U T , U u¼1 g u ¼ 1, g u 2 ½0; 1, and can be used to aggregate U sets. The formulation is expressed as follows: U Y

f ða1 ; a2 ; . . . ; aU Þ ¼

gu

ðbu Þ

(13)

u¼1

where bu is the uth largest one in U number of assessments and gu is the weight of bu. Suppose that ða1 ; a2 ; . . . ; aU Þ are a pair of values (sj, e), j = 1,. . .,g, which comply with the definitions of Eqs. (1) and (2), then Eq. (13) can be modified as follows: ! U  g u Y   1 V0 ðs j ; eÞ1 ; . . . ; ðs j ; eÞU ¼ V0 V0 ðdu Þ (14)

By applying the identified CRs and DRs, the initial HOQ diagram can be constructed. The QFD team evaluates the relationships Rij between CRi and DRj, i = 1,. . .,I; j = 1,. . ., J and the correlations among CRs, L i& ð& 6¼ iÞ , and DRs, T jzð z 6¼ jÞ by using the 2-

& ¼ 1; . . . ; I z ¼ 1; . . . ; J tuple fuzzy linguistic representation model based on the same measurement system as that used in the DR selection. Considering that assessments of L i& ð& 6¼ iÞ and T jzð z 6¼ jÞ might affect & ¼ 1; . . . ; I z ¼ 1; . . . ; J the initial assessment of Rij, a higher L i& ð& 6¼ iÞ or T jzð z 6¼ jÞ & ¼ 1; . . . ; I z ¼ 1; . . . ; J indicates a greater effect on Rij. By applying OWGA operator [42], a modified relationship R0i j between CRi and DRj is proposed to reflect the influence from L i& ð& 6¼ iÞ and T jzð z 6¼ jÞ to Rij. The & ¼ 1; . . . ; I z ¼ 1; . . . ; J modified relationship between CRs and DRs is formulated as follows: ! V  g v Y 1 0 R0i j ðsk ; ek Þ ¼ V V0 ðdv Þ ; i ¼ 1; . . . ; I; j v¼1

¼ 1; . . . ; J;

(17)

where dv is the vth largest assessment in {V1(Rij(sk, ek)),

V1 ðL i& ; ð& 6¼ iÞ ðsk ; ek ÞÞ, V1 ðT jz; ðz 6¼ jÞ ðsk ; ek ÞÞ}. Similarly, & ¼ 1; . . . ; I z ¼ 1; . . . ; J considering that g v should reflect the relative percentage of 1 V0 ðdv Þ in {V1(Rij(sk, ek)), V1 ðL i& ; ð& 6¼ iÞ ðsk ; ek ÞÞ, and & ¼ 1; . . . ; I V1 ðT jz; ðz 6¼ jÞ ðsk ; ek ÞÞ}, the weight of dv could be determined z ¼ 1; . . . ; J as follows: 1

V0 ðdv Þ g v ¼ PV : 0 1 ðdv Þ v¼1 V

(18)

u¼1

Accordingly, using Eq. (14), the availability of CDRi,c, c = 1,. . .,C can be determined according to the following formula: ! 3  g u Y 1 0 Ai;c ðs j ; eÞ ¼ V V0 ðdu Þ ; (15) u¼1

where du is the uth largest assessment in {(p  (V1(UCi,c(sj, e)), (p  (V1(Ric(sk, ek)), (p  (V1(TDi,c(sj, e))} Considering that gu should

reflect

the

relative

percentage

of

0 1

V

ðdu Þ

in

3.3. Determining the scores of the DRs By combing the scores of CRi, ki, i = 1,. . ., I, and the modified relationship between CRi and DRj, R0i j ðsk ; ek Þ, i = 1,. . .,I; j = 1,. . .,J, the scores of DRj can be determined using following formula: W DR j ¼

I   X 1 ki  V R0i j ðsk ; ek Þ i¼1

(19)

[(Fig._4)TD$IG]

W.-C. Ko / Computers in Industry 73 (2015) 117–127

122

4. An illustrative example In this section, an NPP case of the turbo thermal ball grid array (T2-BGA) package (see Fig. 3) is used to illustrate the applicability of the proposed HOQ construction model in the QFD process. It is assuming that the QFD team surveyed and collected five CRs, including package profile’’ (CR1), ‘‘thermal performance’’ (CR2), ‘‘electrical performance’’ (CR3), ‘‘reliability’’ (CR4), and ‘‘co-planarity’’ (CR5) from current and potential customers based on the characteristics and performance specifications of the T2-BGA. 4.1. The proposed HOQ construction model In this example, four current and two potential customers play the role of experts to provide their opinions and score each CR by using the linguistic, numerical, and interval-valued representation method. Assume that three experts adopt an absolute numerical form, which is defined in [0,1], two experts used the linguistic form, and one expert adopted an absolute interval-valued representation method in [d, u], d  u, and d; u 2 [0,1] as measurement systems to provide their opinions for scoring the CRs. In this case, the different linguistic label terms are applied in the linguistic form to the different experts’ measurement systems. Fig. 4 shows the different linguistic terms sets that are characterized according to the membership function in the interval [0,1]. In Fig. 4(a), the linguistic term set {VL, L, SM, MM, M, SH, MH, H, VH} is denoted in linguistic terms as {very low, low, slightly moderate, moderately moderate, moderate, slightly high, moderately high, high, very high}. In Fig. 4(b), the linguistic term set {*VL, *L, *SM, *M, *SH, *H, *VH} is denoted as {very low, low, slightly moderate, moderate, slightly high, high, high, very high}. The linguistic terms in Fig. 4(a and b) appear similar; however, they represented different meanings to different experts. For example, the linguistic term ‘‘slightly moderate’’ represents the lowest, most likely, and highest levels in Fig. 4(a and b). 4.1.1. The scores of CRs According to each expert’ assessment of different representation methods, the QFD team employs the proposed 2-tuple fuzzy Delphi method to aggregate the assessments and reach a consensus on the score of each CR. The relevant processes are described as follows: Step 1. The assessment ki,m, i = 1,. . .,5, m = 1,. . .,6, of the each CR from six experts are listed in Table 1. Step 2. Transform the assessments shown in Table 1 into the fuzzy sets in the BLTS by using Eqs. (4)–(6). Furthermore, the score of each CR’s ti can be converted into a unique data format by using Eq. (7). The transformation outcomes with a unique data format are listed in Table 2. It is assuming that the weight set of the experts is {1, 0.9, 0.8, 0.6, 0.5, 0.4}, the average of all ki,m, m = 1,. . .,6, can be determined by using Eq. (9). The k¯i , i = 1,. . .,5 in Eq. (9) are calculated as 3.44, 7.62, 3.86, 10.62, and 3.00. The difference between ki,m and k¯ i is determined, well explained the original assessment ki,m with ti,m as well as the difference between k¯i and ki,m with ti,m, and then returned to each expert for the next reevaluation run.

Fig. 4. Fuzzy numbers of the linguistic term sets.

Step 3. Similar to Step 1, each expert provides an updated assessment, as listed in Table 3. The  ki;m can also be determined using Eqs. (4)–(6), as well as  t i , which can be obtained from Eq. (7) and is listed in Table 4. The average of all  ki;m , can also be determined by using Eq. (9), and the  k¯i of each CR is obtained as 3.5, 7.55, 3.77, 10.62, and 3.06. The difference between k¯i and  k¯i can be measured by using (11). Because the distance between two adjacent k¯i and  k¯ i is less than 0.1, the consensus condition is satisfied in this case. Therefore, the consensus score of the each CR is

Table 1 The first-run outcomes of CRs. Customer

CR1

CR2

CR3

CR4

CR5

Cust1 Cust2 Cust3 Cust4 Cust5 Cust6

0.23 L SM* [0.42, 0.5] 0.2 0.16

0.64 M H* [0.2, 0.3] 0.31 0.56

0.25 L M* [0.25–0.37] 0.26 0.24

0.76 H SH* [0.7, 0.78] 0.85 0.64

0.16 SM SM* [0.2, 0.24] 0.16 0.16

[(Fig._3)TD$IG]

Gold wire Heat slug

Chip

Molding compound

Solder ball

Substrate 2

Fig. 3. The cross-sectional profile of T BGA.

Table 2 The first-run outcomes of CRs converted to the unique data format. Customer

CR1

CR2

CR3

CR4

CR5

Cust1 Cust2 Cust3 Cust4 Cust5 Cust6

3.14 1.76 4.57 6.40 2.71 2.14

8.86 7.31 11.57 3.41 4.29 7.75

3.43 1.76 6.93 4.26 3.57 3.29

10.57 12.17 9.30 10.27 11.86 8.86

2.14 3.42 4.57 3.00 2.14 2.14

W.-C. Ko / Computers in Industry 73 (2015) 117–127 Table 3 The second-run outcomes of CRs.

123

Table 6 The weights of the three decision attributes of each candidate DR.

Customer

CR1

CR2

CR3

CR4

CR5

CRs

Candidate DRs

gUC

gRi

gTD

Cust1 Cust2 Cust3 Cust4 Cust5 Cust6

0.23 SM SM* [0.25, 0.3] 0.25 0.16

0.64 M SH* [0.3, 0.4] 0.4 0.56

0.25 SM SM* [0.25–0.37] 0.26 0.24

0.76 H SH* [0.7, 0.78] 0.85 0.64

0.16 SM SM* [0.2, 0.24] 0.16 0.2

‘‘Package profile’’ (CR1)

Heat slug profile Heat slug attached material Height of heat slug’’ Material of heat slug Molding flow Heat slug pattern Heat slug exposed

0.302 0.225

0.333 0.360

0.365 0.415

0.239 0.391 0.218 0.382 0.255

0.319 0.291 0.426 0.289 0.364

0.442 0.318 0.356 0.329 0.381

0.255 0.391 0.299 0.243 0.255 0.255 0.366 0.391 0.265 0.244 0.231

0.364 0.291 0.342 0.365 0.364 0.364 0.346 0.291 0.318 0.546 0.405

0.381 0.318 0.359 0.392 0.381 0.381 0.288 0.318 0.417 0.210 0.364

0.235 0.200 0.224 0.302 0.224 0.299

0.353 0.474 0.336 0.333 0.336 0.342

0.412 0.326 0.440 0.365 0.440 0.359

‘‘Thermal performance’’ (CR2)

Table 4 The second-run outcomes of CRs converted to the data format. Customer

CR1

CR2

CR3

CR4

CR5

Cust1 Cust2 Cust3 Cust4 Cust5 Cust6

3.14 3.42 4.57 3.75 3.43 2.14

8.86 7.31 9.30 4.88 5.57 7.75

3.43 3.42 4.57 4.26 3.57 3.29

10.57 12.17 9.30 10.27 11.86 8.86

2.14 3.42 4.57 3.00 2.14 2.71

then determined to be 0.123, 0.265, 0.132, 0.373, and 0.107, respectively, by using (12). If the distance between two adjacent k¯ i and  k¯i exceed 0.1, the re-evaluation process is performed in the next round until consensus is achieved. 4.1.2. DR selection To satisfy each CR, several possible candidate DRs are collected based on the domain knowledge and experience from the crossfunctional QFD team. The QFD team considers the incremental unit cost, potential risk, and technical difficulty of three decision attributes to assess each candidate DR by using the 2-tuple fuzzy linguistic representation approach for the BLTS measuring system. The assessments of the candidate DRs compared with those of each CR are listed in Table 5. Furthermore, the weights of three decision attributes compared with those of each candidate DR can be determined by using Eq. (16). Table 6 shows the calculated outcomes Table 5 The assessments of the candidate DRs of each CR. CRs

Candidate DRs

UC(sj, e)

Ri(sj, e)

TD(sj, e)

‘‘Package

Heat slug profile Heat slug attached material Height of heat slug’’ Material of heat slug Molding flow Heat slug pattern Heat slug exposed area Heat slug thickness Material of heat slug Copper pattern Thermal simulation Heat slug exposed area Heat slug thickness Copper pattern Material of heat slug Electrical Simulation Heat slug pattern Heat slug attached material Heat slug thickness Molding flow Stress simulation Heat slug profile Heat slug thickness Copper pattern

(s3, 0.1) (s6, 0.3)

(s3, 0.2) (s9, 0.1)

(s4, 0.5) (s11, 0.5)

(s6, (s4, (s4, (s3, (s6,

0.3) 0.3) 0.3) 0.1) 0.4)

(s8, (s3, (s8, (s2, (s8,

0.4) 0.2) 0.4) 0.2) 0)

(s11, 0.5) (s4, 0.5) (s7, 0) (s3, 0.5) (s8, 0.4)

(s3, (s4, (s7, (s3, (s6,

0.2) 0.3) 0) 0.2) 0.4)

(s4, (s3, (s8, (s4, (s8,

0) 0.2) 0) 0.2) 0)

(s4, (s4, (s8, (s5, (s8,

profile’’ (CR1)

‘‘Thermal performance’’

(CR2) ‘‘Electrical performance’’

(CR3) ‘‘Reliability’’ (CR4)

‘‘Co-planarity’’ (CR5)

0.2) 0.5) 0.4) 0.5) 0.4)

(s3, 0.2) (s11, 0.3) (s4, 0.3) (s4, 0.5) (s3, 0.1) (s7, 0.3)

(s4, 0) (s10, 0.1) (s3, 0.2) (s4, 0.2) (s7, 0.5) (s13, 0.2)

(s4, 0.2) (s8, 0.4) (s4, 0.5) (s6, 0.5) (s3, 0.5) (s12, 0.5)

(s3, (s4, (s3, (s3, (s3, (s7,

(s4, 0.2) (s10, 0.2) (s4, 0.2) (s3, 0.2) (s4, 0.2) (s8, 0)

(s5, (s7, (s6, (s4, (s6, (s8,

0.2) 0.3) 0.2) 0.1) 0.2) 0)

0.1) 0) 0.5) 0.5) 0.5) 0.4)

‘‘Electrical performance’’ (CR3)

‘‘Reliability’’ (CR4)

‘‘Co-planarity’’ (CR5)

area Heat slug thickness Material of heat slug Copper pattern Thermal simulation Heat slug exposed area Heat slug thickness Copper pattern Material of heat slug Electrical simulation Heat slug pattern Heat slug attached material Heat slug thickness Molding flow Stress simulation Heat slug profile Heat slug thickness Copper pattern

for the weights of the three decision attributes of each candidate DR. By applying the assessments and weights of the three decision attributes of the candidate DRs, the availability of each candidate DR compared with that of each CR can be determined by using Eq. (15), as shown in Table 7. It is assuming that the screen threshold of the availability of a critical DR is set as Dðs0 ; e0 Þ  Dð6; 0Þ, the critical DRs corresponding to each CR are then selected, numbered, and listed, as shown in Table 7. The CRs and their scores, as well as the selected DRs, are then employed in the HOQ construction.

Table 7 The critical DRs corresponding to each CR. CRs

Candidate DRs

‘‘Package profile’’ (CR1)

Heat slug profile Heat slug attached material Height of heat slug’’ Material of heat slug Molding flow Heat slug pattern Heat slug exposed area Heat slug thickness Material of heat slug Copper pattern Thermal simulation Heat slug exposed area Heat slug thickness Copper pattern Material of heat slug Electrical simulation Heat slug pattern Heat slug attached material Heat slug thickness Molding flow Stress simulation Heat slug profile Heat slug thickness Copper pattern

‘‘Thermal performance’’ (CR2)

‘‘Electrical performance’’ (CR3)

‘‘Reliability’’ (CR4)

‘‘Co-planarity’’ (CR5)

A(sj, e) 3.2 8.7 8.2 3.7 6.8 2.5 7.4 3.7 3.7 7.8 3.9 7.4 3.7 9.8 3.7 4.5 4.4 10.8 4.1 7.6 4.3 3.2 4.3 7.8

Selected DR DR2 DR3 DR5 DR1

DR4 DR1 DR4

DR2

DR5

DR4

[(Fig._6)TD$IG]

W.-C. Ko / Computers in Industry 73 (2015) 117–127

124

4.1.3. Modified normalized relationship and the scores of DRs According to the CRs and DRs (i.e., selected DRs), the QFD team adopts SBLTS as the measurement system and the 2-tuple fuzzy linguistic representation model to evaluate the relationship between CRs and DRs, and the correlations among the CRs and the DRs to construct HOQ model. The original assessments are shown in Fig. 5. To obtain a reasonable relationship between CRs and DRs, the modified normalized relationship can be calculated by using Eqs. (17) and (18). Finally, the scores of DRs W DR j can be obtained by using Eq. (19). The normalized outcomes of W DR j are 0.199, 0.252, 0.109, 0.244, and 0.196. The rating result of the DRs that satisfies the CRs is {DR2, DR4, DR1, DR5, DR3}. Based on this sequence, the internal resource is then allocated to the DRs to reflect the contribution of CRs in enhancing the customer satisfaction. 4.2. The Fuzzy HOQ construction model As mentioned, Karsak [18] and Chen and Ko [19,20] employed the fuzzy Delphi method to determine the fuzzy score of the CRs by using a triangular fuzzy number. However, the weights of the different expert opinions were not considered in their studies. Considering that each expert opinion has a different weight, the approaches of Karsak [18] and Chen and Ko [19,20] were modified, and a weight-based fuzzy Delphi method is proposed in this study to determine the fuzzy scores of the CRs by using a fuzzy linguistic measure system. Subsequently, the fuzzy HOQ construction model is developed, which is discussed and compared with the proposed model. The fuzzy linguistic measurement system, which is also applied to other evaluations using a fuzzy HOQ, consists of several linguistic terms that are defined correspondingly using triangular fuzzy numbers. Fig. 6 shows the membership functions of the fuzzy linguistic terms for the fuzzy HOQ. The weight-based fuzzy Delphi method consists of four steps for determining the scores of the CRs in a fuzzy HOQ, and is described as follows: Step 1. The experts (i.e., the current and potential customers) provide the possible score of CRi. The fuzzy score assigned by each expert is presented in the form of a triangular fuzzy number as follows: k˜i;m ¼

h

a  b  c i ki;m ; ki;m ; ki;m ;

m ¼ 1; 2; . . . ; M;

i

¼ 1; 2; . . . ; I;

[(Fig._5)TD$IG]

Fig. 6. The membership functions of the fuzzy linguistic terms for the fuzzy HOQ.

where k˜i;m denotes the score of CRi according to the expert m, and the indexes a, b, c represent the lowest, the most likely and the highest level of k˜i;m . Step 2. Considering the weight of the mth expert, the average of all k˜i;m can be calculated using the following formula: h a  b  c i k˜¯i ¼ k¯i ; k¯ i ; k¯i "PM  a PM   P   # nm ki;m b M nm ki;m c m¼1 nm ki;m P P P ; m¼1 ; m¼1 : (21) ¼

n

n

m m

n

m m

m m

Subsequently, for each expert Custm the differences between k˜i;m and k˜¯i are calculated and returned to each expert for the next re-evaluation run. Step 3. Each expert uses the differences in the previous step as a reference, and then provides a revised linguistic variable (if necessary) of the scores as  a  b  c

0 0 0 0 ; m ¼ 1; 2; . . . ; M; i k˜i;m ¼ ki;m ; ki;m ; ki;m ¼ 1; 2; . . . ; I:

(22) 0

Then the average k˜¯ i;m can also be obtained by using Eq. (21) and its difference with k˜¯ i is calculated using a distance measure [22]:   h  a  0 a  c  0 c i

 b  0 b

 0



d k˜¯i ; k˜¯ i ¼ 0:5 max k¯ i  k¯ i ; k¯ i  k¯i þ

k¯ i  k¯ i

(23)

(20)

This process can be repeated until two adjacent averages become reasonably close. The consensus criterion is assumed to be a small distance, such as d  0.2. Step 4. If there is any change or update information that may lead to a reevaluation of the fuzzy scores of the CRs, the next-round h      i  a b c process begins at Step 1. The final k˜ ¼ k ; k ; k , i = 1,. . .,I, i

i

i

i

is a fuzzy subset in [0,1] that represents the average of the fuzzy scores of the CRi according to the experts’ evaluations in the weight-based fuzzy Delphi method. In the a-cuts aspect, a fuzzy set can fully and uniquely be represented by its a-cuts 

[45]. Therefore, k˜i can be denoted according to its lower and h    i L U upper bounds, ki a ; ki a , which is defined as h    L   a  a i b ki a ¼ ki þ a  ki  ki

(24a)

and h    U   c  b i c ki a ¼ ki  a  ki  ki

Fig. 5. The original assessments of the 2-tuple HOQ.

(24b)

Based on the various a levels, a 2 [0,1], which was the  membership function of k˜i , can be determined. The defuzzified

W.-C. Ko / Computers in Industry 73 (2015) 117–127  value of k˜i can be calculated by using a fuzzy mean (FM) approach [46], which is simple and efficient. The FM is formulated as follows:

PQ 

aq xq  q¼1 aq

q¼1



p ¼ PQ 

(25)



˜ DR can be determined in the form of a-cuts, The fuzzy score W j expressed as  L  U

  ˜ DR ¼ WDR W ; W DR j j j a a " # I I    U X L X 0 0   : (29) ki  Ri j ; ki  Ri j ¼ a

i¼1

where aq and xq represent the membership degree and the representative (pre-calculated) numerical value of the qth output, respectively. Following Mabuchi’s idea [47], the representative   value of the qth output is defined as xq ¼ 1=2 xLq þ xU q . In this case, h    i  L U p is the defuzzified value of ki a ; ki a (i.e., the qth a-cut of k˜i ); xq is the average of the lower and upper bounds of the interval h    i h    i  L U L U values ki a ; ki a at the qth a-cut of k˜i (i.e., 1=2 ki a ; ki a ).  Based on the FM approach, the k˜i can be defuzzified as follows:

ki

PQ

1=2

q¼1

¼

h 

 U i

aq  ki Lq þ ki PQ

q¼1

aq

q

;

i ¼ 1; . . . ; I:

þ

(26)

For comparison purposes, the DR selection process is ignored in the fuzzy HOQ model. The critical DRs are the same as those in the proposed model. The fuzzy relationships R˜ i j between CRi , and DRs, and DRj and the correlations among CRs, L˜ i& ð& 6¼ iÞ & ¼ 1; . . . ; I T˜ jzð z 6¼ jÞ were evaluated by using the fuzzy linguistic measure z ¼ 1; . . . ; J system (Fig. 6). According to the application of the OWGA in Eq. (17), a fuzzy ordered weighted geometric averaging (FOWGA) operator [48] was used to determine the modified fuzzy relation0 ships R˜ i j between CRi and DRj, which was considered to be the influence of L˜ i& ð& 6¼ iÞ and T˜ jzð z 6¼ jÞ . Applying FOWGA, & ¼ 1; . . . ; I z ¼ 1; . . . ; J can be formulated as 0

0 R˜ i j

& ¼ 1; . . . ; I

; T˜ jzð z 6¼ jÞ z ¼ 1; . . . ; J

V   C Y ˜ vv ; bv A¼

v¼1 v

v

(27)

0

a-cuts and the extension principle [49,50], R˜i j can be determined by representing its membership function and deriving the lower and upper bounds of its a-cut as follows: 

R0i j

L a

¼

V  Y  v L bv v a;

(28a)

v¼1

and 

R0i j

U a

¼

V  Y

v¼1

 v U bv v a:

a

j = 1,. . .,J can also be defuzzified by using the FM [46] and Mabuchi’s [47] approaches to rate DRs in the fuzzy HOQ model.

4.2.1. The outcomes of the fuzzy HOQ model In applying the fuzzy linguistic measurement system, membership functions of the linguistic terms, and weight-based fuzzy Delphi method, the experts provide their assessments for the fuzzy scores of the CRs. Table 8 lists the first and second run outcomes of the fuzzy CRs. Because the distances between two adjacent  averages are less than 0.2, the resulting fuzzy scores k˜i of CRs, i = 1,. . .,5 are finally determined as (0.121, 0.321, 0.521), (0.257, 0.457, 0.657), (0.121, 0.393, 0.521), (0.638, 0.838, 0.971), and  (0.121, 0.298, 0.498). The defuzzified value of k˜i , i = 1,. . .,5, can be obtained as 0.141, 0.201, 0.163, 0.363, and 0.132, by using Eqs. (24a), (24b), and (26). In the comparison, the critical DR is adopted in the same outcomes, which are selected according to the 2-tuple HOQ model. Furthermore, the fuzzy relationships R˜ i j between CRi and DRj and the correlations among CRs, L˜ i& ð& 6¼ iÞ

,

& ¼ 1; . . . ; I are evaluated by using the fuzzy linguistic and DRs, T˜ jzð z 6¼ jÞ z ¼ 1; . . . ; J measurement system (Fig. 7). By applying Eqs. (28a), (28b), and (29), the lower and upper bounds of the fuzzy importance rating ˜ DR at each a level can be obtained. Finally, the defuzzified values W j

˜ DR , j = 1,. . .,5, can be obtained by using the FM FM [46] and of W j Mabuchi’s [47] approaches. The normalized outcomes of the ˜ DR are 0.215, 0.273, 0.092, 0.275, and defuzzified values of W j

4.3. Discussion

v¼1

where b˜v is the ith largest set of 8 9 > > < = ; T˜ jzð z 6¼ jÞ . To reflect the relative percentR˜ i j ; L˜ i& ð& 6¼ iÞ > > : ; & ¼ 1;8. . . ; I z ¼ 1; . . . ; J 9 > > = < , b˜v can be defuzziage of b˜v in R˜ i j ; L˜ i& ð& 6¼ iÞ ; T˜ jzð z 6¼ jÞ > > ; : & ¼ 1; . . . ; I z ¼ 1; . . . ; J fied by using the FM approach and vv can be determined by P vv ¼ b = V b , where b is the defuzzified value of b˜v . Based on v

i¼1

˜ DR , W j

0.145. The rating result of DRs is {DR4, DR2, DR1, DR5, DR3}.

1

0 B R˜ i j ¼ f @R˜ i j ; L˜ i& ð& 6¼ iÞ

125

(28b)

The score sets of the CRs from the proposed 2-tuple and weightbased fuzzy Delphi method were {0.123, 0.265, 0.132, 0.373, 0.107} and {0.141, 0.201, 0.163, 0.363, 0.132}, respectively. The importance orders of the CRs scores were the same; however, the scores that resulted from using different methods were different. Carnevalli and Miguel [4] argued that interpreting and analyzing customer opinions is one of the principal difficulties found in applying QFD. CR2 and CR4 were more valuable when adopting the 2-tuple fuzzy Delphi method than they (CR2 and CR4) were obtained using the weight-based fuzzy Delphi method. Conversely, CR1, CR3, and CR5 represented the opposite results from both fuzzy Delphi methods. The different understandings and perceptions of the CR scoring results might have led to different outcomes of DR ratings. In this case, by using the relative calculation processes, the

Table 8 The first/second run outcomes of the fuzzy CRs. Customer

CR1

CR2

CR3

CR4

CR5

Customer1 Customer2 Customer3 Customer4 Customer5 Customer6

L*/L* L*/M* M*/M* M*/L* L*/L* L*/L*

M*/M* M*/M* H*/M* L*/L* M*/M* M*/M*

L*/L* L*/M* M*/M* L*/L* L*/L* L*/L*

H*/H* H*/VH* H*/H* H*/H* VH*/VH* M*/M*

VL*/L* L*/M* M*/M* L*/L* VL*/VL* VL*/L*

[(Fig._7)TD$IG]

W.-C. Ko / Computers in Industry 73 (2015) 117–127

126

linguistic HOQ model is 10.7% related better than that the existing fuzzy HOQ model. 5. Concluding remarks

Fig. 7. The original assessments of the fuzzy HOQ.

rating results of the DRs were {DR2, DR4, DR1, DR5, DR3} when using the proposed HOQ model, whereas the DR ratings were {DR4, DR2, DR1, DR5, DR3} when using the fuzzy HOQ model. The critical rating of the DRs from the both HOQ models was different. Considering the difference between the outcomes from both HOQ models, three points are addressed for discussion. First, concerning the assigned measurement system and the representation form used in the weight-based fuzzy Delphi method, the proposed 2-tuple fuzzy Delphi method was more useful for addressing customer opinions in the HOQ construction practice because it allowed each expert to use their preferred measurement system and representation form to assess the CRs. Second, the 2-tuple linguistic representation model enabled the computation of the linguistic assessment of Rij, , and T jzð z 6¼ jÞ to determine the modified L i& ð& 6¼ iÞ

& ¼ 1; . . . ; I

Acknowledgement This research was funded by Contract NSC 100-2410-H-168005 from the Ministry of Science and Technology[5_TD$IF], Republic of China. References

z ¼ 1; . . . ; J

relationships between CRs and DRs without losing information. Third, the outcomes of the DRs’ ratings when using the proposed HOQ model should be more reasonable based on the more reasonable outcomes of the scores of the CRs and the relationships between CRs and DRs. To maximize overall customer satisfaction, Wasserman [51] used the outcomes of W DR j to create a linear programming model, as follows. J X Z ¼ max W DR j  x j ; j¼1 J X C DR j  x j  B; s:t:

A systematic process for developing the HOQ construction model is proposed in this study. The proposed approaches allow a non-homogeneous assessment from current and potential customers to evaluate the scores of the CRs to reflect their knowledge and preference for understanding and handling the needs expressed by customers. To aggregate non-homogeneous assessments, the 2-tuple fuzzy linguistic Delphi method is proposed to determine the scores of the CRs in the HOQ construction model. A modified relationship between CRs and DRs was determined using the OWGA operator to aggregate the relationship between CRs and DRs and the correlations among the CRs and the DRs to obtain the reasonable relationship between CRs and DRs. Compared with the fuzzy HOQ model, the proposed 2-tuple fuzzy linguistic approach was more useful and did not lose information when determining the scores of the DRs. The DRs’ ratings revealed that the NPP team could effectively allocate limited resources to satisfy the CRs in the NPP process. Although the proposed approaches were developed for non-homogeneous assessments in the evaluation of CRs, the various opinions from different market segment could be considered in future studies of evaluating CRs. In addition, instead of the Delphi method, other approaches might be adopted to determine the consensus assessments, such as the clustering approach.

:

(30)

j¼1

e j  x j  h j ; x j 2 ½0; 1; where Z represents the objective value of the total customer satisfaction. The term xj is defined as the decision variable and it denotes the fulfillment level of DRj. When xj = 0, DRj is a basic one that requires no additional effort or cost. The fulfillment outcome of DRj requires a corresponding percentage of the increased unit cost C DR j to enhance the performance or quality of the new product. The total increased unit cost cannot exceed the budget B. ej and hj are defined as the business completion and technical difficulty, respectively, and they denote the possible range of xj. Suppose that C DR j , j = 1,. . .,5, are 0.7, 0.9, 0.2, 0.9, and 0.2, respectively; ej = 0.05 and hj = 0.95, 8j, The total customer satisfaction that can be obtained with the proposed 2-tuple fuzzy

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