Applying the Pure Linguistics to Construct the Group Decision Based Quality Function
Deployment for Product Improvement
Abstract
This study attempts to introduce the multi-granularity linguistic evaluation approach
into a quality function deployment model to construct a complete linguistic environment for
group decision-making. Generally, vague information is handled by being expressed via fuzzy
number or defuzzilized numeric through QFD activity. However, this study attempts to
employ pure linguistics instead of the fuzzy number approach based on evaluations of
customer needs, relationships between customer needs and solution scenarios, correlation
among solution scenarios, and even priority among solution scenarios. Simultaneously, this
investigation also introduces the multi-granularity linguistic concept that permits individual
evaluators to select commonly used linguistic scales depending on personal preference to
avoid decreasing the sensitivity and realism of evaluations, and to increase the objectivity and
tolerance of results, particularly in relation to the conversion gap between customer needs and
solution scenarios. Furthermore, linguistic two-dimensional analysis is also introduced to
classify solution scenarios into priority and complementary categories. Consequently, the
multi-granularity linguistic based group QFD model proposed in this research differs from
existing approaches in the manner in which it processes information.
Keywords: Quality function deployment; multi-granularity linguistic variable; group decision;
1
linguistic weighted aggregation operator
1. Introduction
Owing to the increasingly competitive business environment, enterprise efforts to
improve their competitiveness are invariably based on innovation and creation of products
that meet rapidly changing customer needs. However how to ensure innovation and new
product development satisfy customer needs is the main challenge facing enterprises
especially in customer oriented marketplaces (Ramanathan and Yunfeng, 2009).
Consequently, this study proposed the novel quality function deployment (QFD) model, based
on group decision-making and natural human linguistics, to help enterprises evaluate the
relationship between products and customer needs.
QFD, one of the most familiar management techniques, can shift the orientations of
improvement, innovation and creation towards customer needs to maximize customer
satisfaction; nevertheless, most manipulations of QFD are numerical. The calculation and
aggregation results are always expressed numerically though in a few cases they are initially
expressed linguistically (Kwong et al., 2007; Lai et al., 2008). However, this study changes
the QFD mechanism into complete linguistic model because the evaluation objects are
generally characterized by imprecise, indeterminate and uncertain information that can not be
represented numerically, such as the satisfaction and importance of customer needs, the causal
relationship between customer needs and solution scenarios, and the correlation among
2
solution scenarios (Temponi et al., 1999). Hence, presenting information in ordinal rather than
numerical form is unrealistic and can create distortions (Karsak, 2004); moreover, evaluators
always waste time deliberating the rationalization for numeric presentation of information
being more inefficient than ordinal presentation. Therefore this study applied ordinal
information with linguistics rather than cardinal information with numeric data that
conformed to human interpretation of the original information to reconstruct the QFD model
and offer speedy, accurate, and useful information to decision makers (Chang et al., 2007;
Wang et al., 2007). Because of QFD belonging to group activities, this study also permitted
an individual to select common usage linguistics to conduct the evaluation. However, how to
solve linguistic cognition differences through group decisions is also crucial for implementing
QFD in situations where multiple evaluators have different linguistic thoughts, and is further
demonstrated in the following sections (Carnevalli and Miguel, 2008).
Figure 1 shows the House of Quality (HOQ), which is the medium for executing QFD.
The main focuses of this study are listed below:

Complete linguistic data usage

Collection of customer needs, evaluation of the relationship between customer
needs and solution scenarios, evaluation of the correlation among solution
scenarios under group decision-making
3

Comprehensive consideration of the interaction between the relationship and
correlation matrices

Adopting an objective approach with high tolerance
Correlation Matrix
Solution Scenarios
Customer
Needs
Relationship Matrix
Priority
for
Customer
Needs
Priority for Solution Scenarios
Figure 1. House of quality
The next section comments on the recent literature on fuzzy QFD. Section 3 details the
construction of the proposed model, and Section 4 then interprets the algorithm of the
proposed model interpreted by the flow chart. Subsequently, Section 5 presents a synthetic
example illustrating the proposed model, and finally the last section presents conclusions and
future research directions.
2. Fuzzy QFD
In research on the linguistics of Fuzzy QFD, Temponi et al. (1999) built a fuzzy
logic–based linguistic evaluation matrix model. Chan and Wu (2005) presented the results of
4
linguistic evaluations and HOQ operation on a crisp value and fuzzy number. Chen and Weng
(2006) adopted the linguistic form to evaluate the weights of customer needs and a
relationship matrix. Defuzzification results, cost and difficulty of solution schemes were then
introduced into multiple objective fuzzy linear programming to determine the execution level
of solution scenarios. Kahraman et al. (2006) combined defuzzification results obtained from
a linguistic evaluation of customer needs using an analytical hierarchy process (AHP) to
weight customer needs, and then used fuzzy linear programming (FLP) to determine the
implementation level of the solution schemes. Büyüközkan et al. (2007) manipulated full
linguistics to construct QFD, and also directly applied aggregation to linguistics. Chen and
Weng (2003), and Chen and Ko (2008 and 2009) performed the HOQ operation by linguistic
evaluation results with membership function and then via   cut defuzzification.
In research on the application and integration of fuzzy QFD, Kim et al. (2000), and
Fung et al. (2006) developed a fuzzy multiple criteria model for HOQ operation and presented
the results via fuzzy numbers that became the parameters of fuzzy regression in prioritizing
solution scenarios. Chen and Ko (2008) and Lee et al. (2008) introduced the Kano quality
model into QFD. Yang et al. (2003) utilized linguistic variables defined in fuzzy numbers to
weight customer needs and identify the relationship matrix in architectural design. Fuzzy
number–based aggregation results were compared with the definition of linguistic variables to
assess the eventual linguistic result. Karsak (2004) employed linguistic variables to weight
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customer needs and relationship matrix in a clothing design context. After obtaining the
defuzzification results, cost and difficulty of solution schemes were incorporated into
multi-objective FLP to resolve the fulfilled rate of solution schemes. Büyüközkan and
Feyzioğlu (2005) developed the ordered weighted geometric (OWG) operator to aggregate the
information from the group-decision QFD model on the application of software design.
Moreover, seven calculations for weighting are proposed to construct a complete numerical
HOQ. Fuzzy linguistic quantifiers are then introduced to aggregate and prioritize solution
scenarios. Bevilacquaa et al. (2006), and Bottani and Rizzi (2006) constructed the HOQ using
a linguistic variable defined by fuzzy numbers to deal with issues of supplier selection and
strategy management for logistics services. Karsak and Özogul (2009) combined QFD, fuzzy
regression and zero-one goal programming to select enterprise resource planning (ERP)
system. The data collected via QFD is used for fuzzy regression and then solved by zero-one
goal programming.
In research on group decision-making on fuzzy QFD, Büyüközkan and Feyzioğlu
(2005), Chin et al. (2009), and Kuo et al. (2009) constructed the numeric HOQ based on
group decision-making, and Büyüközkan et al. (2007) constructed the linguistic HOQ based
on group decision-making.
Carnevalli and Miguel (2008) reviewed and analyzed 157 studies on QFD published
from 2000 to 2006. Although lots of the literature touched upon fuzzy QFD and usage of
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linguistics, most of the literature on practical calculation adopts a numeric approach together
with defuzzification (Kwong et al., 2007; Lai et al., 2008) and thus differs significantly from
this study. Notwithstanding Büyüközkan et al. (2007) constructed a complete linguistic QFD
based on group decision, the usage of multi-granularity linguistics and the integration utility
of correlation matrix have still not been discussed. Consequently, the perspectives of the
literature on obtaining customer needs information differed from that presented in this study.
To summarize, this study is not only more comprehensive and general but also differs from
conventional representations of the results of HOQ based on two-dimensional analysis.
3. Model construction
This section demonstrates the tools and techniques introduced for the modeling in detail.
Besides, this section further demonstrates how to manipulate the pure linguistics directly to
construct the group decision based quality function deployment.
3.1 Tools and techniques
Linguistic variable, linguistic scale uniformity, and linguistic information aggregation
applied in the model would be completed interpretation at this sub-section.
3.1.1 Linguistic variable
The linguistic variable, defined by linguistic scale, is not only employed to evaluate the
importance and satisfaction of customer needs in this study, but also used to evaluate
relationship matrix between customer need and solution scenario and correlation matrix
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among solution scenarios. Moreover, the linguistic variable is formed by several semantic
elements (SEs) within a linguistic term set (LTS) (Herrera, Herrera-Viedma and Martinez,
2000). The SE is defined in the unit interval [0,1] of the linear triangular membership function
using the fuzzy set ( xL , xm , xR ) (Fig. 2), where xL and xR are the left and right limits of
the corresponding SE by the membership function, and xm is the value at which the
membership grade equals 1. Applications can also utilize a trapezoid membership function for
defining SEs within an LTS.
Label
s0
s1
s2
s3
s4
s5
s6
s7
s8
SE
( xL , xm , xR )
None
(0,0,0.12)
Very Low (0,0.12,0.25)
Low
(0.12,0.25,0.37)
Almost Low (0.25,0.37,0.5)
Medium
(0.37,0.5,0.62)
Almost High (0.5,0.62,0.75)
High
(0.62,0.75,0.87)
Very High (0.75,0.87,1)
Perfect
(0.87,1,1)
s0
1
s1
s2
s3
s4
s5
s6
s7
s8
Membership
Grade
0
0
0.12 0.25 0.37 0.50
0.62 0.75 0.87
1
Linguistic
Relation
Figure 2. Definition of linguistic variable S
The linguistic variables considered in this study are finite and totally ordered LTS
(symmetrized at s4 ), which requires the following properties (Herrera, Herrera-Viedma and
Verdegay, 1995):

The set is ordered: si  s j if i  j

The negative operator is defined: Neg ( si )  s j such that j  8  i

Maximization operator: max( si , s j )  si if si  s j
8
9

Minimization operator: min( si , s j )  si if si  s j
3.1.2 Linguistic scale uniformity
Multi-granularity linguistic information is either generated by the evaluator who defines
individual cognition on membership function of LTS by preference, or alternatively is generated by
assessment with different LTS. Therefore, making the multi-granularity linguistic information
uniform requires using the basic linguistic term set (BLTS). BLTS has the same definition as LTS,
only the number of SEs in BLTS must contain all of SE in LTS to avoid reducing semantic
discrimination in the process of uniformity. The transformation function of multi-granularity
linguistic information uniformity  AST is defined below (Herrera, Herrera-Viedma and Martinez,
2000):
Let A  {l 0 , l1 ,  , l p } be a LTS, and S T  {c0 , c1 , , c g } be a BLTS, where g  p , such
that  AST : A  F ( ST ) .
 AS (le )  {(cu , cl ) | u {0,1,, g}}
e
T
u
l e  A
 cl  max min{ l ( x), c ( x)}
e
u
x
e
u
The result of uniformity  AST for any SE of A is a fuzzy set defined in ST , where  le (x)
and  cu (x ) are the membership functions of the fuzzy sets associated with the SEs le and cu ,
respectively. The uniformity generates a new fuzzy set  AST (le )  {( cu , cleu ) | u {0,1,, g}}, where
(cu , cleu ) indicates the membership grade  cleu of each SE cu in BLTS associated with the
9
10
original SE le . Subsequently the characteristic value of the uniformed linguistic information is
g
 u
determined by round ( u g0

u 0
le
cu
)  round ( ) where round is the usual round operation (Herrera,
le
cu
Martinez and Sanchez, 2005).
3.1.3 Linguistic information aggregation
Prioritizing solution scenarios is concerned with the aggregation between the relationship
matrix and priorities of customer needs. As mentioned, as the relationship matrix is evaluated by
linguistic variables and the priorities of customer needs are revealed by normalized weights, the
aggregation should be performed using the linguistic weighted aggregation (LWA) operator, which
is a modified version of the linguistic ordered weighted aggregation (LOWA) operator (Herrera,
Herrera-Viedma and Verdegay, 1996). Let R  {r1 , r2 , , rm } denote a set of SEs evaluated by
linguistic variable S  {s 0 , s1 ,, s g } to be aggregated with a set of normalized weights
W  [w1 , w2 ,, wm ] . The LWA operator F is defined as follows:
F (r1 , r2 ,, rm )  W   B T  C m {wn , bn , n  1,2,, m}
 w1  b1  (1  w1 )  C m 1{ h , bh , h  2,3, , m}
where B is the associated ordered SE vector of R  {r1 , r2 , , rm } , and each SE bi  B is the
i th largest SE in the collection R  {r1 , r2 , , rm } ; W   [ w1 , w2 ,  , wm ] is a set of normalized
weights
concurrently adjusted with B , and  h 
wh
m
w
k 2
, h  2,3,  , m . Variable C m is the convex

k
combination operator of m SEs,  is the general product of an SE by a positive real number, and
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11
 is the general addition of SEs (Delgado, Verdegay and Vila, 1992). If m  2 , then F is defined
as below:
F (r1 , r2 )  W   BT  C 2 {wi , bi , i  1,2}  w1   j  (1  w1 )   i   k
such that k  min{ g , i  round (w1  ( j  i))} , where round is the usual round operation, and
b1   j , b2  i . If w j  1 and wi  0 with i  j i , then the convex combination is defined as
C m  {wi , bi , i  1,2, , m}  b j .
3.2 House of quality deployment
Steps in deployment of HOQ and integration of tools and techniques mentioned in last
sub-section would be detailed in this sub-section.
3.2.1 Customer needs acquirement
Customer needs can be acquired using questionnaires, experiments, interviews, and through
experiences. Maintenance and complaint records can also be utilized. Determining the priorities of
customer needs is the first task in this study that is concerned with evaluator linguistic cognition
and judgment. Therefore, the difference between importance and satisfaction in customer needs is
measured to prioritize customer needs. The prioritizing theorem is as follows: when the importance
of customer need exceeds satisfaction; the customer need did not reached expectation. On the
contrary, relatively less urgent is when satisfaction exceeds importance, meaning that the service
surpassed expectation. But there is something needed to pay attention as soon as evaluators employ
linguistic variables formed by different scales, the results of evaluation for importance and
11
12
satisfaction of customer needs have to perform the procedure of uniformity as mentioned in
Sub-Section 3.1.2 before calculating the priorities of customer needs revealed by normalized
weights.
3.2.2 Customer needs prioritization
The priorities of customer needs can be represented by a weight of magnitude; hence, how to
determine the weight of each customer need is the focus of the following discussion. First, the
difference between the importance and satisfaction of each customer need can be the basis for
weighing need and should perform the linguistic scale uniformity if necessary. The scale adjustment
and normalization process can then acquire the weight of each customer need. Suppose that the
importance and satisfaction of customer needs ( X 1 , X 2 , X m ) are evaluated by linguistic variables
A  {a 0 , a1 ,  , a p } and B  {b0 , b1 ,  , bq } , respectively. Both ai  A and b j  B indicate the
importance and satisfaction of customer need X n ; D n , En and W n are the original difference,
adjusted difference and normalized weight which are defined below:
Original difference
Dn  i  j
n  1,2,, m
Adjusted difference
E n  Dn  q
n  1,2,, m
Normalized weight
Wn 
( Dn  q)
( D1  q)  ( D2  q)    ( Dm  q)
n  1,2,, m
The calculation of original difference cannot avoid generating a negative value when
satisfaction exceeds importance. Therefore, an adjustment is revises the negative value by adding
the value q (Wang, 2010).
12
13
3.2.3 Solution scenarios prioritization
Generally, the solution scenario can be obtained through manifold methods such as
brainstorming, a proposal system and even a small-scale experiment for improvement.
After confirming solution scenarios, the next step is to further evaluate the relationship
between customer needs and solution scenarios. However, most studies only addressed the positive
relationship in the matrix, and treated the correlation matrix as a consultation that could not
explicitly identify utility during the evaluation. Consequently, this study employs linguistic
variables to evaluate the relationship matrix, which can simultaneously display positive and
negative relationships via the arrangement of the linguistic scale. The correlation between solution
scenarios can be modeled indirectly in the relationship matrix, further simplifying the manipulation
of HOQ. However, the linguistic results of evaluations from the relationship and correlation
matrices should also perform the linguistic scale uniformity, as mentioned in Sub-Section 3.1.2,
before aggregation of linguistic information. Prioritizing solution scenarios requires aggregating
linguistic information via the LWA operator mentioned in Sub-Section 3.1.3, with the linguistic
results of evaluations from relationship matrix and the priorities of customer needs revealed by
normalized weights, and so as the aggregation procedure for the linguistic results of evaluations
from correlation matrix.
3.2.4 Linguistic two-dimensional analyzing solution scenarios for synergy
The interworking between the priority and correlation among solution scenarios displayed in
Fig. 3 is further demonstrated via two-dimensional coordinates, where the priority is illustrated on
13
14
the horizontal axis and the correlation on the vertical axis. The solution scenario located within
phase I is superior to other phases because of having both higher priority and higher augmentation
impression on correlation. On the contrary, the solution scenario located in phase III is inferior to
other phases having lower priority and conflict impression. Although the solution scenario located
in phase IV is lower than that located in phase II on the evaluation result of the correlation
correlation, the solution scenario is still slightly superior to the priority. However based on customer
needs, the solution scenario located in phase IV is superior to that located in phase II. Decision
makers can also consider other factors such as cost to differentiate the superiority between phases II
and IV.
Priority on the
Correlation Matrix
High
II
I
Low
High
III
Priority on the
Relationship Matrix
IV
Low
Figure 3. Two-dimensional analysis for solution scenarios
4. Algorithm
The mothodology proposed in this study can be divided into 13 steps which are demonstrated
below in sequence. Figure 4 shows the algorithm in flow chart form.
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15
Identify customer needs
Assess the importance and satisfaction of individual
customer needs based on group decision-making
Judge linguistic
variable unity
Multi-granularity linguistic scale
Prioritize
customer
needs
Single linguistic scale
Uniform linguistic scale for importance and satisfaction
Aggregate group based linguistic information (importance
and satisfaction) for individual customer needs
Compute the original difference for each customer need
Adjust the difference for each customer need
Deploy
house of
quality
Normalize the weights for individual customer needs
Seek solution scenarios
Assess the relationship matrix
based on group decision process
Prioritize
solution
scenarios
Assess the correlation matrix
based on group decision process
Judge linguistic
variable unity
Multi-granularity linguistic scale
Single linguistic scale
Uniform linguistic scale for relationship and correlation
matrices
Aggregate group based linguistic information in the
relationship and correlation matrices
Aggregate the relationship matrix with normalized weights
on customer needs to prioritize each solution scenario
Perform two-dimensional linguistic analysis for solution
scenarios
Figure 4. The flow chart of the algorithm
Step 1. Identify customer needs. Understand and cognize practical customer needs through
general surveys and investigations.
Step 2. Assess the importance and satisfaction of individual customer needs based on group
15
16
decision-making. Allow decision makers to choose their preferred linguistic variable
to perform the assessment.
Step 3. Uniform linguistic scale for importance and satisfaction. To facilitate the aggregation
in Step 4, this procedure only activates when decision makers apply inconsistent
linguistic variables to assess importance and satisfaction for individual customer
needs.
Step 4. Aggregate group based linguistic information importance and satisfaction for
individual customer needs. The aggregation procedure involves manipulating the
linguistic weighted aggregation (LWA) operator to perform the aggregation.
Step 5. Compute the original difference for each customer need. The distance between
importance and satisfaction could be represented by the difference.
Step 6. Adjust the difference for each customer need. Avoid negative values to favor the
weighing procedure in Step 7.
Step 7. Normalize the weights for individual customer needs. Obtain the normalized weights
to represent the priorities for individual customer needs and favor the aggregation of
each pair of customer need and solution scenarios.
Step 8. Seek solution scenarios. Look for appropriate solution scenarios and assess their
practicability.
Step 9. Assess the relationship and correlation matrices based on group decision process.
Allow decision makers to choose preferred linguistic variables to perform the
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17
relationship matrix assessments according to strong or weak relations between each
customer need and solution scenario pair, and thus make correlation matrix
assessments according to the positive or negative relevance between each pair of
solution scenarios.
Step 10. Uniform linguistic scale for relationship and correlation matrices. If the relationship
and correlation matrices are assessed using different linguistic variables, the
uniformity procedure should be performed before aggregation.
Step 11. Aggregate group based linguistic information in the relationship and correlation
matrices. The LWA operator aggregates group based linguistic information from the
relationship and correlation matrices.
Step 12. Aggregate linguistic information based on the relationship matrix with normalized
weights on customer needs to prioritize each solution scenario as well as the
correlation matrix.
Step 13. Perform two-dimensional linguistic analysis for solution scenarios. Manipulate the
two-dimensional coordinates to synthetically demonstrate the priority of the solution
scenario and the result of linguistic aggregation on the correlation matrix.
5. Demonstrative example
The focal company, which specializes in fabricating notebook computers, wants to upgrade
one of their products using QFD improving activities. Two focal customers A and B are applied
linguistic variables  and  separately by preference shown in Fig. 5 to assess the importance
17
18
and satisfaction of five customer needs (sustaining power, convenience for carry-on, multi-function
integration, reception of vision, and artistic modeling) which are further screened out from the
investigation in the marketplace that is listed in Table 1.
Label Semantic
0
1
2
3
4
5
6
None
Very Low
Low
Medium
High
Very High
Perfect
( xL , xm , xR )
(0,0,0.16)
(0,0.16,0.33)
(0.16,0.33,0.5)
(0.33,0.5,0.67)
(0.5,0.67,0.84)
(0.67,0.84,1)
(0.84,1,1)
1
2
3
4
5
6
0.16
0.33
0.50
0.67
0.84
1
Membership
Grade
0
0
Linguistic
Relation
Label Semantic
0
1
2
3
4
5
6
7
8
( xL , xm , xR )
None
(0,0,0.12)
Very Low (0,0.12,0.25)
Low
(0.12,0.25,0.37)
Almost Low (0.25,0.37,0.5)
Medium
(0.37,0.5,0.62)
Almost High (0.5,0.62,0.75)
High
(0.62,0.75,0.87)
Very High (0.75,0.87,1)
Perfect
(0.87,1,1)
0
1
0
1
2
3
4
5
6
7
8
1
Membership
Grade
0
0
0.12
0.25
0.37
0.50
0.62 0.75
0.87
1
Linguistic
Relation
Figure 5. Definitions for linguistic variables  and 
Table 1. The importance and satisfaction for customer needs (before and after uniformity)
Customer A (Linguistic variable  )
Customer
needs
Sustaining
power
Convenience
for carry-on
Multi-function
integration
Reception of
vision
Artistic
modeling
Importance
Before
After
uniform uniform
Satisfaction
Before
After
uniform uniform
Customer B (Linguistic variable  )
Importance
Before
After
uniform uniform
Satisfaction
Before
After
uniform uniform
4
5
2
3
6
6
4
4
5
7
3
4
8
8
3
3
3
4
3
4
7
7
5
5
3
4
3
4
5
5
4
4
6
8
0
0
5
5
6
6
Due to linguistic variables could be defined by distinct linguistic scales with different LTSs,
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19

linguistic variable
constructed by the most SEs of LTS should be treated as BLTS to perform
the uniformity. An example of the uniformity process of customer need “Convenience for carry-on”
assessed from Customer A (  5 ) is displayed below:
A  {l 0 , l1 ,, l p }  0 , 1 , 2 , 3 , 4 , 5 , 6 
ST  {c0 , c1 ,, cg }  BLTS   0 , 1 ,  2 ,  3 ,  4 ,  5 ,  6 ,  7 ,  8 
           0
   max min{   ( x),   ( x)}  0.267
   max min{   ( x),  ( x)}  0.690
   max min{   ( x),  ( x)}  0.893
5
5
5
5
5
0
1
2
3
4
5
5
5
6
5
x
5
x
5
5
6
7
5
x
7
   max min{   ( x),  ( x)}  0.448
5
8
5
x
8
 AS (5 )  {( 0 ,0), (1 ,0), ( 2 ,0), ( 3 ,0), ( 4 ,0), ( 5 ,0.267), ( 6 ,0.690), ( 7 ,0.893), ( 8 ,0.448)}
T
8
 u 
round (
 
u 0
5
u
u 0
8
)  round (
5
0  0  1  0  2  0  3  0  4  0  5  0.267  6  0.690  7  0.893  8  0.448
)
0  0  0  0  0  0.267  0.690  0.893  0.448
u
 round (6.662)  7


5  7

0.893
0.67 0.75 0.84
0.87
1
x
0.75
1
x
x
0.857
SEs  5 and  7
min{  5 ( x),   7 ( x)}
   max min{   ( x),   ( x)}
(a)
(b)
(c)
5
7
5
x
7
Figure 6. The deducing process of uniformity about the membership grade  75
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20
The membership grade of corresponding SEs in BLTS from initial assessed SE  5 can be
determined by simultaneous linear equations. The result of the uniformity set  AST (5 ) illustrates
that the initial SE 5 has the highest membership grade in the SE  7 of BLTS. Therefore,  7
replaces 5 . The deduction process is shown in Fig. 6 to illustrate how to obtain the membership
grade  75 of SE  7 in BLTS from the initial assessment of SE 5 . Table 2 illustrates the
uniformity matrix for linguistic variables  and  , where the contained data indicate the
membership grade of the corresponding SE. The corresponding SE with the highest membership
grade is exhibited within gray background. The results of uniformity in Table 1 can be referred to
Table 2.
Table 2. Uniformity matrix for linguistic variables  and 
horizontal/vertical
0
1
2
3
4
5
6
7
8
Uniformity result
0
1
0.000/1.000 0.069/0.429
2
3
4
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0.069/0.571 0.138/0.862 0.211/0.300
0.138/0.001 0.211/0.700 0.283/0.724 0.353/0.138
-
0.283/0.276 0.353/0.862 0.426/0.567
-
-
0.426/0.433 0.500/1.000 0.570/0.414
-
-
-
0.570/0.586 0.642/0.833 0.715/0.267
-
-
-
0.642/0.167 0.715/0.733 0.787/0.690 0.857/0.107
-
-
-
-
-
-
-
-
-
0
1
3
4
5
-
0.787/0.310 0.857/0.893 0.928/0.552
0.928/0.448 1.000/1.000
7
8
After linguistic scale uniformity for importance and satisfaction, group based linguistic
information aggregation should be proceeded tightly to facilitate computing original difference,
adjusting difference, and normalizing weight for each customer need shown in Table 3. An example
of group based aggregation process of importance for customer need “Convenience for carry-on”
assessed by Customer A (  4 ) and Customer B (  7 ) is displayed below:
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21
FQ ( 4 ,  7 )  W   BT  [0.5,0.5]  [ 7 ,  4 ]T  C2 {( 0.5,  7 ), (0.5,  4 )}  0.5   7  (1  0.5)   4   k
where
k  min{ 8,4  round (0.5  (7  4))}  min{ 8,6}  6
hence
FQ ( 4 ,  7 )  C 2 {( 0.5,  7 ), (0.5,  4 )}  0.5   7  (1  0.5)   4   6
Table 3. Group based linguistic information aggregation results
Customer A
Customer
Customer B
Group aggregation
Original
Adjust
Normal
4
6-4=2
2+8=10
0.192308
8
4
8-4=4
4+8=12
0.230769
5
6
5
6-5=1
1+8=9
0.173077
5
4
5
4
5-4=1
1+8=9
0.173077
5
6
7
3
7-3=4
4+8=12
0.230769
needs
Importance
Satisfaction
Importance
Satisfaction
Importance
Satisfaction
Sustaining
power
Convenience
for carry-on
Multi-function
integration
Reception of
vision
Artistic
modeling
5
3
6
4
6
7
4
8
3
4
4
7
4
4
8
0
The aggregation weights for Customer A and B are equal to 0.5.
The quality improvement project team proposed five feasible scenarios in an attempt to meet
customer needs. Linguistic variables  and  shown in Table 4 are employed respectively to
demonstrate the assessment results for relationship matrix (refer to Table 5) and correlation matrix
(refer to Figure 7).
Table 4. Linguistic variables  and 
Label
0
1
2
3
4
5
6
7
8
Linguistic variable 
Linguistic variable 
(for Relationship Matrix)
(for Correlation Matrix)
Semantic Element
Absolute Harmful
Very High Harmful
High Harmful
Almost High Harmful
No Relationship
Almost High Useful
High Useful
Very High Useful
Absolute Useful
Label
0
1
2
3
4
5
6
7
8
Semantic Element
Absolute Negative Correlation
Very High Negative Correlation
High Negative Correlation
Almost High Negative Correlation
No Correlation
Almost High Positive Correlation
High Positive Correlation
Very High Positive Correlation
Absolute Positive Correlation
Table 5 clearly shows that different scenarios can exert different but related influences on
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single customer needs. For instance, the scenario “Power Subsystem” enhances the customer need
“sustaining power”; however, the scenario “Graphics and TV Tuner” subjects the power supply to
increased loading and adversely affects the customer need “sustaining power”. The scenarios
“Power Subsystem” and “Graphics and TV Tuner” thus conflict. Aggregation results for
relationship matrix (refer to Table 5) indicated that the scenario “Storage Subsystem” has the
highest piority, followed by “Display”. Although the remaining three scenarios have specialized
efficacy, the final priority of solution scenarios is finally determined via a trade-off. An example of
aggregation process for the scenario “Power Subsystem” is as follows:
F (r1 , r2 , , rm )  W   B T  C m {wn , bn , n  1,2, , m}
F ( 7 ,  2 ,  4 ,  4 , 3 )  W   B T  [0.192,0.173,0.173,0.231,0.231]  [ 7 ,  4 ,  4 , 3 ,  2 ]T
 C 5 {( 0.192, 7 ), (0.173,  4 ), (0.173,  4 ), (0.231, 3 ), (0.231,  2 )}
 0.192  7  (1  0.192)  C 4 {( 0.214,  4 ), (0.214,  4 ), (0.286, 3 ), (0.286,  2 )}
C 4 {( 0.214,  4 ), (0.214,  4 ), (0.286, 3 ), (0.286,  2 )}
 0.214   4  (1  0.214)  C 3 {( 0.273,  4 ), (0.364, 3 ), (0.364,  2 )}
C 3 {( 0.273,  4 ), (0.364, 3 ), (0.364,  2 )}
 0.273   4  (1  0.273)  C 2 {( 0.500, 3 ), (0.500,  2 )}
C 2 {( 0.500, 3 ), (0.500,  2 )}  0.500  3  (1  0.500)   2   k
k  min{ 8,2  round [0.500  (3  2)]}  min{ 8,3}  3
C 2 {( 0.500, 3 ), (0.500,  2 )}  3
C 3 {( 0.273,  4 ), (0.364, 3 ), (0.364,  2 )}  0.273   4  (1  0.273)  3   k
22
23
k  min{ 8,3  round [0.273  (4  3)]}  min{ 8,3}  3
C 3 {( 0.273,  4 ), (0.364, 3 ), (0.364,  2 )}  3
C 4 {( 0.214,  4 ), (0.214,  4 ), (0.286, 3 ), (0.286,  2 )}  0.214   4  (1  0.214)  3   k
k  min{ 8,3  round [0.214  (4  3)]}  min{ 8,3}  3
C 4 {( 0.214,  4 ), (0.214,  4 ), (0.286, 3 ), (0.286,  2 )}  3
C 5 {( 0.192, 7 ), (0.173,  4 ), (0.173,  4 ), (0.231, 3 ), (0.231,  2 )}  0.192  7  (1  0.192)  3  k
k  min{ 8,3  round [0.192  (7  3)]}  min{ 8,4}  4
C 5 {( 0.192, 7 ), (0.173,  4 ), (0.173,  4 ), (0.231, 3 ), (0.231,  2 )}   4
Table 5. Aggregation results and scenario priorities for the relationship matrix
Scenario
Need
s
Sustaining
power
Convenience for
carry-on
Multi-function
Integration
Large size
monitor
Artistic
modeling
Aggregation
results
Power
Graphics & TV
Storage
Display
Communication
Subsystem
Tuner
Subsystem
7
3
3
4
5
2
3
3
4
7
4
7
6
6
6
4
4
7
4
4
3
4
6
4
6
4
4
5
4
5
Power Subsystem: High watt Li-ion battery pack
Graphics & TV Tuner: Advanced graphic card & Built-in digital and analog hybrid TV tuner
Display: 15.4 inch WXGA crystalbrite color TFT LCD
Communication: Wireless techniques (LAN & Bluetooth)
Storage Subsystem: Slot-load DVD-dual double-layer
Thus the quality improvement project team further considered the technique correlation and
resource competitiveness among scenarios in performing the assessment and aggregation of the
correlation matrix, as mentioned for the relationship matrix. Although “Power Subsystem”
facilitated the performance of the other four scenarios, it competed for space. Hence the quality
23
24
improvement project team was concerned with space requirement and weight factors associated
with the request for portability.
5
6
6
2
3
5
5
5
4
4
Aggregation
results
5
4
6
5
4
Scenario
Power
Subsystem
Graphics &
TV Tuner
Display
Communication
Storage
Subsystem
The aggregation weights for four pair-wise scenarios are equal to 0.25.
Figure 7. Aggregation results and scenario priorities for the correlation matrix
Table 5 shows that the “Display” and “Storage Subsystem” scenarios have equal priority.
Obviously, equivalent priority increased with the number of scenarios, and thus this study employed
two-dimensional analysis, as shown in Fig. 8 to clarify scenario priorities in the event of ties. Based
on the priority results of two-dimensional analysis for the relationship and correlation matrices, the
scenario “Display” ranks first, and is followed sequentially by “Storage Subsystem”, “Power
Subsystem”, “Communication” and “Graphics & TV Tuner”.
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25
Priority Results on
Correlation Matrix
8
7
6
Display
Power Subsystem
Communication  5
Storage Subsystem
0
1
2
3
Graphics & TV Tuner
5
6
7
8
Priority Results on
Relationship Matrix
3
2
1
0
Figure 8. Two-dimensional analysis for the relationship and correlation matrices
6. Conclusion
The QFD model could be further manipulated based on pure linguistics and group decision
through this study, thus enabling the application of QFD to match practical requirement particularly
to advance the coordination with TRIZ. Moreover, the interaction between the relationship and
correlation matrices within HOQ could also be reinterpreted and endowed with management related
meanings via linguistic two-dimensional analysis. Although the uniformity in linguistic scale
necessary in the group decision process is only exemplified in assessing customer needs in Section
5, the uniformity procedure could also be applied to assess the relationship and correlation matrices
25
26
shown in Fig. 4. How to improve the sensitivity of a pure linguistic QFD model is the next research
topic, and cost-benefit analysis could be also be considered in solution scenarios. Integrating the
result of this investigation with other management techniques such as the Kano quality model
represents a further achievement of this study.
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