A competency evaluation method of human resources managers based on multi-granularity linguistic variables and VIKOR method.
Liu, Peide ; Wu, Xingying
1. Introduction
With the arrival of the global economic integration age, the scope
of the enterprise competition expanded rapidly and the degree of
competition increased unprecedentedly. Ultimately the competition of
enterprise is the competition of talent. Modern human resources managers
thought that human resources managers were the core of all the
management jobs. It emphasized on employees as potential resources and
emphasized on the motivation and development of staff (Wang 2007). And
human resources managers of enterprises were the organizers and actors
in human resources management. They played an important role in human
resources management. The competence level of human resources managers
was decisive on whether human resources management of company was
effective (Castrogiovanni, Kidwell 2010; Davidson, Wang 2011; Hashim
2010; Sharabi 2010). The evaluation results of human resources
managers' competency could be used as (Zhang et al. 2005): (1) the
basis for selecting and training human resources managers; (2) the basis
of making the training policies and measures (3) providing a direction
for the self-development of human resources manager.
The evaluation of human resources managers' competency is not
only the academic focus, but also an important problem which needed to
be solved by many enterprises. Currently, the evaluation of human
resources managers' competency had aroused widely concern between
academia and industrial circles and gotten many research results. Wang
and Hwang (2011) used the analytical hierarchy process (AHP) to analyze
the key factors in evaluating and screening managers in Taiwan. Zhang et
al. (2005) proposed a subjective and objective evaluation method of
human resources managers' competency according to the features and
job description of human resources managers, built subjective
indicators, including educational background and intellectual structure,
personal integrity, ability to manage enterprise culture, ability to
manage change, ability to manage knowledge, ability to transmit human
resource management practices and objective indicators of
multi-knowledge test, including strategic management, organization
behaviorist and human resources management. Zhou and Zhang (2009)
brought forward competency testing indicator system of enterprise's
human resources managers according to the competency testing indicator
system raised by American psychologist Dr McClelland, built a fuzzy
comprehensive evaluation model of enterprise's human resources
management based on fuzzy math and AHP and executed empirical studies;
Liu et al. (2009) used the interview method and questionnaire survey to
gather data, dealt with data by Exploratory Factor Analysis and Analysis
of Variance, and finally worked out a competency model of Chinese
enterprises' human resources managers, which made up of
three-factors and 15 items; Zhao (2008) firstly analyzed fuzzy factor of
competency-based talent selection process and built multi-criteria fuzzy
decision-making math model; Chen (2006) built Chinese enterprises'
competency model of human resources managers including competency of
functional management, competency of management of change, competency of
staff management and competency of strategic management by questionnaire
survey method; Spencer et al. (1994) believed that human resources
managers needed flexible competency, business innovation, interpersonal
understanding, empowerment and team growth; Research project of Ulrich
et al.(1995) stated clearly, participants felt that it proved competency
of human resources managers more efficiently in term of business
knowledge, human resources implement and management of change.
Questionnaire survey results by Gu and Zhu (2001) showed that, human
resources managers of Shanghai enterprises believed that the most
important eight-point competencies in turn were worthy of trust,
problem-solving, ability to identify people, communicative competency,
human resources expertise, learning ability, service awareness and
analysis ability. Ma and Cai (2007) arose ten-point competencies of
human resources managers, including learning ability, systems thinking
ability, service ability, ability to integrate human resources,
strategic performance management, human resources crisis management
capacity, the operational capabilities of information technology, global
capability, resilience and executive ability. Mussari and Ruggiero
(2010) thought that personnel management has been one of the areas of
greatest innovation within the management reform process in western
countries over the last two decades, and analyzed the public
managers' performance evaluation systems and public value creation
from behavioral and economic aspects.
From the past few years, Decision theory and methods based on fuzzy
information have been rapid development (Zavadskas, Turskis 2011; Han,
Liu 2011; Liu 2009; Liu, Zhang 2011), especially the research based on
evaluation information of linguistic form had been the concern of many
scholars. In order to facilitate the experts more accurately to express
their subjective judgments and further improve the efficiency and
quality of group decision making and the availability and flexibility of
network environment group decision support system, the group
decision-making research considered different granularity of linguistic
information given by the experts attracted the attention of scholars.
The so-called multi-granularity linguistic assessment information
referred that different experts used different linguistic evaluation set
for the same decision making problem to give their own set of linguistic
forms of assessment information in the group decision-making, and the
selected set of linguistic evaluation contained many differences on the
number of linguistic phrases and corresponding phrase semantic of
membership functions. Group decision-making process based on different
granularity linguistic evaluation information mainly included group
preference information gathered and group consistency analysis.
Nowadays, research and exploration of group decision-making method based
on different granularity linguistic assessment information had caused
some scholars' interest and concerns of the United Kingdom, Spain
and other countries. But the results were rare. As noted, most of the
existing research results involved gathering group decision information
and converting the different granularity linguistic evaluation
information. About group consistency analysis, Herrera et al. (2005)
studied the group consistency analysis method of the different
granularity linguistic judgment matrix. This method firstly converted
different granularity linguistic assessment information offered by
decision-makers into fuzzy information evaluation set expressed by two-
semantics based on two- semantics linguistic method, then made the group
consistency analysis.
From the above, the current evaluation of human resources
managers' competency was mainly qualitative evaluation and lacks of
quantitative evaluation method. As the evaluation of human resources
managers' competency was mostly qualitative indicators which
generally used the "excellent", "good",
"general" and "poor", and other linguistic
variables. At the same time, because different experts may adopt
different linguistic evaluation sets, therefore assessment information
also had multi-granularity properties. Based on multi-granularity
linguistic assessment information, the paper launched a research for
evaluation of human resource managers' competency, and proposed an
evaluation model of human resources managers' competency based on
multi-granularity linguistic variables and VIKOR method.
2. The evaluation index of human resource managers' competency
The evaluation index of human resources managers' competency
is the basis of human resources managers' competency evaluation. We
built a preliminary evaluation indicator system and considered the
relevant factors by documentary research method, in complying with the
principle of human resources managers' competency evaluation, such
as comparability, objectivity, comprehensiveness, reliability, and
flexibility. Then the human resources managers' evaluation index
systems are constructed based on the opinions of experts, human
resources managers and human resources assess company (shown in Table
1).
3. The VIKOR evaluation model based on the linguistic variables of
the different granularity
3.1. Describing problem of human resources managers'
competency evaluation
Suppose that there are m human resources managers (evaluation
objects) A = ([A.sub.1], [A.sub.2],..., [A.sub.m]), n evaluation
indicators B = ([B.sub.1], [B.sub.2],...,[B.sub.n]), p evaluation
experts E = ([e.sub.1], [e.sub.2],...,[e.sub.p]), experts weight is
[omega] = ([[omega].sub.1], [[omega].sub.2],..., [w.sub.p]), and
[P.summation over (k=1)][[omega].sub.k] = 1. The evaluation indicator
weight is W = ([w.sub.1], [w.sub.2],...,[w.sub.n]), [n.summation over
(j=1)][w.sub.j] = 1 and [w.sub.j] is unknown. Suppose that the
evaluation index values given by the kth evaluation expert compose a
matrix of [R.sup.k] = [[[r.sup.k.sub.ij]].sub.mxn], [r.sup.k.sub.ij] is
the jth index evaluation value of the ith evaluation object by the kth
evaluation expert. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
is the linguistic evaluation set which granularity is [q.sub.k] adopted
by the ith expert. This evaluation question will rank the m human
resources managers.
3.2. Normalize evaluation sets of different granularity by
two-semantics
Two-semantics is a concept based the symbol translation and a
method using a two-semantics (s, a) to represent linguistic assessment
information. Among them, s is a linguistic phrase of predetermined
linguistic set, [A.sub.i] is the difference between linguistic
information calculated and the closest linguistic phrase of initial
linguistic set, which is a value in interval [-0.5, 0.5]. The following
are the related definitions of two-semantics (Zhou, Zhang 2009; Liu et
al. 2009);
Definition 1. Suppose that [s.sub.i] [member of] S is a linguistic
phrase. Then we can get the corresponding two-semantics by the following
translation function [theta]:
[theta]: S [right arrow] S x [-0.5,0.5), [theta]([s.sub.i]) =
([s.sub.i],0), [s.sub.i] [member of] S. (1)
Definition 2. (Herrera, Martinez 2000, 2001; Herrera et al. 2005):
Let S = ([s.sub.0],[s.sub.1],...,[s.sub.g]) be a linguistic term set,
[beta] is a real number in [0, g], and it represents the calculating
result of aggregation for the elements in S, then two-semantics
corresponding to the elements in S can be gotten from the following
function:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where, round(.) is an integer operator of rounding.
Definition 3. (Herrera, Martinez 2000, 2001; Herrera et al. 2005):
Let S = ([s.sub.0],[s.sub.1],...,[s.sub.g]) be a linguistic set,
([s.sub.i], [alpha]) be a two-semantics and then there is an inverse
function [[DELTA].sup.-1] which can convert the two-semantics into
corresponding real number [beta] [member of] [0,g], that is:
[[DELTA].sup.-1]: S x [-0.5,0.5) [right arrow] [0,g-1],
[[DELTA].sup.-1]([s.sub.i], [alpha]) = i + [alpha] = [beta]. (3)
In order to eliminate the influence of different granularity, the
different granularity linguistic matrix R =
[([r.sup.k.sub.ij]).sub.mxn], should be converted to the same
granularity. Suppose that T is the granularity after converted. The
conversion method is shown as follows.
[r.sup.k.sub.ij] = [[r.sup.k.sub.ij]/[q.sub.k]]T [for all]i [member
of] m; [for all]j [member of] n; [for all]k [member of] p, (4)
where [q.sub.k] is the granularity adopted by expert k .
Based on above definitions, it is easy to give the related
calculating model of two-semantics, which including: comparing of the
two-semantics, inverse operator and aggregation operator.
1. The comparing of the two-semantics. Let ([s.sub.i],
[[alpha].sub.1]) and ([s.sub.j], [[alpha].sub.2]) be any two
two-semantics, and there are such rules:
If i > j, then ([s.sub.i], [[alpha].sub.1]) > ([s.sub.j],
[[alpha].sub.2]), which means ([s.sub.i], [[alpha].sub.1]) is superior
to ([s.sub.j], [[alpha].sub.2]); If i = j and [[alpha].sub.1] =
[[alpha].sub.2], then ([s.sub.i], [[alpha].sub.1]) = ([s.sub.j],
[[alpha].sub.2]), which means ([s.sub.i], [[alpha].sub.1]) is the same
as ([s.sub.j], [[alpha].sub.2]); If i = j and [[alpha].sub.1] >
[[alpha].sub.2], then ([s.sub.i], [[alpha].sub.1]) > ([s.sub.j],
[[alpha].sub.2]), which means ([s.sub.i], [[alpha].sub.1]) is superior
to ([s.sub.j], [[alpha].sub.2]); If i = j and [[alpha].sub.1] <
[[alpha].sub.2], then ([s.sub.i], [[alpha].sub.1]) < ([s.sub.j],
[[alpha].sub.2]), which means ([s.sub.i], [[alpha].sub.1]) is inferior
to ([s.sub.j], [[alpha].sub.2]).
2. There is an inverse operator Neg: Neg([s.sub.i], [alpha]) =
[DELTA](g - ([[DELTA].sup.-1]([s.sub.i],[alpha]))).
3. If ([s.sub.i], [[alpha].sub.1]) [greater than or equal to]
([s.sub.j], [[alpha].sub.2]), then max{([s.sub.i],
[[alpha].sub.1]),([s.sub.j], [[alpha].sub.2])} = ([s.sub.i],
[[alpha].sub.1]); and if([s.sub.i], [[alpha].sub.1]) [less than or equal
to] ([s.sub.j], [[alpha].sub.2]), then min{[s.sub.i], [[alpha].sub.1]),(
[s.sub.j], [[alpha].sub.2])} = ([s.sub.i], [[alpha].sub.1]).
4. The distance between two two-semantics: The distance between two
two-semantics A :([s.sub.i], [[alpha].sub.1]) and B :( [s.sub.j],
[[alpha].sub.2]) is:
d(A, B) = [absolute value of [[DELTA].sup.-1]([s.sub.i],
[[alpha].sub.1)]] - [absolute value of [[DELTA].sup.-1]( [s.sub.j],
[[alpha].sub.2])]. (5)
Theorem 1: For any three-semantics A :([s.sub.i], [[alpha].sub.1]),
B: ([s.sub.j], [[alpha].sub.2]) and C :([s.sub.k], [[alpha].sub.3]),
according to formula (5), the distance d(A, B) between A and B satisfies
the following conditions:
(1) A = B [??] d(A, B) = 0 ,
(2) d(A, B) = d(B, A),
(3) d(A,B) + d(B,C) [greater than or equal to] d(A,C).
3.3. Integrating evaluation information of each expert
According to the different evaluation index values which were given
by different experts under different attribute, we can get the
collective attribute values. The combining steps are shown as follows:
[r.sub.ij] = [P.summation over
(k=1)][[omega].sub.k][r.sup.k.sub.ij]
3.4. Using the entropy weight method to calculate attribute weights
(Zhao 2008; Chen 2006)
(1) Calculate [u.sub.ij] (the proportion of the ith object value
under the jth index):
[u.sub.ij] = [r.sub.ij]/[m.summation over i=1][r.sub.ij]. (7)
(2) Calculate entropy [e.sub.j] of the jth index:
[e.sub.j] = -k[[m.summation over (i=1)][u.sub.ij]ln[u.sub.ij], (8)
where k =1/lnm, m is the number of human resources managers
(3) Calculate the weight [w.sub.j]:
[w.sub.j] = 1-[e.sub.j]/[n.summation over (j=1)](1 - [e.sub.j]).
(9)
3.5. Select the best candidate using VIKOR method
VIKOR, which Serbian name was "VlseKriterijumska Optimizacija
I Kompromisno Resenje, means multi-criteria optimization and compromise
solution" (Chu et al. 2007), was developed by Opricovic (1998),
Opricovic and Tzeng (2002). The VIKOR method was developed for
multi-criteria optimization of complex systems (Opricovic, Tzeng 2004).
This method focused on ranking and selecting from a set of alternatives,
and determined compromise solutions for a problem with conflicting
criteria, which can help the decision makers to reach a final decision.
Here, the compromise solution is a feasible solution which is closest to
the ideal and a compromise mean established by mutual concessions
(Opricovic, Tzeng 2007).
Assuming that each alternative is evaluated according to each
attribute function, the compromise ranking could be performed by
comparing the measure of closeness to the ideal alternative. The
multi-attribute measure for compromise ranking is developed from the Lp
- metric used as an aggregating function in a compromise programming
method (Yu 1973; Zeleny 1982). The various m alternatives are denoted as
[A.sub.1], [A.sub.2],...-, [A.sub.m]. For alternative Ai, the rating of
the j th aspect is denoted by [f.sub.ij], i.e. [f.sub.ij] is the value
of jth attribute function for the alternative [A.sub.i]; n is the number
of attribute.
Development of the VIKOR method is started with the following form
of Lp - metric:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
In the VIKOR method, [L.sub.1,i] (as [S.sub.i]) and
[L.sub.[infinity],i] (as [R.sub.i]) are used to formulate ranking
measure. The solution obtained by min [S.sub.i] is with a maximum group
utility ("majority" rule), and the solution obtained by min
[R.sup.i.sub.i] is with a minimum individual regret of the
"opponent".
The compromise ranking algorithm of the VIKOR method has the
following steps:
(1) Determine the best [f.sup.*sub.j] and the worst [f.sup.-.sub.j]
values of all attribute functions, j = 1,2,..., n If the jth function
represents a benefit (if it is cost attribute, it can be converted into
benefit by standardizing), then:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (11)
(2) Compute the values [S.sub.i] and [R.sub.i], i = 1,2,...,m, by
the relations:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (13)
where [w.sub.j] are the weights of criteria, expressing their
relative importance.
(3) Compute the values [Q.sub.i], i = 1,2,..., m, by the following
relation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)
where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
v is introduced as weight of the strategy of "the majority of
criteria" (or "the maximum group utility"), here suppose
that v = 0.5.
(4) Rank the alternatives. Sort the value Q in decreased order. The
position in the front is better than in the behind.
4. Application research
A company planned to select one person to be human resource manager
from four candidates ([a.sub.1], [a.sub.2], [a.sub.3], [a.sub.4]). In
order to improve the accuracy of the evaluation, three experts were
invited to evaluate these candidates, they were the vice president in
charge of the company human resources, a university professor and an
expert of human resource assessment company. Suppose that the 3 person
scored independent and they had the same evaluation weight. The index
evaluation values given by three experts were shown in table 2, table 3
and table 4 respectively. Expert 1 used 5 level linguistic variables =
{very poor, poor, medium, good, very good}, expert 2 used 7 level
linguistic variables = {very bad, very poor, poor, medium, good, quite
good, very good}, Experts 3 used 9 level linguistic variables = {very
bad, very poor, less poor, poor, medium, good, better, very good, best}.
Our goal is to select a human resource manager based on these evaluation
values. (For convenient representation, we only use the subscript of
linguistic variables, for example, [s.sub.4] was expressed by 4).
Decision steps are shown as follows:
(1) Converting evaluation information given by three experts into
evaluation information expressed by 9 level linguistic set (shown as
Table 5, Table 6, Table 7 respectively).
(2) Integrating each expert's evaluation information, we can
get the comprehensive evaluation information shown as table 8.
(3) Using the entropy weight method to calculate attribute weights
(a) Calculating [u.sub.ij] by formula (7) shown as table 9.
(b) Calculating the weights of attributes
W = (0.188, 0.032, 0.014, 0.006, 0.100, 0.031, 0.036, 0.077, 0.084,
0.065, 0.136, 0.001, 0.030, 0.012, 0.105, 0.004, 0.072)
(4) Sorting the alternatives using VIKOR method
(a) Calculating the value of the ideal solution [f.sup.*.sub.j] and
the negative ideal solution [f.sup.-.sub.j] of every index (shown as
table 10).
(b) Calculating the value of [S.sub.i] and [R.sub.i] using formula
(12) and (13), i = 1,2,...,m , [S.sub.i] is comprehensive evaluation
optimal solution, [R.sub.i] is the most bad solution comprehensive
evaluation solution.
S = (0.53, 0.57, 0.62, 0.37) R = (0.14, 0.16, 0.19, 0.10)
(c) Calculating value of benefits' ratio made by scheme
[Q.sub.i] using formula (14), i=1,2,...,m.
Q = (-0.529, -0.743, -1,0)
(d) According to the calculation value Q, sort and make a final
decision. The scheme of minimum value of the sorting Q is the considered
most optimal scheme.
[Q.sub.3] [??] [Q.sub.2] [??] [Q.sub.1] [??] [Q.sub.4]
So choose the a3 candidate as the best solution.
To prove the validity of the method, we use the different method to
recalculate the example. Firstly, according to the maximum deviation
method, we can calculate the weight,
w = (0.0717 0.0498 0.0412 0.0221 0.0757 0.0575 0.0471 0.0854 0.0855
0.0787 0.0896 0.0099 0.0585 0.0490 0.0693 0.0191 0.0898).
Secondly, using the TOPSIS method, we recalculate the example
(Hwang, Yoon 1981; Liu 2009). Step 1: Construct the weighted normalized
matrix (shown as table 11).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (15)
Step 2: Determine the ideal solution and negative ideal solution of
the object (shown as table 12).
Step 3: Calculate the distance, determine the relative proximity
and sort the program.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (16)
[C.sub.i] = [[d.sup.+.sub.i]/[d.sup.+.sub.i] + [d.sup.-.sub.i]] x
(i = 1,2,...,m), (17)
[C.sub.i] = (0.5670, 0.5102, 0.4263, 0.6096).
According to the size of the relative proximity, we can evaluate
the sort merits. The smaller [C.sub.i] is, the better the program is.
[C.sub.3] < [C.sub.2] < [C.sub.1] < [C.sub.4]
So, the best selection is a3.
It is the same result for VIKOR and TOPSIS methods, but these two
methods have their own characteristics (Opricovic, Tzeng 2004). TOPSIS
method is based on the principle that the optimal point should have the
shortest distance from the positive ideal solution (PIS) and the
farthest from the negative ideal solution (NIS). Therefore, this method
is suitable for cautious (risk avoider) decision maker(s), because the
decision maker(s) might like to have a decision which not only makes as
much profit as possible, but also avoids as much risk as possible.
Besides, computing the optimal point in the VIKOR is based on the
particular measure of "closeness" to the PIS. Therefore, it is
suitable for those situations in which the decision maker wants to have
maximum profit and the risk of the decisions is less important for him.
5. Conclusions
In the context of economic globalization, human resources had
become the key of company's competitive. Human resources managers
are the organizers and implementers of human resources management and
play a decisive role in human resource management. The levels of human
resources managers' competency play a decisive role in whether is
effective among human resources management. For the characteristics of
human resources managers' competency, this paper raised evaluation
of human resources managers' competency based on multi-granularity
linguistic variables and VIKOR method, firstly built human resources
manager evaluation system based on competency, and by using the concept
of two-semantic put multi-granularity evaluation information of
different experts into the same granularity of evaluation information.
Then we aggregated the evaluation information of each expert to the
comprehensive evaluation value, weighted every evaluation indicator by
entropy method, get the evaluation value on the ideal solution and
negative ideal solution by VIKOR. At last we determined the sort merits
of every evaluation objects according to the size of interest rate.
Finally by an enterprise application example, we illustrated the
evaluation procedures and validity of the model, showed that the method
was easy to operate, easy to promote the use. Besides, to different
staff of the company, such as position characteristic of production
staff, technical staff, management staff, it can separately make
different evaluation index system and make evaluation order to these
person. Compared with the past quantitative evaluation, this method used
the qualitative language evaluation directly and it's easy to use.
But during the actual use, evaluation index may be both qualitative and
quantitative indicators. The evaluation of this situation will be
further studied.
doi: 10.3846/20294913.2012.753169
Acknowledgement
This paper is supported by the National Natural Science Foundation
of China (No. 71271124), the Humanities and Social Sciences Research
Project of Ministry of Education of China (No. 10YJA630073 and
No.09YJA630088), the Natural Science Foundation of Shandong Province
(No.ZR2011FM036), and Graduate education innovation projects of Shandong
Province (SDYY12065).The author also would like to express appreciation
to the anonymous reviewers and Managing Editor Jonas Saparauskas for
their very helpful comments that improved the paper.
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Peide LIU. Born in China, 1966. Obtained his bachelor and master
degrees in Electronic Technology in the Southeast University, and
obtained doctor degree in Information Management in Beijing Jiaotong
University. Now he is a full-time professor in Shandong University of
Finance and Economics and assistant director of the Enterprise's
Electronic-commerce Engineering Research Center of Shandong. His main
research interests are technology and information management, decision
support and electronic-commerce.
Xingying WU. Born in China, 1990. Obtained her bachelor degree in
Electronic-Commerce in the Shandong Economic University. Now she is
doing the research work for master degree in Shandong University of
Finance and Economics. Her main research interests are information
management, decision support and electronic-commerce.
E-mails:
[email protected] (corresponding author);
[email protected]
Received 10 December 2010; accepted 24 October 2011
Table 1. Human resources manager competency evaluation system
Contents Indicators
A1 Moral level B1 Honesty Degree
B2 Sense of responsibility
B3 Confidentiality
A2 Capability level B4 Learning ability
B5 Ability to manage change
B6 Service capacity
B7 Communication skills
B8 The operational capabilities of
information technology
B9 Implementing competence
A3 Knowledge level B10 Business knowledge
B11 Knowledge of laws and regulations
A4 Professional B12 Recruitment Management
quality Level B13 Training Management
B14 Performance Management
B15 Compensation Management
A5 Health level B16 Mental states
B17 Mass Psychology
Table 2. The index evaluation value by expert 1
(5 level linguistic variables)
B1 B2 B3 B4 B5 B6 B7 B8 B9
a1 2 3 4 1 2 3 4 2 4
a2 1 2 4 2 3 4 2 1 4
a3 1 3 4 2 1 4 1 3 2
a4 1 3 4 2 4 2 4 3 2
B10 B11 B12 B13 B14 B15 B16 B17
a1 3 2 4 2 2 2 4 2
a2 2 3 2 4 4 2 4 1
a3 4 2 1 4 2 1 3 4
a4 1 2 3 2 4 2 3 4
Table 3. The index evaluation value by expert 2
(7 level linguistic variables)
B1 B2 B3 B4 B5 B6 B7 B8 B9
a1 2 4 6 3 4 3 2 4 5
a2 2 4 2 5 6 3 3 1 4
a3 1 3 3 2 1 4 5 3 2
a4 4 3 4 5 1 2 3 5 4
B10 B11 B12 B13 B14 B15 B16 B17
a1 6 1 3 4 6 3 2 4
a2 5 3 5 6 5 2 1 3
a3 6 5 4 3 2 5 4 5
a4 3 2 6 6 5 5 2 5
Table 4. The index evaluation value by expert 3
(9 level linguistic variables)
B1 B2 B3 B4 B5 B6 B7 B8 B9
al 6 7 4 8 2 4 2 8 6
a2 l 2 4 6 7 8 4 6 3
a3 1 3 5 8 7 5 4 3 2
a4 5 4 6 3 1 6 7 8 9
B10 B11 B12 B13 B14 B15 B16 B17
al 2 1 5 6 7 2 5 2
a2 5 5 6 7 3 1 5 7
a3 6 7 8 3 7 1 5 8
a4 4 3 2 5 6 7 8 5
Table 5. The index evaluation value by expert 1
a1 a2 a3 a4
B1 (4,-0.4) (2,-0.2) (2,-0.2) (2,-0.2)
B2 (5,0.4) (4,-0.4) (5,0.4) (5,0.4)
B3 (7,0.2) (7,0.2) (7,0.2) (7,0.2)
B4 (2,-0.2) (4,-0.4) (4,-0.4) (4,-0.4)
B5 (4.-0.4) (5,0.4) (2,-0.2) (7,0.2)
B6 (5,0.4) (7,0.2) (7,0.2) (4.-0.4)
B7 (7,0.2) (4.-0.4) (2,-0.2) (7,0.2)
B8 (4,-0.4) (2,-0.2) (5,0.4) (5,0.4)
B9 (7,0.2) (7,0.2) (4.-0.4) (4.-0.4)
B10 (5,0.4) (4.-0.4) (7,0.2) (2,-0.2)
B11 (4,-0.4) (5,0.4) (4.-0.4) (4.-0.4)
B12 (7,0.2) (4.-0.4) (2,-0.2) (5,0.4)
B13 (4,-0.4) (7,0.2) (7,0.2) (4.-0.4)
B14 (4,-0.4) (7,0.2) (4.-0.4) (7,0.2)
B15 (4,-0.4) (4.-0.4) (2,-0.2) (4.-0.4)
B16 (7,0.2) (7,0.2) (5,0.4) (5,0.4)
B17 (4,-0.4) (2,-0.2) (7,0.2) (7,0.2)
Table 6. The index evaluation value by expert 2
a1 a2 a3 a4
B1 (3,-0.4) (3,-0.4) (1,0.3) (5,0.1)
B2 (5,0.1) (5,0.1) (4,-0.1) (4,-0.1)
B3 (8,-0.3) (3,-0.4) (4,-0.1) (5,0.1)
B4 (4,-0.1) (6,0.4) (3,-0.4) (6,0.4)
B5 (5,0.1) (8,-0.3) (1,0.3) (1,0.3)
B6 (4,-0.1) (4,-0.1) (5,0.1) (3,-0.4)
B7 (3,-0.4) (4,-0.1) (6,0.4) (4,-0.1)
B8 (5,0.1) (1,0.3) (4,-0.1) (6,0.4)
B9 (6,0.4) (5,0.1) (3,-0.4) (5,0.1)
B10 (8,-0.3) (6,0.4) (8,-0.3) (4,-0.1)
B11 (1,0.3) (4,-0.1) (6,0.4) (3,-0.4)
B12 (4,-0.1) (6,0.4) (5,0.1) (8,-0.3)
B13 (5,0.1) (8,-0.3) (4,-0.1) (8,-0.3)
B14 (8,-0.3) (6,0.4) (3,-0.4) (6,0.4)
B15 (4,-0.1) (3,-0.4) (6,0.4) (6,0.4)
B16 (3,-0.4) (1,0.3) (5,0.1) (3,-0.4)
B17 (5,0.1) (4,-0.1) (6,0.4) (6,0.4)
Table 7. The index evaluation value by expert 3
a1 a2 a3 a4
B1 (6,0.0) (1,0.0) (1,0.0) (5,0.0)
B2 (7,0.0) (2,0.0) (3,0.0) (4,0.0)
B3 (4,0.0) (4,0.0) (5,0.0) (6,0.0)
B4 (8,0.0) (6,0.0) (8,0.0) (5,0.0)
B5 (2,0.0) (7,0.0) (7,0.0) (1,0.0)
B6 (4,0.0) (8,0.0) (5,0.0) (6,0.0)
B7 (2,0.0) (4,0.0) (4,0.0) (7,0.0)
B8 (8,0.0) (6,0.0) (3,0.0) (8,0.0)
B9 (6,0.0) (3,0.0) (2,0.0) (9,0.0)
B10 (2,0.0) (5,0.0) (6,0.0) (4,0.0)
B11 (1,0.0) (5,0.0) (7,0.0) (3,0.0)
B12 (5,0.0) (6,0.0) (8,0.0) (2,0.0)
B13 (6,0.0) (7,0.0) (3,0.0) (5,0.0)
B14 (7,0.0) (3,0.0) (7,0.0) (6,0.0)
B15 (2,0.0) (1,0.0) (1,0.0) (7,0.0)
B16 (5,0.0) (5,0.0) (5,0.0) (8,0.0)
B17 (2,0.0) (7,0.0) (8,0.0) (5,0.0)
Table 8. The integrated evaluation matrix
a1 a2 a3 a4
B1 (4,0.1) (2,-0.2) (1,0.4) (4,0.0)
B2 (6,-0.2) (4,-0.4) (4,0.1) (4,0.4)
B3 (6,0.3) (5,-0.4) (5,0.4) (6,0.1)
B4 (5,-0.4) (5,0.3) (5,-0.3) (4,0.3)
B5 (4,-0.4) (7,-0.3) (3,0.4) (3,0.2)
B6 (4,0.4) (6,0.4) (6,-0.2) (4,0.1)
B7 (4,-0.1) (4,-0.2) (4,0.1) (6,0.0)
B8 (6,-0.4) (3,0.0) (4,0.1) (7,-0.4)
B9 (6,0.5) (5,0.1) (3,-0.3) (6,-0.1)
B10 (5,0.0) (5,0.0) (7,0.0) (3,0.2)
B11 (2,0.0) (5,-0.2) (6,-0.5) (3,0.1)
B12 (5,0.4) (5,0.3) (5,0.0) (5,0.0)
B13 (5,-0.1) (7,0.3) (5,-0.3) (5,0.4)
B14 (6,0.1) (5,0.5) (4,0.4) (6,0.5)
B15 (3,0.2) (2,0.4) (3,0.1) (6,-0.3)
B16 (5,-0.1) (4,0.5) (5,0.2) (5,0.3)
B17 (4,-0.4) (4,0.2) (7,0.2) (6,0.2)
Table 9. The value of [u.sub.ij]
a1 a2 a3 a4
B1 0.363 0.160 0.122 0.356
B2 0.326 0.200 0.228 0.246
B3 0.282 0.205 0.239 0.273
B4 0.240 0.282 0.249 0.229
B5 0.213 0.399 0.200 0.188
B6 0.214 0.308 0.280 0.197
B7 0.220 0.214 0.229 0.337
B8 0.289 0.157 0.212 0.342
B9 0.322 0.252 0.134 0.291
B10 0.249 0.248 0.344 0.159
B11 0.127 0.308 0.367 0.198
B12 0.258 0.258 0.240 0.243
B13 0.220 0.327 0.210 0.243
B14 0.270 0.245 0.194 0.290
B15 0.221 0.167 0.215 0.397
B16 0.247 0.226 0.260 0.267
B17 0.169 0.199 0.340 0.293
Table 10. The value of [f.sup.*.sub.j]
and [f.sup.-.sub.j]
[f.sup.*.sub.j] [f.sup.-.sub.j]
B1 4.057 1.362
B2 5.847 3.581
B3 6.304 4.590
B4 5.342 4.342
B5 6.704 3.162
B6 6.352 4.057
B7 6.018 3.819
B8 6.609 3.028
B9 6.542 2.724
B10 6.971 3.219
B11 5.676 1.962
B12 5.352 4.980
B13 7.304 4.685
B14 6.542 4.390
B15 5.676 2.390
B16 5.323 4.495
B17 7.209 3.581
Table 11. The weighted normalized matrix
[([v.sub.ij]).sub.mxn]
a1 a2 a3 a4
B1 0.2909 0.1284 0.0976 0.2854
B2 0.2910 0.1782 0.2033 0.2199
B3 0.2597 0.1891 0.2205 0.2519
B4 0.1007 0.1182 0.1045 0.0961
B5 0.2710 0.5074 0.2544 0.2393
B6 0.2543 0.3655 0.3326 0.2334
B7 0.1848 0.1799 0.1920 0.2835
B8 0.4765 0.2586 0.3488 0.5643
B9 0.5595 0.4373 0.2329 0.5057
B10 0.3967 0.3944 0.5489 0.2535
B11 0.1757 0.4256 0.5084 0.2738
B12 0.0530 0.0529 0.0493 0.0499
B13 0.2873 0.4271 0.2740 0.3180
B14 0.2989 0.2714 0.2150 0.3204
B15 0.2185 0.1657 0.2132 0.3934
B16 0.0942 0.0860 0.0991 0.1019
B17 0.3217 0.3790 0.6476 0.5578
Table 12. The ideal solution and negative
ideal solution of the object
[V.sup.+.sub.j] [V.sup.-.sub.j]
B1 0.2909 0.0976
B2 0.2910 0.1782
B3 0.2597 0.1891
B4 0.1182 0.0961
B5 0.5074 0.2393
B6 0.3655 0.2334
B7 0.2835 0.1799
B8 0.5643 0.2586
B9 0.5595 0.2329
B10 0.5489 0.2535
B11 0.5084 0.1757
B12 0.0530 0.0493
B13 0.4271 0.2740
B14 0.3204 0.2150
B15 0.3934 0.1657
B16 0.1019 0.0860
B17 0.6476 0.3217
